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= 300. Although test method and aging temperature have difference, our results are similar to that by four-point bending tests The evolution and accurately measurements of mechanical parameters of freestanding 8YSZ coating play an important role in appraising the reliability and durability of TBCs. The freestanding 8YSZ samples were successfully prepared by APS technique. The corresponding mechanical properties were measured by SENB and DIC techniques. The bending failure process of 8YSZ was simulated by XFEM. Using the determined experimental data and attempting different energy release rate, the material parameters of XFEM were evaluated, which would be used to predict the delamination and spallation of TBC with irregular geometry. The main conclusions can be summarized as follows,The KIC of freestanding 8YSZ coatings by SENB tests changes from 1.12 MPa m1/2 to 2.45 MPa m1/2 before N

= 150, and then decreases to 1.62 MPa m1/2 as N

= 300. The corresponding σb firstly increases from 35.66 ± 6.13 MPa at as-received to 71.76 ± 7.25 MPa at N

= 50 due to the sintering and densification, and then it slightly decreases to 24.70 ± 0.40 MPa when N

= 300 because of the formation of much micro cracks.The GI of 8YSZ coatings estimated by XFEM ranges from 71 to 175 J/m− 2 for different heat-treated 8YSZ samples. The corresponding KIC was deduced within the linear elastic fracture mechanics, which consists well with that by the SENB tests.Effects of charge distribution around bubbles on charge induction and transfer to a ball probe in gas–solid fluidized bedsThe model of Park et al. (J. Electrostat. 55 (2002) 135) on charge induction and transfer between charged particles surrounding a rising bubble and a ball probe is modified to take into account the charge buildup on particles remote from the bubble, and the particle charge density distribution in the vicinity of the bubble. With particle properties, such as dielectric constant and conductivity, estimated from existing correlations, the model simulation results change only slightly when both the background charge density and a distribution of charge density around a spherical bubble are introduced into the original model. However, significant improvement in agreement between the model and experimental results is achieved when the contributions from the bubble wake and drift carrying highly charged particles are included.distance between centre of probe and image charge q′ (see distance between centre of probe and point charge q (see diameter of cylindrical drift following a bubble, mYoung's modulus of elasticity of probe, PaYoung's modulus of elasticity of particle, Paheight of cylindrical drift following a bubble, mvertical distance between probe centre and tip of bubble injector, mspecific charge of bed particles in dense phase remote from bubble, C/kgdistance between field point and source point, mdistance between centre of probe and bubble, mdistance between point P on probe and point charge q, q′ (see radial distance from centre of bubble, mradial distance from axis of cylindrical drift, melectrical potential on surface of probe, Velectrical potential on surface of a charged particle, Vradial component of particle velocity, m/sthickness of bubble in two-dimensional column, melectrical conductivity of ball probe, 1/Ω melectrical conductivity of particle, 1/Ω mpermittivity of vacuum or air, 8.854×10−12

F/mrelative permittivity or dielectric constant, i.e. Π/Π0contributed from part a, b, c, respectivelyIn industrial gas–solid fluidized beds, electrostatic charges can cause agglomeration, nuisance discharge and even the danger of explosion Recently, a simple charge induction and transfer model was developed In this paper, we present the simulation results of the modified Park et al. The distribution of specific particle charge density in C/kg surrounding a bubble (shown in ) is assumed to follow an exponential decay function given bywhere qm0 is the particle charge density far from the bubble (i.e. background charge density of bed materials), approximately equal to the average charge density in the bed; rB′ is the distance from the centre of the bubble; An and B are constants.Particle holdup inside the bubble is neglected, so that there are assumed to be no charges inside the bubble.The charge density per unit volume surrounding the bubble is related to the charge density per unit mass bywhere ρs is the particle density and ε is the voidage. is estimated by the superposition of three simple contributions: (i) a uniformly charged bed with a specific charge qm0, (ii) a charged spherical ball with a charge density equal to −qm0 and (iii) charged particles surrounding the bubble with an exponentially decaying charge distribution, q″′m=Anqm0e−B[(r′B/RB)−1]2 and zero charge density inside the bubble.. The bubble wake and drift are first ignored. The bubble rises at a constant velocity, UB, with the centre of the probe lying on the axis of the rising bubble. The y coordinate of the bubble centre C is then −L+UBt, where L is the distance between the tip of the bubble injector and the centre of the ball probe and UB is the bubble rise velocity. Using polar coordinates, we can express the positions of point P on the surface of the electrostatic ball probe and point B on the bubble surface, respectively asThe distance between the centre of the probe and point B on the bubble surface is thenwhile the distance between point P on the probe surface and point B on the bubble surface isInstead of the surface charge density assumed by Park et al. With the dielectric constant assumed to be macroscopically uniform throughout the bed, the method of images Therefore, on the surface of the grounded ball probe, r=RP and , Π0 is the permittivity of vacuum. Πr=Π/Π0 is the relative permittivity of the fluidized particles and Π is the permittivity of medium. For a packed bed of glass beads, Πr was measured to be 3.0 are used to calculate r1, r2, ∂r1/∂r and ∂r2/∂r. With the aid of represents the surface charge density induced by the charge on the control volume inside and around the bubble. It is necessary to integrate this expression over the entire field. The simulation was carried out for the three additive components shown in based on the model equations presented above. The total induced charge is the sum of three terms:Part a: uniformly charged bed. The induced charge should be constant because of the uniform distribution of volume charge density throughout the whole bed. Therefore,The constant is taken as zero in the following calculation of overall charge induction because only dynamic changes of induced charge contribute to the current flow.Part b: charged spherical ball. In the second term, there is no charge outside the hypothetical particle-filled bubble. The induced charge is only generated from the charge inside the bubble. Integrating over the volume of the ball and substituting qv=−qm0(1−ε)ρs we obtainThe total volume charge density is then integrated over the surface of the electrostatic ball probe to obtain the total induced charge at any time: the total induced charge can be written asPart c: charge particles surrounding the bubble. In part c, there is no charge inside the bubble. The induced charge is only generated from charged particles around the bubble. Integration of over the volume outside the bubble and over the surface of the electrostatic ball probe together with the charge distribution function The induced current can then be calculated fromIn addition to charge induction, direct charge transfer takes place when charged particles collide with the probe. Therefore, the total charge on the probe is given bywhere Vs is the particle velocity. K is a dimensional constant related to the ball probe characteristics, particle surface characteristics, specific charge of particles and particle properties. Park et al. where η is a correction factor. Us and UP are electric potential or work function for the particle surface and probe surface, respectively, withwhere subscripts s and p denote the particle and probe, respectively. d and D are diameters and σ is electrical conductivity. Also m*, E* and r* are the relative mass, contact modulus and relative radius, such thatwhere m is mass, r and R radius, γ shear strain, and E is Young's Modulus. Substituting which is a constant in a system of given particles and ball probe. Then K can be expressed as is related to the local particle velocity and local solids concentration allows the transfer electrical current to be calculated asIf the ball probe lies on the axis of the rising bubble, the absolute particle velocity along the path of the collision is thenwhere the distance between the centre of the bubble and the probe is r′=−L+UBt. The bubble rise velocity for isolated bubbles in a two-dimensional fluidized bed and letting Itransferred=−dQtransferred/dt, we obtainCharges are assumed to be transferred by collision not only from the thin layer of particles at the surface of the bubble, but also from particles in the dense phase surrounding the rising bubble. As in the calculation of the induced charge, the transfer charge is obtained as the sum of the transfer charges from the three terms shown in Part a: uniformly charged bed. The entire region has the same charge density, qv0, but the particle velocity varies as given by , before the bubble passes through the probe, i.e. for –L+UBt<−RB,while the bubble encloses the probe, i.e. for −RB⩽–L+UBt⩽RB, the particle velocity in the bubble is Vs=UBAfter the bubble has passed the probe, i.e. for –L+UBt>RB,Part b: charged spherical ball. In the second term, there is no charge around the bubble, while the particle velocity inside the bubble equals the bubble velocity, UB. Therefore, before the bubble passes through the probe, i.e. for –L+UBt<−RB,While the bubble is enclosing the probe, i.e. for −RB⩽–L+UBt⩽RB,After the bubble has passed the probe, i.e. for –L+UBt>RBPart c: charged particles surrounding the bubble. For the third term there is no charge inside the bubble and the charge density on the probe is qv=Anqv0e−B(|r′|/RB−1)2 or qm=Anqm0e−B(|r′|/rB−1)2, with r′=−L+UBt. Therefore before the bubble reaches the probe, i.e. for –L+UBt<−RB,While the probe is enclosed by the bubble, i.e. for −rB⩽–L+UBt⩽rB, since there are no particles inside the bubbleAfter the bubble has passed the probe, i.e. for –L+UBt>RB,The total transfer current and charge are then given byThe total induced and transferred charges on a ball probe caused by passage of a single bubble were simulated based on the above model equations via numerical integration using a computer program written in FORTRAN. A two-dimensional fully circular bubble with a negative specific charge 1.6E–6 C/kg was used in the first simulation. The distance between the tip of the bubble injector and the probe was 0.205 m, as in the experimental set-up by Park et al. to be 0.358 m/s for a bubble of diameter 50 mm and thickness 22 mm, while the diameter of the ball probe was 3.2 mm. The particles were assumed to be 321 μm glass beads fluidized by air. The bubble was assumed to rise at steady velocity, with constant diameter and a fully circular cylindrical shape throughout the entire interval of interest. shows the predicted induced charges versus time. It can be seen that the induced charge generated from part b with a negative specific charge has a negative value, while the induced charge generated from part c with δq/RB=0.2 and An=0.3 has a small positive value. The lowest peak occurs when the bubble centre passes the probe centre. shows the predicted transferred charge. This is similar to the result of Park et al. demonstrate that a higher charge density around the bubble causes only a small incremental contribution to the total charge induced on, and transferred to, the probe.where V is the voltage output across the resistance, R, which is 1 MΩ, and the total amplification is 1000. However, the current flow through the ball probe, Ip, should be different from Itotal flowing through the resistor because of the existence of a 10 μF capacitor as shown in . Based on the electric circuit shown in , the total current flowing through the probe, Ip, should be estimated byBy definition, the cumulative charge on the ball probe, QP, can be obtained fromTraces of voltage, current and charge appear in . The label “nose” indicates alignment of the nose of the bubble with the centre of the probe, whereas “bubble-wake interface” represents the moment when the bubble-wake interface contacts the probe. It is seen that the minimum charge, Cmin, from Park et al. occurs after the bubble passes the probe, whereas the peak from with the modulation from the capacitor considered occurs when the centre of the bubble passes through the probe. Compared with the charge based on , the minimum charge, Cmin, is higher based on , but the charge transfer, Ctransfer, remains the same. It is also found in that a maximum charge, Cmax, occurs after the bubble passes through the probe based on the corrected current from compares the corrected experimental results with the current model simulation, with parameters qm0 and K′ obtained by solving two equations simultaneously, matching experimental values of Cmin and Ctransfer to the model. It is seen that the model simulation shows good agreement with the experimental data, especially in the region before the bubble passes the ball probe. The peak minimum charge in occurs while the centre of bubble pass through the probe. However, the model fails to predict the region around the maximum peak after the bubble passes the probe. show the effect of charge density distribution around the bubble (represented by the two parameters, An and δq) on the fitted parameters qm0 and K′. It is seen that as the specific charge, An, increases, the highly charged particle layer around the bubble, δq, increases, qm0 increases, while K′ decreases when the simulation results are matched with the experimental values of Cmin and Ctransfer. The variation in the distribution of charge density around the bubble, however, results in almost the same profile of the total charge, which still cannot predict a maximum peak and the region around the maximum peak, suggesting that the contribution from bubble wake and drift may also need to be considered in the model.Real bubbles in gas–solids fluidized beds are not circular, but are kidney-shaped with a solids-containing wake . A bubble wake angle, ϕ, of 118° is chosen based on Rowe and Partridge Part c: charged wake. Before the wake touches the probe shows the predicted induced charge and charge transfer versus time for Anwake=−0.5. compares the experimental results with the model simulation, with qm0 and K′ fitted with experimental values of Cmin and Ctransfer. The variation is seen to be insignificant when the bubble is negatively charged (i.e. Anwake=−0.5), neutral (i.e. Anwake=0) or positively charged (Anwake=0.5). The peak minimum charge occurs slightly later for Anwake=−0.5, i.e. the charge density in the wake has an opposite sign of charge in the bed, while the peak occurs a little bit earlier for Anwake=0.5, i.e. the charge density in the wake has the same sign as the charge in the bed. Overall, the inclusion of the contribution from the bubble wake is still insufficient to predict the region around the maximum.As shown above, the model with a higher charge density distribution around the bubble or a wake behind the bubble cannot predict the peak region of the measured charge vs. time curve which occurs after a bubble passes the probe. The contribution from bubble-induced solids drift drawn upwards behind the bubble is considered next. shows the charge distribution around the bubble and in the drift. It is assumed that the charge density around the bubble remains uniform while the drift is approximated as being of cylindrical shape with different charge density. Particles in the drift volume are assumed to have a velocity of Vs=0.38UB, the charge distribution is estimated by superposition of three simple contributions: (a) a uniformly charged bed with a specific charge qm0; (b) a charged circular cylindrical shape with a charge density equal to −qm0; and (c) a charged cylindrical column with charge density equal to (Andrift−1)qm0. The simulation was carried out for these three additive components based on the equations presented above, except that is modified to account for the drift geometry shown in Part c: charged drift. For point B in the drift, according to is integrated over the volume of the drift. In the drift:, is then integrated over the surface of the electrostatic ball probe to givePart a: uniformly charged bed. Before the bubble reaches the probe, is employed.While the bubble encloses the probe, is used. After the bubble has passed the probe, but drift encloses the probe, the particle velocity in the drift is Vs=0.38UB. Therefore,After the drift cylinder has passed the probePart c: charged drift. Before the drift reaches the probeWhile the drift cylinder is enclosing the probeAfter the drift cylinder has passed the probe shows simulated induced charge versus time as a single bubble with drift passes the probe. It can be seen that the drift has little influence on the region at the front of the bubble, with both the value and position of minimum induced charge remaining essentially the same. However, the charge in the drift with Andrift=1.26 contributes significantly to the maximum induced charge after the bubble passes the probe. presents the three components which contribute to the total charge transfer. compares the experimental results with the model simulation, with parameters qm0, K′ and Andrift obtained by matching experimental values of Cmin, Ctransfer and Cmax. It is seen that the prediction is improved significantly in the region around the maximum peak when the contribution from the bubble drift is considered. Unlike previous results without considering the effect of bubble drift as shown in is predicted to reach a maximum positive value after the bubble passes through the probe, consistent with the experimental results, Cmax. The simulated maximum peak shifts to the right with increasing length of the drift cylinder, while the drift has little influence on the position of the minimum peak. Simulation with hd/RB=6 gives a good match with respect to the location of the peak. The more gradual change of the experimental curve following the bubble passage suggests that the contribution from the particle motion in the drift and nearby region induced by the bubble motion cannot be simply represented as a cylindrical drift region of limited length and diameter. Discrepancies between the predictions and experimental measurements after the bubble passes the probe may thus be due to the assumption in the model that the drift has a cylindrical shape with a uniform charge density. In practice, the drift region is known to exist as a sharp figure shape The effect of the capacitor in the electric circuit used in the experiment of Park et al. The higher charge density particle layer around the bubble has some effect on the total charge induction and transfer to the ball probe. With a higher charge density around the bubble, both the specific charge of bed particles and charge transfer coefficient, qm0 and K′, fitted from experimental data, are lower. For a thicker high-charge-density particle layer around the bubble, the fitted qm0 is higher while the fitted K′ is lower. Bubble wake and drift has little influence on the region ahead of the wake and the drift. However, the particle charge in the drift region contributes significantly to the region around the maximum. To fully understand the charge transfer behaviour in gas–solids bubbling fluidized beds, the distribution of charges in regions around and behind the bubble needs to be measured.Linear and non-linear behaviour of steel plates with circular and rectangular holes under shear loadingIn this work, linear buckling and the non-linear behaviour of steel plates with one perforation subjected to shear loading was studied. The influence of the dimension, position with respect to the two main axes, shape (circular or rectangular) and orientation of a hole with respect to the panel slenderness and aspect ratio were all investigated.In both circular and rectangular holes, the strong influence of hole dimensions on the shear buckling coefficient was observed, and the values of the shear buckling coefficient fell with the plate aspect ratio. Small differences in buckling coefficients were noted in rectangular plates with various hole diameters, and buckling coefficients were practically not influenced by the orientation of the rectangular hole. In both rectangular and circular holes, the coefficient remained constant, regardless of hole position for a given distance from the edge.Linear buckling and non-linear behaviour were compared by observing different shear failure modes for slender and thick perforated plates. Elastic and plastic regions were found, on the basis of critical slenderness, for some common geometries.panel height (sub-multiple of panel width)The problem of plate stability under shear loading is of particular interest for steel structures, particularly bridges. Openings are often unavoidable in webs of steel beams and plates, due to the need for inspection and maintenance, and also for aesthetic reasons. In these situations, the presence of one hole in a plate may cause redistribution of shear stresses with significant reduction in stability. The equation of the critical load for unstiffened elastic panels was introduced by Bryan Considerable research on this topic was conducted by Basler Significant studies were carried out by Redwood et al. Other significant work has been developed on plates with holes by Roberts and Azizian In the present work, a parametric investigation in the linear and non-linear fields on perforated plates subjected to shear loading was developed and post-critical behaviour of simply supported perforated panels was studied. The following parameters were considered as influencing the post-critical behaviour of square and rectangular perforated plates subjected to shear loading: (a) hole size; (b) hole position along main axes; (c) panel slenderness; (d) shape (circular or rectangular) of holes and (e) orientation of rectangular holes.A sensitivity analysis to define the shape and dimensions of the elements was developed. Discretizations with the following elements were considered: (a) square elements with four nodes for the entire model; (b) square elements for the entire model except the zone around the hole, where triangular elements with three nodes were used; and (c) triangular elements for the entire model. shows the out-of-plane displacements of the critical deformed shapes, with the three discretizations, for a square plate with a circular hole (a) and a rectangular plate with a rectangular hole (b). Deformed shape and buckling coefficient are not significantly influenced by mesh element shape or size, so that plate elements with four nodes and six degrees of freedom for each node were used for the following analyses. The typical size of the element was about b/20, and the elements along the perimeter and near the hole had dimensions of b/50 or πd/40.Regarding boundary conditions, the four edges were simply supported along the z-axis. Elastic restraints in the x- and y-directions were considered at the four angle nodes of the plate. The rigidity of the elastic restraints was negligible (numerically null), allowing displacements of the angle nodes along the x- and y-directions, and did not influence the distribution of internal stresses and the stability of the plate. The load was directly applied to the nodes as a system of conservative forces which did not change direction during the deformation process. shows the typical loading scheme and boundary conditions of the perforated plate. For the sake of simplicity, panel height b is also a sub-multiple of panel width a (see ). In the following, positions x and y of the hole along the x- and y-axes, hole dimension d and panel width a were divided by b in order to obtain dimensionless quantities (x/b, y/b, d/b, a/b).The results obtained with the present numerical procedure were compared with those of Paik shows the τcr/τy vs. d/b diagram for square plates and three different values of d/b (chosen in the range of hole sizes developed in the following analyses). Comparing the results of the present work with those of Paik A50 steel was considered for linear and non-linear analyses. The elastic modulus was E=206,000 N/mm2 and Poisson's ratio ν=0.3. For non-linear analyses, the material stress–strain assumption was elastic-perfectly plastic with yield stress fy=345 N/mm2.Hole diameters with ratios d/b=0.1, 0.3 and 0.5 were considered for the following buckling analyses, to evaluate shear buckling coefficient kτ in perforated plates. Variations of the hole position along the horizontal and vertical axes of the plate were analysed and the behaviour of the buckling coefficient was described. shows the kτ vs. x/b diagram (x/b is the ratio between horizontal coordinate x and the sub-multiple of the horizontal width of panel b, see ), for plates with a/b=1 and circular holes with d/b=0.1, 0.3 and 0.5, when the centre of the hole moves along the x-axis.The influence of hole size on buckling coefficient kτ was observed. A great reduction in the shear buckling coefficient occurs when hole dimension increases: for holes with d/b=0.5, kτ is about one-third of the value corresponding to the whole panel (without openings). Hole position had a lesser influence on kτ which remained almost constant with x/b. For holes with d/b=0.1, a slight reduction in kτ from the value corresponding to the whole panel was observed when x/b increases. shows the kτ vs. x/b diagram, for rectangular plates with a/b=2 and circular holes with d/b=0.1, 0.3 and 0.5, when the centre of the hole moves along the x-axis. The influence of hole size on buckling coefficient kτ is again evident. A reduction in the shear buckling coefficient occurs when hole dimension increases: for holes with d/b=0.5, kτ is less than half of the value corresponding to the whole panel (with d/b=0.0). Hole position does not substantially influence kτ, which remains almost constant with x/b. shows the kτ vs. x/b diagram, for rectangular plates with a/b=3 and circular holes with d/b=0.1, 0.3 and 0.5, when the centre of the hole moves along the x-axis. A reduction in the shear buckling coefficient occurs when hole dimension increases: for holes with d/b=0.5, kτ is about half of the value corresponding to the whole panel. Hole position does not substantially influence kτ, which remains almost constant with x/b, except when x/b varies from 0.3 to 0.6. The reduction in kτ, when hole size increases, is less evident in this last case when compared with square panels ( lists average shear buckling coefficients (almost constant with x/b) for a/b=1, 2, 3 and d/b=0.1, 0.3, 0.5.A general reduction in kτ when d/b and a/b increase is shown. For d/b=0.5, the shear buckling coefficient remained almost the same when a/b varies. Significant variations were obtained for d/b=0.3 (between square and rectangular panels) and, above all, for d/b=0.1. shows the kτ vs. y/b diagram (y/b is the ratio between vertical coordinate and panel height) for plates with a/b=1 and circular holes with x/b=0.5 and d/b=0.1, 0.3 and 0.5, when the centre of the hole moves along the y-axis from an edge (y/b=0.1) to the opposite (y/b=0.9). Since the horizontal position of the centre of the hole (x/b=0.5) corresponds to the midspan of the square plate, variations of kτ with y/b are symmetrical. However, the shear buckling coefficient remains almost constant when y/b varies for each hole diameter. For d/b=0.1, the value of kτ is very close to that of the whole panel. shows the kτ vs. y/b diagram for plates with a/b=2 and circular holes with x/b=0.5 and d/b=0.1, 0.3 and 0.5. For d/b=0.1, kτ remains almost constant when y/b varies and is very close to that of the whole panel. For d/b=0.3 and 0.5, the curves are not symmetric as for square panels (), since x/b=0.5 is not the symmetry axis of the panel, and a reduction in kτ when y/b increases is observed. In particular, kτ assumes high values when the hole is close to the zone of the plate in which shear forces converge (far from the shear compression band), i.e. y/b<0.5 and x/b<1 (or y/b>0.5 and x/b>1). Correspondingly, kτ is reduced when the hole is close to the zone of the plate in which shear forces diverge (in the shear compression band), i.e. y/b>0.5 and x/b<1 (or y/b<0.5 and x/b>1). shows the kτ vs. y/b diagram for plates with a/b=3 and circular holes with x/b=0.5 and d/b=0.1, 0.3 and 0.5. The values of kτ vs. y/b curves for plates with a/b=3 are similar to those of plates with a/b=2 (), so that the same observations are still valid. For y/b=0.2 and 0.3 and holes with d/b=0.1 and 0.3, the shear buckling coefficient is close to that of the whole panel. compares kτ vs. y/b=curves, in plates with a/b=3, circular hole with d/b=0.3 and 0.5, and hole centre in x/b=0.5 and 0.9. The curves diverges for y/b<0.5, with smaller values of kτ for x/b=0.9, and practically overlap for y/b=>0.5.Rectangular holes with dimensions d×1.5d, with rounded angles having a curvature radius of 0.25d and two different orientations were examined. The hole was set parallel to the transversal (vertical) y-direction in one case, and called RS. In the other, the hole was set parallel to longitudinal (horizontal) x-direction, and called RL. shows the load scheme of a plate with rectangular holes and orientations RL and RS. shows the kτ vs. x/b diagram for square plates and holes with d/b=0.1, 0.3 and 0.5. with the corresponding one for circular holes (), the same conclusions are valid regarding hole size and position, i.e. the strong influence of hole diameter on kτ and the lesser influence of the position along the x-axis. For d/b=0.1, kτ falls slightly when x/b increases; for d/b=0.3 and 0.5, kτ slightly increases when x/b increases. For each hole size and position kτ is always less than that of the corresponding plate with a circular hole. shows the kτ vs. x/b diagram for rectangular plates with a/b=2 and holes with d/b=0.1, 0.3 and 0.5. Again, kτ falls when hole diameter increases and the lesser influence of hole position along the x-axis is observed. The kτ values for rectangular plates with a/b=2 are lower than those for square plates, and there are smaller differences among the various hole diameters. shows the kτ vs. x/b diagram for rectangular plates with a/b=3 and holes with d/b=0.1, 0.3 and 0.5. The observations for plates with circular holes () regarding hole size and position remain valid (significant influence of the former and almost null influence of the latter). kτ is less than that for square plates (), with small differences among the various hole diameters. lists average shear buckling coefficients (almost constant with x/b) for a/b=1, 2, 3 and RS holes with d/b=0.1, 0.3, 0.5. A general reduction in kτ when d/b and a/b increase is again shown.Shear buckling coefficients for square and rectangular perforated plates with d/b=0.3 and 0.5 are very close; for d/b=0.1, the values are significantly different. shows the kτ vs. x/b diagram for square (a/b=1) and rectangular plates with a/b=2 and 3 and holes with d/b=0.1, 0.3 and 0.5. shows average shear buckling coefficients (almost constant with x/b) for a/b=1, 2, 3 and RL holes with d/b=0.1, 0.3, 0.5. A general reduction in kτ when d/b and a/b increase is again shown., kτ remains practically the same for RS and RL holes. Shear buckling coefficients for square and rectangular perforated plates with d/b=0.3 and 0.5 are very close; for d/b=0.1, the values are significantly different.A50 steel was considered for non-linear analyses. The elastic modulus was E=206,000 N/mm2 and Poisson's ratio was ν=0.3; the material stress–strain assumption was elastic-perfectly plastic with yield stress fy=345 N/mm2. shows the τcr/τy vs. λ diagram for square plates and circular holes with d/b=0.1 and 0.5, located in the centre of the panel (x/b=0.5). The gray curves were obtained by linear buckling analysis, and black ones by non-linear analysis. The reduction in the τcr/τy ratio from d/b=0.1 to 0.5 is clear. shows the τcr/τy vs. λ diagram for rectangular plates with a/b=2 and circular holes with d/b=0.1 and 0.5, located at x/b=0.5., lower values of critical shear stress are obtained for a/b=2 and x/b=0.5, particularly for high values of slenderness λ. Non-linear analysis of the plate can therefore give the deformed shape of the plate shown in , in which plasticisation of the zone near the hole causes sliding of the parts of the plate separated by the hole. This circumstance, more evident in rectangular plates, cannot be observed in linear analyses, in which buckling occurs without yielding.The distribution of Von Mises stresses is shown in for thick (a) and slender (b) panels. Stress distribution is quite different: the thick panel shows the failure mode described above, with excessive plasticisation of the zone near the hole, whereas, for the slender panel, collapse occurs due to buckling (before yielding), with two shear bands and a different deformed shape. shows the τcr/τy vs. λ diagram for rectangular plates with a/b=2 and circular holes with d/b=0.1 and 0.5, located in x/b=1 (centre of the panel). The curves are similar to those of plates with a/b=2 and holes in x/b=0.5 (), so that similar observations may be made. shows the τcr/τy vs. λ diagram for rectangular plates with a/b=3 and circular holes with d/b=0.1 and 0.5, located in x/b=0.5 (centre of the first sub-panel). Smaller values of critical stresses are observed with respect to panels with a/b=2 ( shows the τcr/τy vs. λ diagram for rectangular plates with a/b=3 and circular holes with d/b=0.1 and 0.5, located in x/b=1 (between the first and second sub-panels). The curves are similar to those of plates with a/b=2 and holes in x/b=0.5 (), so that similar observations may be made. shows the τcr/τy vs. λ diagram for rectangular plates with a/b=3 and circular holes with d/b=0.1 and 0.5, located in x/b=1.5 (in the centre of the second sub-panel). The curves are similar to those of plates with a/b=3 and holes in x/b=0.5 ( shows elastic and plastic fields in the d/b vs. λ diagram for square and rectangular plates with a/b=2 and 3 and various hole positions.For square panel with hole in x/b=0.5 (centred hole), λcr falls when d/b increases. For example, for λ=110, plates without holes and perforated ones with d/b=0.1 collapse due to material yielding, whereas perforated plates with d/b=0.3 and 0.5 do so because of elastic buckling. For plates with a/b=2 and 3 and holes in x/b=0.5 (eccentric hole), λcr remains almost constant when d/b increases. For plates with a/b=2 and holes in x/b=1 and plates with a/b=3 and holes in x/b=1.5 (centred hole), λcr increases when d/b increases from 0.0 to 0.1, then it decreases slightly when d/b increases from 0.1 to 0.3, and finally remains constant from 0.3 to 0.5. Similar observations are valid for plates with a/b=3 and holes in x/b=1. Therefore, the elastic and plastic regions for shear loading of square and rectangular panels change according to the position of the hole in the panel, since hole position influences the critical deformed mode and the number and location of shear bands.Non-linear analyses of plates with a/b=1, 2 and 3 and hole sizes with d/b=0.1, 0.3 and 0.5 give the curves in , shown in τcr/τy vs. d/b diagrams for λ=70 (a) and λ=120 (b).For λ=70, τcr/τy does not substantially vary with the aspect ratio of the plates for every hole position, and falls when d/b increases. For λ=120 (slender panel), τcr/τy for square plate and centred hole is higher than in other cases. A fall inτcr/τy when d/b increases is again observed. Critical stresses for λ=70 are about twice those for λ=120.In this work, a parametric investigation was developed in linear and non-linear fields on plates with one hole, subjected to shear loading, and post-critical behaviour was studied. The following parameters were considered as influencing the post-critical behaviour of plates with one hole subjected to shear loading: (a) hole size (d/b=0.1, 0.3, 0.5); (b) hole position along main axes (x/b ratio and y/b ratio); (c) panel slenderness; (d) hole shape (circular or rectangular) and (e) orientation of rectangular hole (RS and RL).Regarding plates with circular holes, kτ assumes high values when the hole is close to the zone of the plate in which shear forces converge. Correspondingly, kτ is reduced when the hole is close to the zone in which shear forces diverge. As regards slenderness, for thick panels, critical stress does not substantially vary with the aspect ratio of the plates for every hole position, and falls when d/b increases. For slender panels, critical stress for square plates and centred holes is higher than that of rectangular plates. A reduction in critical stress when d/b increases is generally obtained. In plates with one rectangular hole, two orientations were considered and similar conclusions were drawn for rectangular holes regarding hole size and position, i.e. the strong influence of hole dimensions on kτ and the lesser influence of the position along the x-axis.Non-linear analysis of the plate generally reveals the plasticisation of the zone near the hole, causing sliding of the two parts of the plate separated by it. This circumstance, more evident in thick rectangular plates, cannot be observed in linear analyses in which buckling occurs without yielding. Conversely, in slender rectangular panels, collapse generally occurs due to buckling (before yielding), with two shear bands and a different deformed shape.Investigation of residual stresses in thick-walled vessels with combination of autofrettage and wire-windingWire-winding and autofrettage processes can be used to introduce beneficial residual stress in the cylinder of thick-walled pressure vessels. In both techniques, internal residual compressive stress will increase internal pressure capacity, improve fatigue life and reduce fatigue crack initiation. The purpose of this paper is to analyze the effects of wire-winding on an autofrettaged thick-walled vessel. Direct method which is a modified Variable Material Properties (VMP) method has been used in order to calculate residual stresses in an autofrettaged vessel. Since wire-winding is done after autofrettage process, the tangent and/or Young's modulus could be changed. For this reason, a new wire-winding method based on Direct Method is introduced. The obtained results for wire-wound autofrettaged vessels are validated by finite element method. The results show that by using this approach, the residual hoop stresses in a wire-wound autofrettaged vessel have a more desirable distribution in the cylinder.Wire-winding and Autofrettage are two techniques which used to introduce residual stress at the inner cylinder of thick-walled pressure vessels. This internal residual compressive stress increases the amount of internal pressure capacity, improve fatigue life and reduce fatigue crack initiation.Wire-winding process is a safe method for reinforcing and prestressing pressure vessels and frame-structures. It has some more advantages such as; reducing stress concentration, preventing rapid failure and thereby increasing safety factor. In earlier literature, constant tensile stress was used for all layers of wire during wire winding process as the simplest method. Then Comstock In Autofrettage process, internal surface of a thick-walled vessel or tube is pressurized so that inner part of its wall deform plastically. When internal pressure is released, residual compressive stresses at the inner part of cylinder is resulted. This residual stress will increase internal pressure capacity and improve fatigue lifetime. Material behavior, yield criterion, Bauschinger effect and hardening law are the effective parameters in amount of calculated residual stresses. The effects of these parameters have been analyzed in the different studies It should be noted that autofrettage is a more convenient process. But it produces tensile stress in outer part of the cylinder wall. Also, maximum available compressive hoop stress is limited in this process, while in wire-winding technique there is no residual stress limitation. Wire-winding is a safe technique that prevents rapid failure and introduces compressive residual stress in whole of the cylinder wall. So, combination of these two techniques could have better benefits in comparison to solo application of them. By wire-winding of an autofrettaged vessel, the obtained compressive residual hoop stress at the inner part of vessel will increase and tensile residual hoop stress at the outer part will decrease. So, residual hoop stress in a wire-wound autofrettaged vessel has a more desirable distribution in the cylinder.The purpose of this paper is to analyze the effect of the wire-winding process on an autofrettaged thick-walled vessel in constant axial strains condition. Direct method is used in this analysis in order to calculate residual stress in autofrettage process. The existing analytical methods for wire-winding are applicable for a vessel with constant Young's modulus and elastic behavior. But according to material behavior, tangent and/or Young's modulus could be changed in autofrettage unloading step or reverse yielding (depending on material behavior or autofrettage pressure in loading step). Because wire-winding is done after autofrettage process, a new wire-winding method based on Direct Method is introduced to calculate residual stresses in this situation. In this work, after reviewing the required theories of autofrettage process and ASME code formulation for wire-winding, the new wire-winding method is explained in Section . Then, solution process of Direct method and finite element method (FEM) will be presented for a wire-wound autofrettaged vessel In Section . Afterward, residual hoop stresses will be obtained and compared in six different cases. At first case and in Section , the results of new wire-winding method are compared to ASME formulation results for wire-wound vessels. In the second case, Direct and FE methods was compared to validate the results in Section presents the obtained results for comparison of residual stresses before and after wire-winding process. In Sections , the residual stresses in wire-wound autofrettaged cylinders are compared with autofrettage and wire-winding processes, separately. Next, the residual stress is calculated for winding wires after autofrettage in different end conditions in Section shows a cylinder with total compressive stress distributions.In this section, the Direct Method for calculation of residual stress in autofrettage process is reviewed. Then, ASME code equations for wire-winding are explained. Next, the new wire-winding method would be presented.where εij and σij are the strain and stress components and δij is Kronecker Delta. Also νeff and Eeff are the effective Poisson's ratio and effective Young's modulus, respectively, which are defined by:where E is Young's modulus, ν is Poisson's ratio and Ø is the scalar valued function depending on material behavior, that given by:In the above equation, εeqP and σeq are the equivalent plastic strain and equivalent stress, respectively. According to Eqs. , νeff and Eeff are depended on the final state of stress, uniaxial stress–strain curve, Poisson's ratio and Young's modulus. Complete distribution of νeff and Eeff is needed to use constitutive equation. For this purpose, projection and energy methods are proposed by Jahed and Dubey For calculating residual stress in an autofrettaged thick-walled vessel, the cylinder cross section would be divided into several infinitesimal strips. The material properties, νeff and Eeff, remain constant for points of a specific strip in each solution. Hence, an axisymmetric elastic solution can be used for each strip. For the next solution, the values of the corresponding modulus should be updated. shows cross section of a thick-walled cylinder and an isolated strip on it Here p is the internal pressure of the vessel. Also, r1 and r2 are internal and external radii and p1 and p2 are internal and external pressures of each strip.The VMP method was only able to calculate stress distribution in plane stress and plane strain conditions. To modify this theory, Farrahi et al. For each strip, the inside and outside displacements of the strip, u1 and u2, can be related to its inside and outside pressures, P1 and P2, and constant axial strain εz∗ as follows:{u1u2}=[c11c12c21c22]{P1P2}−{νeffεz∗r1νeffεz∗r2}where r1 and r2 are internal and external radii. Multiplying the inverse of coefficient matrix [c] in both sides of Eq. [c11c12c21c22]−1{u1u2}={P1P2}+{P1pseP2pse}Here p1pse and p2pse is termed as pseudo pressures and defined as follows:{P1pseP2pse}=−[c11c12c21c22]−1{νeffεz∗r1νeffεz∗r2}Also, components of coefficient matrix [c] are given by:c11=(1+νeff)Eeffr13r22−r12[1−2νeff+r22r12]c12=2(1−νeff2)Eeffr1r22r22−r12c21=2(1−νeff2)Eeffr12r2r22−r12c22=(1+νeff)Eeffr23r22−r12[1−2νeff+r12r22]Note that in all relations, the positive direction of pressure is the same as the positive radial direction. For calculation of pseudo pressure vector, constant axial strain εz∗ must be initially determined. The calculation of εz∗ for different end conditions and also solution algorithm are presented by Farrahi et al. In order to calculate residual stresses, the unloading stress–strain curve of each strip should be defined at the end of loading. The unloading process is considered the same as a loading process with new defined curves for each strip. Residual stress distribution will be obtained by subtracting result from the second analysis from those of loading These compressive stresses are function of the tensile stress in each wire during winding, Sw(x), and the number of wire layers. The radial stress, σr(x), and the tangential stress, σt(x), are defined by the following equations at any diameter of the cylinder, x1σr(x1)=−[1−(DIx1)2]∫DifDw(xx2−DI2Sw(x))ⅆxσt(x1)=−[1+(DIx1)2]∫DifDw(xx2−DI2Sw(x))ⅆxwhere x is the diameter coordinate, DI is the inside diameter, Dif is the diameter of the interface between cylinder and winding and Dw is the instantaneous applied outside diameter of wire zone. The corresponding stresses at any diameter of wire zone, x2 (<Dw), are as follows σr(x2)=−[1−(DIx2)2]∫x2Dw(xx2−DI2Sw(x))ⅆxσt(x2)=Sw(x2)−[1+(DIx2)2]∫x2Dw(xx2−DI2Sw(x))ⅆx shows the dimensions which are used in Eqs. At the end of the winding process, Dw can be replaced by external diameter, Do.There are a few methods for calculating residual stress in wire-winding process such as ASME code equations. But these equations are only applicable for a vessel with constant Young's modulus and elastic behavior for cylinder and wires. For some materials, such as DIN 1.6959, Young's modulus could be changed in autofrettage unloading step which is depended on loading plastic strain. Also, tangent modulus would be changed after reverse yielding in plastic zone. So, a new method is required to calculate residual stresses of wire-winding after autofrettage process.In this method, wire layers are wound layer by layer based on Direct Method. For winding a new layer, an individual strip should be defined. This strip could be assumed as a thin-walled vessel which its thickness is equal to wire thickness. If the new layer is wound with a hoop stress equal to Sw, then pressure under this layer, Pw, could be calculated as follow:where t is the thickness of the wire layer. This pressure is applied to the vessel and the wound layers as an external pressure. So, stress distribution which is caused by this new layer could be calculated by Direct Method under open end condition. The hoop stress in this layer is Sw, while the radial and axial stresses are equal to zero. When iterations are completed, the calculated stresses are added to the previous residual stresses. Then, other new layers could be wound according to this method and after winding each layer, calculated residual stresses should be added to previous residual stress in cylinder and wire layers. Finally, residual stresses of wire-winding process are obtained for the vessel under elastic (with constant or variable Young's modulus) or plastic behavior. Moreover, stress distribution on cylinder and wire layers could be calculated when internal working pressure is applied to the vessel. It should be noted that during wire-winding process, each strip in the vessel will continue its own autofrettage unloading curve.In this section, solution process of Direct Method and FE method for wire-winding of autofrettaged vessels will be explained.Direct Method will be used in order to analyze wire-wound autofrettaged vessel as a numerical method. Firstly, residual stress would be calculated in the cylinder of an autofrettaged thick-walled vessel according to the Section description. The end condition could be assumed as plane strain, open-end, and closed-end conditions. Then, wire-winding process (only open-end condition) will be added to autofrettaged vessel. For this purpose, wire layers would be wound layer by layer and residual stresses, which are obtained by new method, would be added to the previous stresses according to Section . Also, each strip of the cylinder has a particular unloading curve, which is related to the plastic strain in loading step, and will continue it during wire-winding process. Von Mises yield criterion is used for both wire-winding and autofrettage process. Based on above explanation, a computer program is developed in order to calculate residual stress in a wire-wound autofrettaged vessel.In the FEM modeling, autofrettage and wire-winding processes will be done in sequence. The vessel is assumed as an axisymmetric model and the autofrettage process is modeled in two stages. In the loading step, desired autofrettage pressure is applied to inner surface of vessel. Then inner pressure is removed in unloading step in order to calculate residual stresses. The Bauschinger effect is modeled by defining two virtual temperature profiles which will change the yield stress of the plastic deformed region In this section, first of all, residual stress in cylinder and wire layers is calculated by new method for a wire-wound vessel. These results would be compared to the results obtained from ASME code equations. Then, residual stress is determined by new method and FE method for a wire-wound autofrettaged vessel in order to validate the results. This comparison includes two wall ratios (ratio of outer cylinder radius to inner radius), k = 2 and k = 2.5, for wire-wound autofrettaged thick-walled vessels. Afterward, the residual hoop stresses are calculated for autofrettaged vessels with and without wire-winding. Then, the residual stresses are compared with an autofrettaged vessel and a wire-wound vessel, independently. Also, different end conditions will be studied. Finally, wire-wound autofrettaged cylinders with only compressive residual stress are presented.In order to compare this work with the literature (Direct Method for autofrettaged vessels . The wire material has a similar behavior in loading too.Also, overstrain (the percent of wall thickness which gets into plastic zone in loading step) in autofrettage process is considered 70% for both wall ratio. show the normalized residual hoop stress and radial stress versus normalized radial position in wire-wound vessels (in cylinder and wire layers) at two different wall ratios, respectively. Twenty layers with constant winding stress, Sw = 720 MPa, are wound around the vessel. The thickness of each wire layer is one hundredth of the outer cylinder radius. show an excellent agreement between ASME code equations and new method in these two elastic cases. In the next section, the results of new method will be compared with FEM results for wire-winding after autofrettage process (after plastic deformation in cylinder wall). shows the normalized residual hoop stress versus normalized radial position in wire-wound autofrettaged vessels for new method and FE method at two different wall ratios. Autofrettage and wire-winding processes are done under closed-end and open-end condition, respectively. Twenty layers with constant winding stress, Sw = 720 MPa, are wound around the vessel. The thickness of each wire layer is one hundredth of the outer cylinder radius. In FEM modeling, vessels are composed by 100 and 120 elements through its cylinder thickness for k = 2 and k = 2.5, respectively. Also, two elements are assumed for each winding layer. shows a very good agreement between two methods. The normalized residual hoop stress at inner radius is −0.60 for k = 2and −0.89 for k = 2.5., Direct method results of residual hoop stress for wire-wound autofrettaged vessels are compared to residual hoop stresses before wire-winding process which are presented by Farrahi et al. shows, residual hoop stress in a wire-wound autofrettaged vessel is reduced in all part of the vessel cylinder. This means that compressive stress increase and tensile stress decrease. This new stress distribution is more desirable in order to increase the vessel's internal pressure capacity, improve fatigue life and reduce fatigue crack initiation. Moreover, the positions of reverse yielding, which is located between 0 and 0.2 normalized radial position, move to left because of increasing in compressive stress at inner part of cylinder. presents a comparison between the vessels shown in and autofrettaged vessels under closed-end condition with maximum residual hoop stress at inner radius. Maximum available normalized hoop stresses with the autofrettage process (overstrain in these vessels is close to 100%) are −0.56 for k = 2 and −0.86 for k = 2.5 at inner cylinders radius, while shows more compressive residual stresses at inner radius of wire-wound autofrettaged vessels.As expected, distribution of residual hoop stress in a wire-wound autofrettaged vessel is more desirable in comparison to an autofrettaged vessel. In addition to more amount of compressive hoop stress at the inner part of cylinder wall, there is considerably less amount of tensile hoop stress at the outer part, which can decrease crack growth in this part at working condition. Also, maximum available compressive hoop stress could be increased by winding more wire layers. shows comparison between vessels shown in and wire-wound vessels with same residual hoop stress at inner radius. The required number of wire layers with constant winding stress, Sw = 720 MPa, is 46 and 85 layers for k = 2 and k = 2.5, respectively.Although stress distribution in a wire-wound vessel cylinder is more desirable than stress distribution in a wire-wound autofrettaged vessel, but the winding of this number of wire layers is very difficult in practice and increase outer radius of the vessel that often is not desirable. In addition, more amount of compressive hoop stress at the inner part of a wire-wound autofrettaged vessel will increase fatigue life. show the residual hoop stress in wire-wound autofrettaged vessels under different autofrettage end-condition with 70% overstrain for two wall ratios., plane strain and closed-end condition have a very similar stress distribution, while open-end condition introduces a stress distribution with less amount of stress. So, in order to access better stress distribution, the autofrettage process should be done under plane-strain or close-end condition, according to available facilities.It should be noted that by increasing the number of wire layers or winding stress, it is possible to obtain a wire wound autofrettaged vessel with only compressive hoop stress in whole cylinder. shows only compressive hoop stress distribution in throughout the cylinder of a wire-wound autofrettaged vessel with 30 and 55 wire layers and 70% overstrain for k = 2 and k = 2.5, respectively.By using optimum autofrettage pressure, increasing wire layers and/or winding tensile stress, more amount of compressive stress is available.In this paper, residual stresses of wire-wound autofrettaged vessels were studied and the results for different types of vessels were compared. Direct Method (which is modified of VMP method) was used in order to calculate residual stress in vessel for autofrettage process. Also, a new approach based on Direct Method has been presented in order to calculate residual stresses of wire-winding process on an autofrettaged vessel. By considering obtained results, the following conclusions can be highlighted:A new method is presented in order to calculate residual stresses of wire-winding process in a vessel with elastic (with constant or variable Young's modulus) or plastic behavior.This new method has an excellent agreement with existing theories for vessels with constant elastic material behavior. Also, for other conditions, a very good agreement between obtained results and FEM results has been observed.The residual hoop stress in a wire-wound autofrettaged vessel has a more desirable stress distribution in all part of the vessel. This means that compressive stress increase and tensile stress decrease in the cylinder. As a result, this new stress distribution increases the amount of internal pressure capacity, improve fatigue life and reduce fatigue crack initiation.Against autofrettage process, maximum available compressive hoop stress is not limited in a wire-wound autofrettaged vessel. Also, there is less amount of tensile stress at outer part of a wire-wound autofrettaged cylinder.By considering same residual hoop stress at inner radius, a wire-wound vessel needs much more wire layers, which is very difficult in practice and increase outer radius of vessel. Moreover, a wire-wound autofrettaged cylinder has better stress distribution at inner part for increasing fatigue life.Autofrettage with plane strain and closed-end condition have a very similar stress distribution in a wire-wound autofrettaged vessel, while open-end condition introduces a stress distribution with less amount of stress.By applying an optimum autofrettage pressure, increasing the number of wire layers or winding tensile stress, a wire-wound autofrettaged vessel with only compressive stress in wall is accessible.Additive manufacturing of a novel Ti-Al-V-Fe alloy using selective laser meltingTi-1Al-8V-5Fe (Ti-185) and other Fe containing β -Ti alloys are attractive because of their high strength and low cost. These alloys, however, cannot be produced through ingot casting due to strong Fe segregation and the formation of β flecks. Selective Laser Melting (SLM) was successfully used to produce Ti-185 components starting from elemental Ti and Fe powders, and an Al-V master alloy powder with irregular shape. Microstructure analysis of the as-built components demonstrated that SLM can be used to produce a very fine grain microstructure with nano-scale precipitates and non-detrimental Fe segregation. The findings are interpreted in terms of the rapid solidification conditions during SLM. Compression test results reveal that ultra-high strength and reasonable ductility can be achieved in the as-built as well as heat treated samples.Additive manufacturing (AM) is an emerging technology for producing near-net-shaped components directly from powders or wires melted by a high-power-density heat source. The main advantage of AM is its ability to directly produce complex geometries with minimal material waste. New material options are required that take advantage of the corresponding rapid solidification rates.Titanium alloys provide components with high specific strength and high operating temperatures. In recent years, (near) β -Ti alloys have been widely explored owing to their higher strength, and improved combinations of toughness and fatigue resistance as compared to other Ti alloys []. These alloys contain high additions of β stabilizing elements (Mo, V, Cr, Fe). Wide-scale adoption of β -Ti alloys is limited due to high costs, which are partly due to the cost of the Mo, V, and Cr alloying elements. Ti-1Al-8V-5Fe (Ti-185) is a unique low-cost β -Ti alloy, containing lower cost alloying elements, notably Fe, as compared to Ti-10V-2Fe-3Al (Ti-1023) and Ti-5Al-5V-5Mo-3Cr (Ti-5553) while offering high strength and fatigue life. Although Ti-185 was patented more than 50 years ago, it is not commercially viable using traditional processing. This is because strong micro-segregation of Fe occurs during casting [], resulting in large variations in composition and leading to the precipitation of brittle phases. For the few niche applications where Ti-185 is currently utilized, the alloy is heat-treated to produce a microstructure consisting of a β matrix with primary α phases at the grain boundaries as well as a nano-scale distribution of α precipitates within the grain interiors.] developed a processing route for Ti-185 consisting of powder metallurgy followed by thermo-mechanical processing. In this way, both the segregation of Fe and the formation of detrimental β fleck phase were bypassed (β flecks are β phase regions strongly enriched with β stabilizing elements such as Fe and/or Cr []). Although the properties were excellent (1655 MPa tensile strength and 4–6% elongation), a lengthy and costly sintering treatment and multiple rolling steps were required for component fabrication []. Starting from the same material, Devaraj et al. [] then developed a hierarchical nano-structured alloy with very fine primary and secondary α within the β -matrix by using an aging treatment below the β -transus temperature. This microstructure resulted in a unique combination of strength and ductility, surpassing available commercial Ti alloys.In the present study, the use of Ti-185 as a novel material for Selective Laser Melting (SLM) (a powder-bed based AM technology) is investigated. Compared to the α + β grades, very few studies on AM of β titanium alloys have been published []. This is thought to be due to the limited powder stock available for SLM. The main objective of this work is to develop a printed component of Ti-185 alloy having minimal segregation and porosity, and reasonable mechanical properties. During AM of metals, the cooling rates are estimated to reach up to 103–104 °C/s [], which could greatly reduce Fe segregation and minimize the formation of the β flecks, ensuring that the optimal component yield strength and toughness is achieved. Eylon and Froes pointed out that Ti-185 should only be used with processes enabling rapid transformation from the liquid to the solid state []. It would thus appear that AM, characterized by high solidification rates, is uniquely suited for processing Ti-185.Ti-185 powder was obtained from ADMA Advanced Materials Products, Inc., Hudson, Ohio. The powder is an elemental mixture of titanium, iron, and a vanadium-aluminum (V-Al) master alloy. First, the powder was ball milled and sieved to achieve the appropriate size distribution for SLM. Ball milling, traditionally used in powder metallurgy, has also been used in recent years to develop elemental powders suitable for AM processes []. The use of elemental powder as feedstock also contributes to material saving costs and allows for future flexibility in alloy design. The powder characteristics (size distribution, flowability and apparent density) were measured using a laser diffraction technique and Hall tests following ASTM standards B212 []. Second, an EOS-M280 SLM apparatus was used to build a series of sample coupons for metallographic examination and mechanical testing. The base plate was a Ti-5553 near-β titanium alloy, preheated to 80 °C. A stripe laser pattern was used with the laser power, scanning speed, hatch spacing and layer thickness being 370 W, 1035 mm/s, 0.12 mm and 0.06 mm, respectively. During every new layer, the stripes were rotated counterclockwise by ∼67° as compared to the previous layer. This set of parameters was equivalent to a power density of approximately 50.4 J/mm3, and was used based on values published previously []. An argon atmosphere was maintained throughout the build process. Third, samples were cut, ground and polished with a mixture of 10% hydrogen peroxide in colloidal silica as the last polishing step. Kroll’s solution was used to etch the samples. Fourth, optical and electron microscopy were performed, along with electron back-scatter diffraction (EBSD) and energy-dispersive spectroscopy (EDS) for microstructural and chemical analyses. X-ray diffraction (XRD) was also carried out in order to identify the phases present in both the powder and the as-built samples. Finally, compression tests were performed on cylindrical samples 5 mm in diameter and 8 mm height using a universal MTS machine at nominal strain rate of 1 × 10−3 s−1. Teflon tape was used as a lubricant between the samples and the platens. presents an overview of the Ti-185 powder characteristics. a shows the back-scatter electron image of the Ti-185 elemental powder. As can be seen, the powder has irregular shape as a result of being fabricated using ball milling. The XRD results show the three main constituents of the powder as titanium, a vanadium-aluminum master alloy and iron particles. The powder has a relatively wide size distribution with the particle diameters at 10%, 50% and 90% in the cumulative distribution being 21, 51, and 68 μm, respectively. The Hall flowability test indicates that the powder had no flowability, and an apparent density of 3.1 g/cm3.a and b show optical micrographs of the SLM-built sample in the as-polished and etched conditions. The individual build layers are visible, along with a small amount of porosity. Using image analysis techniques, the average porosity content was evaluated to be ∼0.62%, which is much lower than typical powder processing techniques. Using the Archimedes method, the density of the as-built structure was measured to be 4.6618 g/cm3 which is very close to the theoretical density of this alloy, i.e. 4.6676 g/cm3. c shows an XRD map of the Ti-185 as-built sample shown in b, confirming the presence of both the body centered cubic β phase and the hexagonal close-packed α phase. A corresponding EDS line scan of ∼300 μm and equivalent to 5 deposition layers, d, showed no macroscale gradients in any of the alloying elements. This is consistent with solidification occurring only at the scale of the powder layer. The average oxygen content of the as-built sample was determined via inert gas fusion method (ASTM E1409-13) to be ∼0.78 wt.%. Note that a second XRD pattern, a Ti-185 sample subsequently heated to 1200 °C, is also shown in demonstrate that Ti-185 can be produced using the SLM process to create a high-integrity additively-manufactured structure, but what does the microstructure look like? In , optical micrographs of the as-built Ti-185 structure are shown. a shows a low-resolution optical image of the as-built sample; the grain size is rather uniform, with a mean value of ∼ 13 um, b. The very fine β grain structure produced by SLM is in sharp contrast to the large β grains that form when β -Ti alloys are produced via casting [], which then requires extensive thermomechanical post-processing for the refinement. Further, none of the detrimental β flecks were seen in any of the optical/electron microscopy observations.Another interesting observation is the variations in contrast as can be seen along the build direction in a. Some areas of the microstructure are brighter as compared to the surrounding matrix as highlighted in b. To further investigate this observation, high resolution EBSD maps were obtained of the as-built microstructure. shows the EBSD band contrast map of the as-built sample depicting high angle grain boundaries. At this resolution, α phase particles cannot be seen. b shows a high-resolution EBSD image of the identified white square. As can be seen, the microstructure actually consists of a β matrix in white with fine α phase films along the grain boundaries, as well as α precipitates within the grains. The interior α precipitates appear to have an orientation relationship with the β matrix, suggesting that these precipitated from β during cooling. An interesting observation from b is that it appears that the α phase is inhomogeneously distributed even within a single β grain. It is hypothesized that this inhomogeneous distribution of α phases is responsible for the “white band” contrast seen in b that appears on a repeating basis. The EDS elemental map of Fe, c also shows the inhomogeneous distribution of the α phases. Specifically, areas having limited α phase contain 8–11 wt.% Fe while areas with a higher density of the α phase contains 2–5 wt.% Fe. This is consistent with Fe being an effective β stabilizer. Thus, although there was no macro-segregation of alloying elements (d), there is clearly local partitioning and segregation of alloying elements on a layer-by-layer basis during SLM, leading to an inhomogeneous distribution of the α phase within individual grains. shows a schematic of the thermal history experienced by a single layer of elemental Ti-185 powder during the SLM process. This schematic can be used to propose a mechanism for the α phase formation seen in . The powder first experiences melting and solidification, stage 1. During this process, the liquid transforms into the β-phase, as confirmed by the Thermo-Calc Scheil calculations []. Next, the layer is heat treated during deposition of the successive layers, stages 2 and 3. If the temperature achieved during this in situ heat treatment exceeds the β-transus temperature, a fully β- beta structure will develop. The XRD results presented in c verify this hypothesis, as it shows that a sample heat treated at 1200 °C for 10 min followed by water quenching consists of fully β-phase structure. However, heat treatment will also take place below the β- transus temperature as further layers are added to the build. In this case, the α phase can form at the boundaries as well as interior of the β-beta matrix, stage 3. A higher oxygen content such as the one seen in the Ti-185 alloy increases the β-transus temperature, thus expanding the range in which the formation of the α phase can occur. Similar microstructures developed through in situ heat treatment during SLM have been reported for other titanium alloys [a is a bright field TEM image of the as-built sample. Analysis of the selected area diffraction pattern, c, confirm the presence of the α phase as well as a small fraction of ω phase. The α phase has a plate-like shape with an average length of 305 nm and a width of ∼55 nm. The ω phase is very fine, <50 nm, and is located in contact with the α phase. This suggests nucleation of the α phase from the ω phase as reported in the literature []. The TEM image has also revealed the presence of a high dislocation density, e, in the as-built sample. This is a common feature of AM material due to the high thermal stresses that develop during the fast cooling rates [After the SLM processing, additional heat treatment can be introduced to further modify the microstructure, as sketched at the end of . The aging treatment may change the morphology and distribution of the α phase seen in b and/or lead to grain growth depending on applied temperature and its duration. shows the microstructure of the as-built sample aged at 800 °C and 960 °C for 1 h and 30 min, respectively, followed by a water quench. At the lower heat treatment temperature, a., a fine grain distribution is maintained as the grain boundaries are pinned by the α phase. A uniform distribution of α phase within the β matrix is achieved, c. However, at 960 °C, the grains have grown larger, b, as compared to the samples aged at 800 °C. The process of α phase spheroidization has also taken place, d. Based on the diffusivity of Fe in the β phase [], a diffusion distance of 16 μm was calculated at 800 °C for 1 h. This distance is comparable with the scale of the precipitate heterogeneity seen in b, and explains the observed uniform distribution of the α phase. shows compression test results on the as-built sample as well as the sample heat treated at 960 °C for 30 min. As can be seen, the as-built material shows a very high compression strength, reaching ∼1.7 GPa at a plastic strain of 0.1 prior to failure. The corresponding hardness was measured to be ∼470 HV. As a result of the heat treatment, both the compressive strength and strain to failure have increased, to ∼1.8 GPa and 0.3, respectively. The compression strength of both the SLM as-built and heat treated Ti-185 alloy are seen to be significantly higher in comparison to the powder processed as-sintered Ti-185 alloy as well as the in situ heat treated Ti-5553 alloy developed through the SLM process, The excellent combination of high strength and plasticity in the as-built sample is achieved as a result of four main contributing factors: (1) the fine grain size of the as-built sample that strengthens via a Hall-Petch type relation []; (2) a high dislocation density present in AM-built structures that has been estimated to reach 1015 m/m3 and coming close to values seen in heavily deformed metals [], nano-scale alpha (α) phase distributed within the β-beta matrix that provide dispersion strengthening []; and (4) high oxygen content that hardens Ti via solid solution strengthening []. In the heat treated sample, the modification of the alpha phase distribution without a significant change in the beta grain size is seen to provide an improved combination of strength and plasticity, the details of which require further investigation. Future work will also examine the effect of oxygen content; lowering the oxygen content (e.g. below 0.4 wt.%) is expected to lead to further improvements in ductility and toughness.An Fe-containing Ti alloy prone to embrittlement due to severe segregation during ingot casting, Ti-185, has been successfully produced by SLM. The combination of the small grains found in the as-built Ti-185 and the absence of these β flecks provide strong metallurgical evidence that Ti-185 is a promising material for SLM. A remarkable combination of strength and plasticity is achieved as a result of a very fine-grained structure, nano-scale alpha phase distributed within the beta (β) matrix, high dislocation density as well as high oxygen content. This process can open a new avenue for developing a new family of Fe-containing titanium alloys for additive manufacturing.Influence of substrate treatment on the tribological properties of DLC coatingsDue to the very thin nature of DLC coatings, the substrate must carry the main part of the applied load. If the substrate has insufficient strength to carry the contact load and thus support the coating, plastic deformation will occur, leading to premature failure of the coating. The challenge to improve the properties of hard DLC coatings by thermo-chemical pre-treatment of the substrate has gained much attention in recent years, leading to a new method called duplex treatment. In the present study, a hydrogen-free hard carbon coating deposited on plasma nitrided AISI 4140 steel was investigated with respect to microhardness, residual stress, scratch adhesion and dry sliding wear resistance. The pin-on-disc results showed that nitriding of the substrate improves the wear resistance of the hydrogen-free hard carbon coating as compared to the hardened substrate. The improvement can be related to the increased load carrying capacity of the steel substrate and to improved coating to substrate adhesion.Diamond-like carbon (DLC) coatings have attracted significant attention recently owing to their desirable properties. In relation to tribological aspects, these coatings exhibit low friction and high wear resistance along with extreme hardness, high elastic modulus, as well as thermal and chemical stability Plasma nitriding of the steel substrate before coating deposition has been widely used to improve the mechanical properties of the substrate as well as the coating. However, such research work was mainly focused on ceramic coatings deposited on tool steels The aim of this study was to investigate the possibilities of using hard and brittle DLC coatings also in the case of softer substrates, typically used in machine element applications. Therefore, a hydrogen-free hard carbon coating, also known as a tetrahedral-amorphous-carbon (ta-C) coating, was deposited on low alloy steel (AISI 4140). The steel substrate was plasma nitrided before coating deposition, and the effect of the plasma treatment on mechanical properties such as: adhesion; hardness; and wear resistance of the DLC coating was investigated.The substrate material used in this study was tempered (650°C) AISI 4140 steel with the following composition (wt.%): 0.5% C; 1.0% Cr; 0.2% Mo. The test specimens were surface treated using duplex technology, consisting of plasma nitriding and DLC coating deposition, and carried out as a two-step process. In step one, the steel specimens were plasma nitrided in a sensor controlled plasma nitriding unit in two different gas mixtures of either 75% H2–25% N2 or 99.4% H2–0.6% N2. Two different gas mixtures were used in order to promote or prevent formation of the compound layer over the diffusion zone. To prevent formation of the compound layer, a 99.4% H2–0.6% N2 gas mixture was used, while usage of a 75% H2–25% N2 gas mixture led to the formation of a 5-μm thick γ′ (Fe4N) compound layer over the diffusion zone. For comparative purposes a third group of specimens was thoroughly hardened and tempered to a hardness of approximately 600 HV. The details of the nitriding and hardening processes are listed in . Before coating, thermo-chemically treated specimens were polished to an average surface roughness of ∼0.03 μm and sputter-cleaned using an Ar ion beam. In step two, a 0.5-μm thick hydrogen-free hard carbon coating was deposited on the steel surface by pulsed vacuum arc evaporation at a deposition rate of 30 nm/min and a substrate temperature in the range of 20–80°C. A thin Ti interlayer between the substrate and the DLC coating was applied to improve coating adhesion to the substrate. More detailed information on DLC coating deposition can be found in Ronkainen et al. The morphology of the coated specimens was observed by Scanning Electron Microscopy (SEM), and the composition of the coatings determined by High Resolution Auger Electron spectroscopy (HRAES), also used to characterise the coating–substrate interface. In addition micro-Raman spectroscopy of the DLC coating was utilised. Coating hardness and Young's modulus were determined using the nano-indentation technique (Nano Indenter XP). Indentations were performed to a maximum penetration depth of approximately 50 nm using a maximum load of 5 mN. The Berkovich tip area function was determined by the procedure described by Oliver and Pharr For evaluation of the wear resistance of duplex treated specimens, a pin-on-disc test was applied. Duplex treated pins (φ 2 mm) were loaded against a 52 100 bearing steel disc with a hardness of 700 HV and an average surface roughness of ∼0.4 μm. Unlubricated wear tests were carried out at about 20°C in air with 50% humidity and a sliding speed of 1 m/s. Tests were conducted under 30 N (pH≈120 MPa) and 60 N (pH≈150 MPa) loads for a sliding distance of 1000 m. shows the cross-sectional SEM image and the Raman spectrum of a DLC coating used in this study. SEM examinations showed that the DLC coating had a smooth appearance with only a few inhomogeneous particles or droplets on the surface which, however, did not cause any increase in surface roughness. The surface roughness remained the same after coating deposition (Ra=0.03 μm). Also, examinations at higher magnification revealed a very dense and uniform microstructure with no evidence of columnar morphology. Regardless of the substrate treatment used, continuity across the substrate/DLC coating interface was evident.The micro-Raman spectrum of the DLC coating used in this study revealed a broad peak concentrated at ≈1560 cm−1 (b). The spectrum is typical of most carbon films classified as amorphous carbon (a-C) HRAES concentration depth profiles of C, Fe, N and Ti measured on DLC coated hardened and plasma nitrided specimens are shown in a,b. It can be seen that coated specimens have a multilayer architecture, with an almost pure carbon coating deposited on the surface, a thin Ti interlayer used to improve coating-to-substrate adhesion, and the bottom steel substrate (a). However, in the case of plasma nitrided substrates an increased nitrogen concentration in the substrate and a gradual decrease in titanium and nitrogen concentrations between the Ti interlayer and the substrate were detected, as shown in The hardness of the steel substrate, as well as of the composite, measured by Vickers microhardness tester, was found to be substrate treatment-dependent (). Compared to the hardened substrate with a surface hardness of 600 HV, plasma nitriding in 99.4% H2–0.6% N2, which led to the formation of a compound-free diffusion zone, increased the surface hardness of the steel substrate to 650 HV. Changing the nitriding parameters to produce a 5-μm thick γ′ compound layer over the diffusion zone (75% H2–25% N2) increased the hardness of the steel substrate even further, to 850 HV. It is evident in that besides increased substrate hardness, the nitriding process also improved the hardness of the composite.The hardness of the DLC coating used in this study was determined using the nano-indentation method and was found to be 70.1±7, with a Young's modulus of 571±51 GPa and a residual stress over 10 GPa.Results of the scratch test showed a similar coating failure mechanism for hardened and plasma nitrided substrates. At a critical load (LC1) of about 2 N, transversal cracking of the DLC coating occurred, but neither spalling nor chipping failure was observed (b). Complete removal of the coating finally occurred at a critical load (LC2) of about 10 N. However, as compared to hardening, plasma nitriding was found to give increased critical loads. As shown in , the highest critical loads were attained in the case of plasma nitrided substrates with the γ′ compound layer.The steady state coefficients of friction for duplex treated pins sliding against uncoated ball bearing steel disc are shown in . The coefficient of friction was 0.15 when a hardened or plasma nitrided substrate (nitrided in a 99.4% H2–0.6% N2 gas mixture) was used, but decreased to 0.10 when a compound layer was present (). The same trend was observed for 30- and 60-N loads.As in the case of the scratch test, plasma nitriding of the substrate improved the wear resistance of DLC coated pins, as shown in . The pin wear rate values were in the range from 1.3×10−6 to 2.0×10−6 mm3/Nm for DLC coated hardened pins and from 0.9×10−6 to 1.2×10−6 for DLC coated plasma nitrided pins, nitrided in a nitrogen-poor atmosphere (99.4% H2–0.6% N2). In both cases the DLC coating was worn out after 1000 m of sliding, regardless of the load used (). However, plasma nitriding of the substrate reduced coating removal rate and by using plasma nitrided substrates with a γ′ compound layer superior sliding wear properties without DLC coating being worn out were obtained (The increased hardness of the steel substrate obtained by plasma nitriding improves its load-carrying capacity and thus ensures good support for the thin and brittle DLC coating. Previous investigations Results of the scratch test indicate that nitriding of the steel substrate has a beneficial effect on the adhesion of the DLC coating. It is likely, due to the high affinity of Ti for nitrogen, that there is interdiffusion between the nitrided substrate and the thin Ti interlayer. The nitrided layer may react with the deposited Ti interlayer to form an additional TiN layer Analysis of the wear test results shows that proper selection of the substrate treatment and treatment conditions can lead to greatly improved sliding wear properties of the DLC coating. Compared to coated hardened substrates, plasma nitrided and DLC coated specimens show better wear resistance, which can be attributed to the increased load carrying capacity of the steel substrate, smoother stress and hardness gradients at the interface and improved coating to substrate adhesion.The results of this investigation also showed that the γ′ compound layer produced under proper nitriding conditions does not necessarily need to be treated as an undesirable product of nitriding, requiring post finishing operations Plasma nitriding of the steel substrate improves its load carrying capacity and its ability to sufficiently support the hard and brittle DLC coating. On the other hand, plasma nitriding improves coating-to-substrate adhesion, most probably through interdiffusion between the nitrided substrate and the thin Ti interlayer deposited at the beginning of the coating process. Combining these two effects, plasma nitriding can significantly improve the wear resistance of DLC coated surfaces.When the proper nitriding conditions are used, the compound layer produced does not necessarily need to be treated as an undesirable product of the nitriding process. In the case of duplex treatment, such a layer will act as an intermediate hard layer, taking an active part in the process of improving the load-carrying capacity and leading to superior sliding wear resistance of the DLC coated steel surface. Therefore, removal of the compound layer before the coating process may be omitted.Effects of helium implantation on creep rupture properties of low activation ferritic steel F82H IEA heatThin plate specimens of a low activation ferritic steel, F82H IEA, were cyclotron-implanted with helium at 823 K to concentrations of 100 and 300 appm. Creep rupture properties were subsequently measured at the same temperature and were compared with those from unimplanted controls. No meaningful deterioration by helium was discerned in terms of both creep rupture time and elongation. In addition, the fracture surface remained transgranular and ductile after helium implantation, and no indication of grain boundary failure induced by helium was detected. These results would suggest good resistance of this material toward helium embrittlement.Among the candidates for first wall structural material of the prototype fusion reactor and beyond, the highest priority is placed on low activation ferritic steels in Japanese and European programs mainly because of their prominent maturity For this purpose, we have conducted creep tests on a representative low activation ferritic steel, F82H, after hot helium implantation using an accelerator.The International Energy Agency (IEA) modified F82H (Fe–0.09%C–7.82%Cr–1.98%W–0.19%V–0.04%Ta–0.004%Ti–0.07%Si–0.1%Mn–0.003%P–0.001%S) The specimens were then subjected to helium injection at 823 K, the upper limit temperature of this steel for fusion applications, using an α-beam from a cyclotron. The incident energy of α-particles was varied between 0 and 20 MeV with an energy degrader, resulting in uniform helium loading over all the specimen depth. Lateral homogeneity was achieved by beam wobbling in the other two directions. The implanted helium concentrations were about 100 and 300 appm. An infra-red lamp heater was applied for target temperature control.Post-implantation creep tests were performed in a vacuum at the same temperature on electro-mechanically controlled machines, in which the applied load is monitored with a load cell and a deviation from the nominal load is compensated by pull rod motion on the basis of feedback signals. Utilizing these computer installed rigs, deviations from the stated temperature and stress during creep tests were less than ±1 K and ±1 MPa, respectively. For comparison, unimplanted reference samples which received thermal histories identical to the implanted ones were similarly tested. After creep rupture, the fracture surfaces were studied under a scanning electron microscope (SEM) to determine the failure mode.Details of the experimental procedures and instrumentation have been given elsewhere compares creep behavior of a helium bearing specimen and an unirradiated companion both applied with a nearly equal stress at each implantation level. The creep curve was hardly affected by helium at a level of 100 appm He, while implantation to 300 appm He seems to have resulted in a creep life extension. These features can be seen in as well, in which standard creep strength vs rupture time relation is represented. The time to rupture values of a specimen containing 100 appm He and a corresponding helium free control which crept at almost the same stress normally fell within less than a factor of 2. This is the usual variation of creep rupture times in thin specimens were analyzed by the method of linear regression based on a creep power law, tr∝σ−n, and the results are summarized in The stress exponents of implanted and unimplanted cases were very similar. This fact implies that the creep mechanism was not changed by helium introduction. The somewhat large errors shown in the table are probably attributed to the usage of miniature size specimens and the strong stress dependence of the rupture time.To establish whether the above-mentioned increase of the creep lifetime by helium for 300 appm He implantation is statistically significant or not, the t-test was carried out under a null hypothesis that an experimentally obtained rupture time is equal to that estimated from the creep power law of counterpart data, since misjudgement might be induced when one draws a conclusion from a few data points, even if there seem to be a clear trend. The null hypothesis was rejected with a significance level less than 5% or 10% for every instance. This strengthening by helium was, thereby, statistically significant. Small helium clusters and/or bubbles in the matrix which impede dislocation motion by pinning The elongations at rupture are plotted in against creep rupture time. On average there was no distinguishable difference among all test series and the overall scatter lay within a commonly acceptable error band. Helium thus caused no effective reduction in rupture elongation, when injected up to 300 appm He. The observed rupture strains were distributed from 3% to 6% and were considerably lower compared to those of bulk specimens indicates typical results of fractographic inspections on ruptured specimens. The fracture surfaces of implanted and unimplanted materials did not differ in character, revealing the same transcrystalline and ductile fracture mode. No evidence of grain boundary separation induced by helium was found. As regards helium effects on fracture morphology, it has been reported (a) and (c)) and those decorated with dimples (less necked parts: (b) and (d)), and proportions of each were evaluated on the basis of line analysis. The estimated percentages of the latter were spread from 11% to 55%, and there observed no substantial effect of helium on the amount of dimple fracture. Thus, the above-mentioned helium effect of supressing necking did not appear in our case.The mechanical response of a low activation ferritic steel, F82H, to implanted helium was investigated through post-implantation (Timpl.=823 K, CHe=100, 300 appm) creep testing at 823 K. The material demonstrated that it is quite insensitive to high temperature helium embrittlement in the present range of test conditions. The salient results which led to this conclusion are:Both creep rupture time and elongation were not degraded by helium implantation up to 300 appm. Furthermore, helium prolonged the creep lifetime in the case of 300 appm He implantation.Creep rupture was completely intragranular and ductile, irrespective of the presence or the absence of helium, and regardless of helium concentration. Helium, therefore, did not bring about any kind of intergranular decohesion.A comparison of models for predicting the true hardness of thin filmsInstrumented indentation is widely used to characterize and compare the mechanical properties of coatings. However, the interpretation of such measurements is not trivial for very thin films because the hardness value recorded is influenced by both the deformation of the film and that of the substrate. An approach to extract the mechanical properties of films or coatings as an alternative to the experimental hardness measurement versus the indentation depth involves the use of composite hardness models. However, there are always uncertainties and difficulties in correctly deconvoluting the film hardness in experiments on composite materials.To justify their approach, some authors argue that their model is correct if the predicted hardness obtained for the coating provides a good fit to the experimental data. This condition is, of course, necessary, but it is not sufficient. A good fit to the experimental curve does not guarantee that a realistic value of the film hardness is deduced from the model. In this paper, different models to describe the composite hardness were tested by indenting a Ni–P coating. Its thickness was chosen to be sufficiently large such that its mechanical properties were perfectly known. We show that some models extensively used in the literature are inadequate to extract the film-only hardness without the effects of the substrate when the indentation range is too limited, although they predict the composite hardness very well.► Models with only 2 parameters are more robust than models with 3 parameters. ► The Jönsson Hogmark model works well even so the indentation depth is low. ► The reverse analysis may give erroneous coating hardness if data are pertubated.The characterization of the mechanical properties and, more precisely, the hardness of coatings is of paramount importance in industry because of multi-material development and the related economic stakes It is therefore necessary to create a model for the coupled substrate–coating behavior under indentation, where the substrate influences the coating hardness measured and the coating influences that of the substrate. One of the first models developed by Bückle Hk=∑i=112HiPi∑i=112Pi=Hf∑i=1kPi+Hs∑i=k+112Pi∑i=112Pi.The measured hardness, Hk, that we shall call “composite hardness” Hc, includes the coating hardness Hf, and the substrate's one Hs according to the formula:where the coefficient a varies between 0 (Hc

=

Hs) and 1 (Hc

=

Hf).Nearly all models designed to determine the coating hardness are expressed according to this formula. The a-coefficient of the model depends on the coating thickness, the penetration depth (for a perfect Vickers diamond, h is equal to a seventh of the print diagonal d) and various adjustable parameters determined empirically or based on physical considerations. We also considered the so-called indentation size effect (ISE), i.e., the apparent hardness increases with decreasing load for a massive material according to the relation:Hf=H0f+Bfh=H0f1+αfthandHs=H0s+Bsh=H0s1+αsthin which the subscripts f and s are related to the film and the substrate, respectively; B and α are constants; H0 is the so-called absolute hardness i.e. the macrohardness independent of the applied load; the slope B is related to the ISE, and t is an arbitrary value taken in this work to be the coating thickness. The right-hand side of these equalities was chosen because α is dimensionless. This variation has been validated by Farges and Degout Authors who propose a new model generally justify its reliability by showing that the knowledge of Hs and the results assumed for Hf determine Hc with a good approximation. This validation is not relevant because the unknown value is not the “composite” hardness, which is experimentally measured, but the hardness of the coating. To avoid this error, our study of the robustness of various models is based on a material with a coating of sufficient thickness so that its hardness can be measured independently. We propose a methodology to estimate the robustness of various models to predict the ‘true’ hardness of a coating. Hardness measurements are thus developed for a composite material corresponding to this coating deposited on a metallic substrate. A robust model is not necessarily valid, but a model that is not robust can lead to an erroneous evaluation of the coating hardness if the experiments entail uncertainties.The paper is organized as follows. In the next section, we briefly introduce three well-known models, called Jönsson and Hogmark (JH), Korsunsky (K) and Puchi-Cabrera (PC), which are used to deduce the coating hardness from experimental data. We then provide the experimental conditions (tested specimen and load–indentation depth measurements) in is devoted to the precise description of the methodology used to study the robustness of the three models, analyze the results and compare the predictions for the film hardness obtained by the various models when the experimental data are noisy (corresponding to measurement errors) or truncated (corresponding to the limits of the experimental device). The paper ends with some conclusions in Since the pioneering work of Bückle, several models to express the composite hardness as a function of the film and substrate hardnesses have been proposed in the literature. We shall limit our work to the most often cited models that do not include the Young's modulus of the coating, which can differ noticeably from that of the bulk material because of the microstructure (e.g., columnar microstructure or crystallographic texture), the gradient of the chemical composition or the residual stresses. The nanohardness measurement is often possible but difficult when the coating is very thin because it is influenced by the substrate. The nanohardness is generally higher than the micro or macrohardnesses because of the indentation size effect (ISE) This model, which is among the oldest, assumes that the composite hardness can be expressed using an area law of mixture of the indented surfaces in the film and the substrate:where Af and As are the load supporting area of the film and the substrate, respectively, and A

=

Af

+

As the total area on which the mean pressure acts.From simple geometric considerations, the a-coefficient was found to be:where C is a constant that depends on the geometry of the indenter and on the film deformation during indentation. For a Vickers indenter, C takes the value of 0.140 if the coating is plastically deformed during the indentation to accommodate the shape of the indenter or 0.0727 if crack formation occurs in the coating. We must emphasize that the a-coefficient should be between 0 and 1. Consequently, if h is lower than Ct (i.e., Ct

/

h

> 1), the substrate does not influence the composite hardness, and a is equal to 1. Vingsbo et al. ) for the coating and the substrate in the composite hardness calculation. We proposed a second improvement ) instead of the simplification recommended by . This simplification implies that the composite hardness is a linear function of the inverse diagonal depth, as in Eq. Hc=H0s+Bs+2CtH0f−H0sh+2CtBf−Bs−C2t2H0f−H0sh2−C2t2Bf−Bsh3Some authors added a degree of freedom to Eq.  by assuming that C is not constant but variable Korsunsky and co-workers based their analysis on the work-of-indentation and the way the energy was expended during indentation. While searching for solutions that can determine the coating and substrate hardnesses by extrapolating to the limits, Hc, according to this model, is given by:where h

/

t is the relative indentation depth and kk is a fitting parameter related to the film thickness. In this model, both the film and the substrate hardness are independent of the applied load because Hc is assumed to approach the coating hardness asymptotically for an infinitely low indentation depth. Korsunsky et al. are nevertheless conscious of the limits of this hypothesis in the microhardness or macrohardness domains and propose to introduce the hardness variation with the load in another paper to be published., because it is obvious from our results that the coating hardness varied with the applied load.To improve the previous model, Korsunsky et al. introduced a complementary variable X instead of the exponent “2” assigned to the relative indentation depth and obtained:This model has one more constant (one degree of freedom) than Eq. , the model is less robust, which is the reason we do not present the results related to Eq. Puchi-Cabrera suggested a volume law of mixture (composite hardness as a function of the indented volumes in the coating and the substrate) based on a simple geometric diagram of the indented areas, which is different than the model of Jönsson and Hogmark This equation is merely that of Bhattacharya and Nix The material under study was a 55-μm-thick electroless nickel–phosphorus coating deposited on a stainless steel (Z12C13) shovel floodgate obturator (300 mm thick) intended for the oil industry. The H properties were obtained by force controlled depth-sensing indentation measurements with a Zwick macrohardness device ZHU2.5 and a Vickers pyramidal indenter (with a square base and a 136° angle between the opposing faces of the pyramid). During the instrumented indentation test, the applied load and the resulting depth of penetration of the indenter were continuously recorded, and a full set of data, including load, depth and time, were recorded. According to the manufacturer, this device can apply variable loads between 5 and 2500 N with an error lower than 1% and record a displacement up to 4 mm with a 0.04 μm resolution. Because the displacement was measured directly between the surface of the indenter and the indenter tip through a glass scale, the indentation depth was deduced from the displacement after compliance correction. The load–indentation depth curve was used to determine the hardness under load The hardness under the test force was called the “Martens hardness” shows the load–displacement plot recorded on the nickel/steel specimen used to study the robustness of the three models.HM corresponds exactly to the Vickers hardness, HV, assuming that the elastic recovery does not affect the measure of the indentation residual diagonal length. We verified both the repeatability and this assumption for the material in consideration by plotting a series of successive data at increasing peak-loads at the same location () and comparing the remaining print diagonals measured after unloading by optical microscopy with the maximal penetration depth under load () for measurements performed at different locations. The Vickers diagonal length measured by optical microscopy was seven times the indentation depth recorded by the testing machine, and thus every hardness value recorded in the instrumented indentation test can be transformed in Vickers hardness. The indentation depth was greater than 5.5 μm, and thus the surface area could be assumed to be that of an ideally shaped Vickers indenter without considering the rounding at the tip. Consequently, the results are presented as the Vickers hardness number (VHN), and the units (kgf/mm2) are omitted following convention (100 VHN = 0.9807 GPa). versus h

/

t (RID) as commonly reported for the K and PC models and in versus t

/

h for the JH model. For the lower loads (lower indentation depths), the composite hardness varies linearly with 1 /

h as expected for the film hardness:The variation of the film hardness with the load applied was verified by conventional microhardness tests performed with a Leitz “Miniload” hardness tester in the load range of 0.1–5 N. For the maximum load, the indentation diagonal, d, is 33.6 μm and consequently the indentation depth (h

=

d

/ 7) is lower than the tenth of the coating thickness. As a result, the variation of hardness versus the reciprocal indentation depth verifies Eq.  that represents the film hardness. The absolute hardness (H0f

= 530) is obtained by extrapolation to an infinite penetration depth of the experimental data lower than the 1/10th of the coating thickness. In the same way, the substrate hardness, measured independently after removing of the coating, varied with the applied load such that:Based on these experimental data, we assumed first that both the coating and the substrate hardnesses were perfectly known. Then, we searched the parameters to fit the model curve with experimental data by least squares minimization for the three models under study so that the difference between the models and the experimental data was minimized. reports the value of all constants involved in the models. We then considered the three “theoretical model curves” to compare the robustness of the models. These theoretical plots (corresponding perfectly to the model selected) were then perturbed to represent experimental uncertainties. Moreover, the data that corresponded to the smallest indentation depths were deleted to reflect the real case where the film is so thin that it is impossible to create indents that satisfy the requirement to obtain the hardness of the coating alone. All of the details in each step of this methodology are presented in the following section with the value of the proposed threshold and random noise. are considered. The true film and substrate hardnesses are, respectively stated as quoted in Eqs. . The composite hardness is thus represented as a function of the indentation depth. However, the indentation depth sampling does not have a linear evolution versus time. This sampling effect can affect the statistical estimation of the model parameters. This artifact can then lead to the introduction of a bias in the model coefficients. To avoid this bias, the sampling rate must be iid, i.e., independent and identically distributed random variables. In order not to be influenced by the indentation depth time distribution during the experiment, a linearization process was performed. A new indentation depth distribution is proposed with one hundred points. Depths are regularly distributed from the minimum (5.6 μm) to the maximum (158.7 μm) depth values and the corresponding hardnesses are then estimated using local smoothing tools. This new data set represents the hardness evolution and was used to test the robustness of models.Second, for each model, the fitting parameters in the a-coefficients were calculated to best match the experimental results. This procedure led to “theoretical model curves” whose values are given in brackets in . These parameters then remained unchanged during stages 3 and 4. It should be noted that the Jönsson and Hogmark model does not require any parameter estimation. Indeed, we assumed that the coating was plastically deformed (C

= 0.140) because no cracks were observed near the print.Third, the three previous curves were truncated by deleting the data corresponding to an indentation depth smaller than 10, 20, 40, or 80 μm, which correspond, respectively, to a relative experimental indentation depth (h

/

t)exp larger than 0.182, 0.364, 0.727 or 1.455. In doing so, we placed ourselves under the experimental conditions that correspond to the determination of the hardness of thin films, where it is not possible to measure the properties of the film only. Therefore, four curves were proposed for each model.Fourth, random Gaussian noise centered at 0 with a standard deviation of 0.1 μm was added to every indentation depth value. This stage was performed 5000 times by Monte Carlo simulations to give 5000 “experimental noise curves” for a given model. The hypothesis assumed that the experimental points were obtained independently from each other, as in the case of classic Vickers hardness tests (not instrumented). The problem of the instrumented test uncertainty is more complex and will be the subject of a further publication.Fifth, for all of the 5000 previous curves and for every truncated set of data and every model, the film hardness (H0f and αf in Eq. ) and the fitting parameters were computed with nonlinear regression in such a way that the quadratic difference between the “experimental noise curve” for a given model and the “theoretical model curve” was minimized. The downhill simplex method was developed for this aim, and the Nelder and Mead algorithm was used represents the 5000 coating hardness evolutions corresponding to the experimental curves for the three models and a cut off of 40 μm (i.e., the experimental values corresponding to a RID, h

/

t, smaller than 0.727 were ignored). The hardness evolution for the “experimental noise curve” and for the “theoretical model curve” is represented for the worst case (i.e., largest negative value of αf) in (a2, b2, c2). For the Korsunsky (b) and Puchi-Cabrera (c) models, this value corresponds to an incorrect estimation of both H0f and αf compared to the expected values. H0f was estimated to be 3190 VHN (31.28 GPa) and 1283 VHN (12.58 GPa) compared to the true 530 VHN (5.2 GPa), respectively, and αf was estimated as − 0.2083 and − 0.1479 compared to the true value of 0.06112, respectively. Nevertheless, for each model, (a2, b2, c2) shows that the estimation of these parameters can correctly predict the data of the “experimental noise curve”. The worst case for the Jönsson–Hogmark model leads to an estimate of 535 VHN for H0f and 0.04741 for αf. Thus, the film hardness is correctly estimated, and the error in its estimation is lower than the one observed in the Korsunsky and Puchi-Cabrera models. shows the coating hardness estimation corresponding to the same RID (40 μm cut-off) and shows that these values are centered on the theoretical ones. The JH model, with only two unknown quantities, H0f and αf, is more robust than those with one or two additional fitting parameters and seems to be the best model to predict the coating hardness. shows H0f and Bf estimations for the three models in the same diagram. Five thousand couples were estimated for each of the three models. The evolution of the three sets shows that these parameters are linearly correlated for each model. The linear evolution shown in of Bf versus H0f demonstrates that all of the curves cut the same point in the hardness evolution diagram as a function of the inverse RID. This correlation was previously shown in each model in , where all of the curves intersect at the same pivot point. As observed earlier summarizes the results obtained for each cut-off in the estimations of the hardness parameters of the coating. allows the user to determine the range of experimental data to be considered so as to allow for efficient determination of the coating mechanical properties. If the range of data is low enough, a strong deviation from the real values is observed, especially for the K and the PC models.According to the results above, the following observations can be formulated for the different models under study:The Jönsson Hogmark model (JH) is the most robust. According to the noise and/or the number of points considered, the coating hardness computed (H0f and αf) varies in a weak interval around the theoretical value of 530 VHN (), for example, the standard deviation, σ, is 2.41 for H0f and (h

/

t)exp

≥ 0.182.The evaluation of the coating hardness using noisy experimental results remains acceptable whether the diamond penetration depth is weak or strong. This result is contrary to the assertions generally found in the bibliography, which state that the JH model gives a poor fit when the indentation depth is shallower than the coating thickness or at the substrate-dominated end gives a

= − 2.24 and therefore a negative coating hardness in Eq. , which also corresponds to a negative indented area. Physically speaking, the a-coefficient varies between 0 and 1. Moreover, only the case where h

>

Ct must be considered in Eq. . When the indentation depth is lower than the critical value Ct, the measured hardness is the coating hardness.The Korsunsky et al. model (K) has a hardness variation range superior to that of the JH model for H0f (σ

= 25.74 for H0f and (h

/

t)exp

≥ 0.182). The interrelationship between H0f and Bf is important (). If the RID is greater than 0.182, H0f may take values between 504 and 555, given the standard deviation. It was shown that some aberrant values are calculated when data corresponding to h

/

t lower than 1.455 are deleted (H0f

> 1015HV).The Puchi-Cabrera (PC) model presents a significant H0f variation range () (σ

= 47.6 for H0f and (h

/

t)exp

≥ 0.182). If the critical RID increases and is greater than 1.455, the standard deviation can be greater than the mean of the estimated values (σ

= 651 for H0f and (h

/

t)exp

≥ 1.455). As with the Korsunsky model, there are negative slopes for the variation of the coating hardness for (h

/

t)exp

≥ 1.455. In this model, all unknown quantities and fitting parameters are also correlated, which explains the lack of robustness: it is always possible to find a combination of {H0f, Bf, kp, np} quadruplets to ensure that the a-coefficient verifies the experimental data in Eq.  regardless of the physical meaning of these coefficients. This explains why some authors consider that their model is valid when applied to coatings whose hardness is unknown and therefore cannot be verified.By considering a fitting parameter X as a variable in Eq. , the Korsunsky model may be improved to best match the experimental data if the data set is sufficiently large (one more degree of freedom), but the model is less robust because all coefficients are strongly correlated (results non-represented in this paper).An electroless Ni–P coating deposited on a steel substrate, which was sufficiently thick to measure its hardness experimentally, was indented to test the robustness of three composite hardness models. The hardness variation versus the indentation depth or the diagonal print was recorded. These models were then used to describe the composite behavior of the “coating–substrate”, and the parameters of every model were estimated to fit the experimental data using an inverse method approach. The three plots were considered the “experimental models curves” for testing the robustness of the models. For all models, excellent fits were obtained, provided that sufficient data were available. We progressively deleted experimental data corresponding to the lower indentation depths and applied Gaussian noise to simulate experimental errors. The Jönsson and Hogmark model was the most robust and the most effective because the fitting process returned reasonable values for the coating hardness. This efficiency was shown whether the indentation depth was high or low. This model was the most robust because it uses only two variables: the coating hardness and the hardness variation with the applied load. Some authors increase the number of fitting parameters to better fit the composite hardness curve with the experimental data. They find, as expected, that the quality of the fit increases as the number of parameters involved increases. They do not always reach the expected result and also decrease the robustness of their model while introducing some interrelationships between the coefficients. The results may be very different from the true hardness of the coating, as shown in . This behavior was shown with the Korsunsky model with three fitting parameters (H0f, αf, kk) and the Puchi-Cabrera model with four fitting parameters (H0f, αf, kp, np).The reverse analysis to determine the film hardness from the composite hardness is not unique in the case of limited data and experimental errors. Moreover, adding fitting parameters to the composite model enhances the nonuniqueness. The Jönsson Hogmark model, with only two fitting parameters (the film hardness and the hardness variation with the applied load), is more robust than models with one or two additional parameters in predicting a realistic value of the film hardness.Chemical modification of zein by bifunctional polycaprolactone (PCL)Prepolymer was synthesized by use of PCL and hexamethylene diisocyanate (HDI), and then used to prepare modified zein-based polymers (ZPs). Solid-state 13C NMR results showed that at least four amino acids (Glu, Gln, Tyr and His) reacted with the prepolymer, and urea–urethane links were prominent. Thermal analysis indicated that micro-phase separation formed between zein matrix and PCL–HDI (PCLH) component in ZPs. With the increasing PCLH content, the melting point of PCL in ZP decreased, and the Tg of zein reduced due to plasticizer role of PCLH. The breaking elongation of modified zein containing 10% PCLH content, increased about 15 times while its strength at break only reduced by about 2 times than that of commercial zein. In addition, with the increasing PCLH content, the flexibility of modified zein sheet improved dramatically with negligible reduction in strength. This indicates that PCL was an elastic fraction in ZPs. Therefore, it is an effective way to improve the mechanical properties of zein by modification with PCL, showing a potential in the field of biodegradable polymers.Protein is one of the most important renewable resources and can be used as biodegradable material Zein, an alcohol-soluble protein extracted from corn or corn gluten meal, has attracted attentions due to its hydrophobic property. Commercial α-zein has two components with molecular weights of 24,000 and 22,000, respectively Chemical modification is another way to enhance the mechanical properties of zein. Sturken Polycaprolactone (PCL) is one of the few synthetic polymers that are biodegradable In this study, the aim was to improve the toughness of zein material by using low quantity of PCL. PCL/hexamethylene diisocyanate (HDI) prepolymer was synthesized to prepare modified zein-based polymers (ZPs). The synthesizing conditions, structure, thermal properties, and mechanical properties of modified zein were investigated.α-zein (SHOWA ZEIN™) containing 96.3% protein, and 3.4% water, supplied by Showa Sangyo Co., Ltd in Japan, was vacuum-dried at 105 °C for 48 h before use. PCL diol (Mw=2000, CAPA® 2200) was supplied by Solvay Interox Ltd, Cheshire, UK. The hydroxyl value is 56 mg KOH/g, and the water content is less than 0.02%. HDI (Wako first Grade), Tin (II) 2-ethylhexanoate, and DMF (dehydrated for organic synthesis) were purchased from Wako Pure Chemical Ind., Ltd. Dibutyl -tartrate (DBT, 98%) was from Aldrich (USA).Peak-height method was used to measure the isocyanate group (NCO) content in prepolymer by use of fourier transform infrared spectroscopy (FTIR). PCL blends with different HDI concentration were prepared in melting state at 65 °C in 5 ml glass tubes, then cooled quickly and were recorded with a FTIR spectrometer (Nicolet Avatar 320) using an attenuated total reflectance (ATR) cell at room temperature. ATR method instead of transmission method was used owing to that the former was convenient and quick for testing solid or semi-solid samples. The resolution and scanning time were 2 cm−1 and 32 times, respectively. The height ratio of peak at 2272 cm−1 to the one at 1724 cm−1 (Rir) was obtained to normalize the isocyanate groups content in the blends, where the absorption peak at 2272 cm−1 resulted from the isocyanate groups, and at 1724 cm−1 mainly from CO in PCL. The Rir was defined as follows:where H2272 and H1724 correspond to the peak height at 2272 cm−1 and peak height at 1724 cm−1, respectively. Three duplications were done for each sample. A standard curve for height ratio of peak to NCO content was plotted and used to predict NCO content in prepolymer. The NCO content was calculated using the following equation:where WHDI is the weight of HDI, WT is the total weight of HDI and PCL, and the NCO content in HDI is 49.96%.where WL and WT correspond to the weight loss of sample and the total sample weight before extraction, respectively. Three duplications were done. The extracted powder sample was vacuum-dried at 133 Pa and 45 °C for 24 h, then coded as ZP30, which means modified zein containing 30 wt% PCL in feed. ZPs with different PCL content were prepared by changing the ratio of zein to PCL, and coded as ZP10, ZP20, ZP40, and ZP50, respectively. All samples of ZP10, ZP20, ZP30, ZP40, and ZP50 were coded as ZP10-50. As controls, samples with no PCL (coded as CZ) and with no zein (coded as PCLHE) were also prepared under the above synthesizing procedure, respectively. CZ means commercial zein, and PCLHE, shorten from PCL–HDI–ethanol, is a derivative from prepolymer and ethanol. All samples were stored in a silica gel desiccator for following tests. The procedure of synthesizing ZPs is shown in . The PCL–HDI component in ZPs was coded as PCLH, whose structure is shown in The powder samples were compression-molded according to our previous procedure The FTIR spectra of samples were recorded with the above FTIR spectrometer under the similar conditions.Vacuum-dried sample (1.3 mg/ml) was dissolved in sodium dodecyl sulphate (SDS)/sample buffer solution with 1% 2-mercaptoethanol for sodium dodecyl sulphate polyacrylamide gel electrophoresis (SDS-PAGE) experiment. Both Sample solution and standard protein solution (Protein Marker 7701S, Biolabs Inc. New England) were heated at 100 °C for 5 min. The sample solution (10 μl) was applied to a slab polyacrylamide gel contained with 10% resolving gel and 3% stacking gel. Electrophoresis was done at 10 mA current for 5–7 h to determine the molecular weight and composition of CZ. By use of a densitometer (CS-9300PC, Shimadzu), unmodified zein content in ZPs was qualitatively evaluated on the base of the relative intensity of stained bands in the images of electrophoresis where WU and WT are the unmodified zein content and total zein content, respectively.Solid-state 13C NMR experiment was carried out at ambient temperature on a NMR spectrometer (Bruker AVANCE-600) at the resonance frequency of 150.92 MHz. The NMR spectra were obtained with cross polarization technique, using magic angle sample spinning and high-power decoupling (CPMAS). A 6 μs π/2 pulse was used with a 1 ms contact time, 10000 scans, 4 s of recycle time and a 60 kHz decoupling bandwidth. The 13C chemical shift scale was set with glycine as a solid external reference standard. The samples were packed into zirconia rotors and spun at 8 kHz.Differential scanning calorimetry (DSC) analysis was performed with a thermal analyzer (DSC220C, Seiko Instrument, Japan) under nitrogen atmosphere. Samples were packed down and sealed into aluminum pan with lid. Indium was used for temperature and heat capacity calibration of the instrument. The glass transition temperatures (Tg, the midpoint of glass transition), the change in heat capacity (ΔCp), and melting temperature (Tm, the maximum of melting peak) were determined by heating samples (10 mg) from 32 to 140 °C at a rate of 10 °C/min, followed by cooling down to −120 °C at a rate of 30 °C/min, and then rescanned at a rate of 10 °C/min to 210 °C. All samples were analyzed in triplicates.Powder sample was molded into a disk (5 mm diameter and 1.5 mm height) in a home-made mold by use of the above Mini Test Press. Compression-molding pressure (8 kN) was kept for 1 min at 25 °C. The disk was vacuum-dried at 133 Pa and 45 °C for 36 h, heated to 90 °C for 3 h to melt crystals, and then quenched in liquid nitrogen. Finally, disk was vacuum-dried at 25 °C for 12 h to remove possible moisture, and stored in a desiccator containing P2O5 for a week. Thermal properties of disks were analyzed on a dynamic load thermomechanical analyzer (DTMA) (TMA/SS150C, Seiko Instrument Inc., Japan) in compression mode under nitrogen atmosphere. Indium and Tin were used to calibrate the temperature scale of furnace. A sinusoidal stress (offset, −20 g; amplitude, 10 g; frequency, 0.1 Hz) was applied on sample to produce a strain. Scanning was performed from −95 to 230 °C at a scanning rate of 2 °C/min. Linear thermal expansion rate (Rexp), measured by probe, was evaluated by the following equation:where HT, H−95, and H25 are the height of disk at a given temperature, at −95 °C, and at 25 °C, respectively. Samples were tested in triplicates. The curves of loss tangent to temperature, and Rexp to temperature were plotted.Samples were annealed at 90 °C for 2 h, and then stored in a desiccator for 10 days before using for X-ray diffraction studies. At 28.5 °C, wide-angle X-ray diffraction patterns (WXRDPs) were recorded with an X-ray diffractometer (Shimadzu XRD-6000, Japan) and with Cu Kα radiation at 40 kV and 30 mA in the range of 2θ=5–40°. A typical pattern was selected from three replications for analysis.The mechanical properties of the sheets were measured using an Instron tensile tester (Instron 5542, USA) according to ASTM D882-81 with some modification. Sheets with dimensions of 110×10×(0.1–0.4) mm3 were stored in a silica gel desiccator, in which relative humidity (RH) was about 0%, for 26 days. The testing temperature and RH was 25.5 °C and 70%, respectively. Stress-strain curves, strength at break and breaking elongation were recorded at 25 mm/min of tensile speed. At least five replications were used in each treatment., the content of CO groups in PCL soft segments was almost constant during modification. Therefore, the height ratio of peak at 2272 cm−1 to the one at 1724 cm−1 (Rir) can be used to quantitatively determine NCO content in prepolymer. NCO content was often analyzed by the method of dibutylamine back titration . A good linearity can be observed on this curve. As we calculated, the primary NCO content at the start of polymerization was 7.2%, and the final NCO content when total PCL consumed was 3.6%. Hence, it is effective to measure the NCO content in prepolymer because the NCO content range in the curve was from 1.3 to 7.6%. By use of this standard curve, the NCO content in prepolymer at a given time could be measured easily, which is shown in . Without any catalyst, NCO content kept as high as 5.8% after 420 min of reaction, indicating that NCO and OH groups reacted slowly. When the catalyst concentration increased to 0.03%, NCO content decreased quickly from 7.2 to 5.0% within the first 60 min, and kept constant during the later 290 min (above data not shown in ). Once 0.12% of the catalyst was used, the NCO content decreased sharply to about 3.9% within 20 min as shown in , which resulted from the effect of Tin (II) 2-ethylhexanoate. After 2 h, at the second stage, almost all hydroxyl groups of PCL were reacted with NCO groups. If the reaction continued after the second stage, the residual NCO would react with the urethane groups on molecular chains of prepolymer, which made cross-linking occurred in the third stage . In order to verify the correction of reaction ratio, the experiments were repeated three times along with controls. One control experiment was to extract CZ and another was to extract residual PCL by Soxlet extraction. The weight loss of CZ and PCLHE were 0.5±2.1%, and 98.4±0.7%, respectively. This indicated that in CZ there was no compound that was soluble in toluene, and PCLHE could be extracted almost completely. Therefore, it is effective to extract residual PCL residuals out of ZPs. The average reaction ratio of PCLH for ZP10-50 is 96.9%, higher than the reaction ratio (89%) of starch-g-PCL reported by Tang et al. The electrophoresis pattern of CZ, ZP10-50 is shown in . CZ had two bands with molecular weight of 2.33×104 and 2.12×104, which is similar with that the report from Paulis, whose results showed two components in α-zein . The average value of unmodified zein content for ZP20-50 was only 3.3 wt%, implying that the polymers could be considered as a pure modified zein.FTIR spectra of CZ, ZPs, PCLHE, prepolymer and PCL diol are displayed in . Compared with the spectrum of PCL diol, the spectrum of prepolymer had a new peak at 1528.7 cm−1, which was a mixed contribution of the N–H in-plane bending and the C–N stretching of urethane groups , suggesting a successful modification. The absorption band of carbonyl of PCLH in ZPs (1733 cm−1) was upshifted about 8 wavenumbers than that in PCLHE (1724.6 cm−1), which indicates that the structure of PCL was changed dramatically.Owing to that part of ZP50 was insolvable, resulting from cross-linking, solid samples were used for NMR analysis. The solid 13C NMR spectra of CZ, ZP50 and PCLHE are shown in . On the basis of previous works in 13C NMR analysis of PCL (PCLHE). Compared with the spectrum of PCL reported by Wang et al. . Their structure and chemical shifts are summarized in . The chemical shift peaks of terminal carbons from Arg, Asp, Asn, Thr, Ser, and Cys occurred at 159.4 ) showed less intensity peaks in ZP50 spectrum than in CZ spectrum, which further inferred that phenolic hydroxyl groups of Tyr also could react with NCO groups. A little peak at about 181 ppm (, CZ), which was assigned to the C-terminal carbonyl of Glu and Gln, disappeared in the spectrum of ZP50, implying that –COOH group of Glu and –NH2 group of Gln had almost completely reacted with NCO group of prepolymer. Therefore, urea–urethane links was prominent in total ureathane links because NH2 groups in Gln were the main parts in total active side groups DSC thermograms for CZ, ZPs, and PCLHE are exhibited in . The ΔHm for PCL diol (Mw=2000) at the second scanning was 71 J g−1). The degree of crystallinity of PCLHE was calculated as 32.5±0.8% on the base of the ΔHm value of completely crystalline PCL (142 J g−1) ). The melting point of PCL decreased from 57 to 33 °C with an increase of zein content (). This is due to the ‘diluent effect’ of PCLH, which is associated with the mole fraction of crystallizable component in ZPs . The Tg of zein in ZPs decreased nonmonotonously with the increasing PCLH content. But according to the Gordon–Taylor equation ). Two major fractions of soy protein isolates (7S and 11S fractions) had different but close glass transitions . Z22 should show a more obvious transition than that of Z24, owing to that Z22 was richer than Z24 in CZ (). Therefore, we considered that the bigger transition at 180.1 °C to Z22 fraction and the smaller transition at 200.1 °C to Z24 fraction of zein, respectively. Of course, a direct evidence is to separate the two fractions and study their Tgs, respectively.DTMA was further used to determine the Tg of ZPs because it is sensitive to glass transition of polymer than DSC . A big relaxation peak for CZ was observed at 180.4 °C, which was associated with glass transition of zein. The height of this peak reduced gradually due to the reduction of zein content in ZPs. This is in agreement with that of ΔCp value at glass transition, which decreased while zein content reduced ( peak height is proportional to the volume fraction of the material undergoing the transition, and the change in ΔCp is related to the weight fraction of the polymer participating in glass transition reduced slowly from 180 to 171 °C with the increasing PCLH content, indicating that it is certain for Tg of zein in ZPs to decreased monotonously while the amount of PCLH raised. Similar trends can be seen on the T(E′) and T(E″). But this trend could not be observed in DSC data (), which supports the above assumption that weak glass transition made the Tg of zein in ZPs ill-defined by use of DSC. The reduction of Tg in ZPs originated from the plasticizer role of PCLH, a common phenomenon in polymer that can be quantitatively described increased from 180.4±0.8 to 189.4±1.4 °C, owing to the greater heat resistance of sample with increasing height. The related curve was not shown. In peak at 205.6 °C can be seen for CZ, and reduced with the reduction of zein content in ZPs. This transition can be observed clearly in the curve of linear expansion rate (. This small transition was also found in DSC curve (). This evidence and the above DSC data make us further believe that this small transition was a glass transition of one compound in zein. But this transition has not been well reported before.) and no dramatic decrease in Tg of zein matrix implied that zein matrix and PCLH component were in micro-phase separation. However, the decreases of Tm of PCL crystal () indicated a partial miscibility between zein matrix and PCLH component. Therefore, ZPs were heterogeneous in which zein matrix and PCLH component were partial miscible.WXRDPs of CZ, ZP30, ZP50, and PCLHE are shown in . PCLHE showed two sharps peaks and a shoulder peak at 2θ=24.5°, 22.2°, and 20.4°, respectively. The results are in agreement with the report of Bogdanov et al. ), which leaded to the melting of PCL crystal in ZP30 and ZP50, and crystallization peak for PCLHE.Typical stress/strain curves of CZS and ZPS10-50 are shown in . Final water content in zein material should be considered because the mechanical properties of zein are significantly affected by water. In this study, all sheets were stored in a silica gel desiccator for 26 days to measure the mechanical properties of these modified zein materials at dry state, because it is easy to evaluate the fragility of zein at dry state. The error bars of strength at break and breaking elongation are also displayed in . CZS exhibited a brittle failure with no yield point on its stress/strain curve, and showed high strength (24.5 MPa) but low breaking elongation (4.3%). Santosa et al. reported that zein sheet plasticized by oleic acid (0.5 g/1 g zein), stored at 50% RH for 48 h in a desiccator, showed 9.4 MPa of tensile strength and 5.9% of breaking elongation , ZPS10), the breaking elongation increased to 66%, about 15 times than that of commercial zein, and strength at break only decreased about 2 times compared with that of commercial zein. The stress/strain curve of ZPS10 also showed a yield point, suggesting a ductile failure. The toughness of zein modified by a little amount of PCLH, improved quickly, resulting from the flexibility and elasticity of PCL. With the increasing PCLH content, the breaking elongation increased dramatically and strength at yield point decreased drastically, but the strengths at break constantly ranged from 9.3 to 11.9 MPa, indicating that under the condition of almost constant strength, PCLH component can significantly enhance the elasticity of zein-based material. For ZPS50, the strength at break was 10.7 MPa, only a decrease of 0.6 MPa compared with that of ZPS10, but the breaking elongation was as high as 522%. Zein component provided strength and PCL component provided flexibility, which is similar with the known polystyrene–polybutadiene–polystyrene (SBS) resin in which polystyrene improves the strength of SBS and polybutadiene enhances the elasticity of SBS. The data about mechanical properties of PCLHE was not available because it was a wax-like material and could not be used for stress/strain test. The relationship between the structure and properties of the sheets will be studied furthermore in our later work.Zein-based polymers with various PCLH content were synthesized. The average reaction ratio of PCLH was as high as 97.5%. FTIR results showed that the PCLH content in polymer increased with the increasing PCLH content in feed, indicating a successful modification. At least four amino acids (Glu, Gln, Tyr and His) reacted with prepolymer, and urea–urethane links were prominent in ureathane groups. Thermal analysis implied that ZPs were micro-heterogeneous due to the formation of micro-phase separation. The Tg of modified zein diminished with the increasing PCLH content as observed from DTMA analysis, but similar result could not be obtained from DSC analysis due to errors resulted from the weakness of ΔCp. The melting point decreased with the increasing PCLH content. A novel small glass transition for zein was found at about 201 °C, which can be observed on DSC curve, and was further proved by DTMA results. After 10% PCLH was crosslinked with zein, the breaking elongation of zein sheet increased about 15 times, and strength at break reduced only by about 2 times, compared with commercial zein. Furthermore, with the increasing PCLH content, the flexibility of modified zein sheet improved dramatically but the strength remained roughly constant. Therefore, it is very effective to improve the toughness of zein by the modification.Assessment of parameters governing the steel fiber alignment in fresh cement-based compositesThe main aim of this paper is to measure the induced torque needed to rotate a steel fiber, hence an experimental and parametrical analysis of factors governing steel fiber alignment in cement pastes and mortar, rotating from static position and rotating in a dynamic fluid is here presented. To aim this objective, a set of rheological tests has been conducted to assess the torque necessary to rotate steel fibers immersed into different fresh cement paste and mortar mixes with Bingham fluid behaviour. Fibers of different aspect ratios (length/width) and different geometry, straight and hooked-end, have been evaluated as they are the more commonly used. On the other hand, different parameters (type of mixture, size of aggregates, volume fraction of aggregates) affecting cement mixtures are also analysed and their influence in fiber orientation discussed.Fiber alignment depends on external torques applied to fibers, immersed into a cement-water-aggregate viscous system, that can be produced during or after casting. The flowability of the fresh suspension with fibers produces a load/pressure that generates a torque that can align them. Fiber alignment is a main goal to pump the fresh material. Hence, the factors that govern fiber alignment are studied which increase the post-cracking strength of cement-based composites under load along its life service due to casting or pumping. To that end, a set of tests has been conducted to assess the torque necessary to rotate steel fibers immersed into different fresh cement paste and mortar mixes with Bingham fluid behaviour. Fibers of different aspect ratios(length/width) and different geometry (straight and hooked-end) have been evaluated. On the other hand, different parameters (type of mixture, size of aggregates, volume fraction of aggregates) affecting cement mixtures are also analysed and their influence on fiber orientation is discussed. The values obtained here are between 1 and 14 N·mm of dynamic yield torque and 0.1 and 0.5 N·mmmin for viscoplastic torque per fiber, depending on fiber geometry, are helpful to improve the fiber alignment in cement-based composites reinforced with fibers through a design and production based on these parameters.Steel fibers are used increasingly as a discrete reinforcement in composites with a brittle cement matrix, to enhance their tensile strength or flexural strength, ductility, toughness, fatigue and impact resistance The mechanical efficiency of a Fiber Reinforced Cementitious Composite (FRCC) depends not only on the volume fraction (χf) but mainly on the percent of them aligned with the reduced stress supported Several researchers studied methods to predict the fiber alignment Different mechanisms can induce torque-fiber alignment in fresh concrete. The procedure of concrete placement into a mould has been recognized to have a major impact on fiber orientation, both due to the casting direction and due to preferential fiber alignment induced by the casting element itself The effect of flowability of FRCC has been also studied, because it is one of the parameters that can increase the volume fraction χf of aligned fibers Fiber alignment in FRCC depends on many factors, like fiber properties (shape, material, aspect ratio) and on the fresh properties of the cementitious fresh material (shear stress (τ), yield stress (τ0), plastic viscosity (μ∞) and on the placing and casting method, as it will modify the velocity of the fluid and hence the shear rate of the material (γ̇) defined also as ∂u/∂y. Orientation of rigid fibers can be externally induced only when the cement-based composite is still a fluid. This early stage, after mixing, by assessment of the rheological properties of such cementitious composites, fibers can be rotated through an external torque T, that must to overcome the initial static yield shear stress of the fresh cementitious materials The constitutive equation of Bingham shear rate (γ̇) is commonly expressed as a two parameter model (τo and μ∞). To model the stress-deformation behaviour of viscoplastic fluids:The steel fiber considered, rotates in a fresh cementitious composites which is a non-newtonian fluid. On the other hand, fresh cement-based composites can be considered as suspensions behaving as Bigham fluid Banfill and Tattersall Some experimental procedures based on torsional pendulum have been applied by Attention should be drawn to the fact that the fresh cement pastes and mortars is often characterized by thixotropic behaviour Roussel The variation of yield stress under thixotropic conditions can be measured at two points. Initially the structure is able to admit a certain amount of stress before it is broken down and starts to flow, this amount is usually called the static yield stress τo(s) (also refered to as shear-growth shear stress). Under shear flow, the structure and bonding network is broken down, resulting in lower yield stress: dynamic yield stress τo(d)This research work aims at assessing the rheological parameters governing the effect of external induced torque on fiber rotation, to understand the factors governing the phenomenon of fiber alignment. This assessment was performed as follows: industrial fibers with different aspect ratios and geometries (hooked-end and straight) were fixed to a probe of a commercial rheometer (). Fibres were immersed in a set of plain mortars and cement paste, which had different mix designs and different rheological parameters. The work of a single fiber was analysed, as fibers in a volume fraction around a 2% are considered in a dilute solution, with low possibility of interaction between fibers The main aim of this study was to measure the induced torque on a steel fiber immersed into a controlled rotating fresh cement-water-aggregate system. This section contains the description of the experiments conducted.An ordinary Portland cement type CEM I 52.5R, according to UNE-EN 197-1:2011-Part 1: Composition, specifications and conformity criteria for common cements, has been used. The cement had a specific weight of 3.077 g/cm3, a specific Blaine fineness of 3552 m2/kg; its chemical composition is presented in . The particle distribution of the cement has been obtained through a sample suspended in ethanol with a Mastersizer S, Malvern particle size analyser (). The initial and final setting times were 118 and 178 min respectively.A quartz CEN-standard sand, complying with DIN EN 196-1 and DIN EN ISO 679, was used to mix the all the mortars considered in rheological tests. The moisture content was tested around to 0.07 wt% in all the cases. Chemical composition and mineralogical phase analysis of this sand (determined on a Bruker AXS D8 Advance X-ray diffractometer and Rietveld refinement method) values are presented in The characteristic of CEN-Standard Sand is their own specific grain size distribution. It ranges between 0.08 and 2.00 mm and the different sand fractions are blended in defined portions to be compliant with DIN EN 196-1. The maximum aggregate size DMax was established sieving with square mesh widths, obtaining three samples with 2 mm, 1 mm and 0.5 mm maximum aggregate size. The particle size distribution of the different series of sand samples through differential sieving procedure is presented in In order to understand the influence of sand with different maximum diameters of the particle suspension affecting the fiber rotation, a reference cement paste with a maximum particle size (Dmax) of 0.063 mm and three mortars with same concentrations of sand but different maximum aggregate size (Dmax), of 0.5 mm, 1 mm, 2 mm, were tested. On the other hand, the role of aggregate concentration on the fiber due rotation was also studied. Hence, one reference cement paste (0% aggregate concentration), and three mortars with 2 mm maximum aggregate diameter and 0%, 50% 66% and 75% aggregate volume where also tested. Five different mortars and one reference cement paste were designed in order to obtain similar rheological parameters and their proportions are presented in all of them with the same CEM I 52.5R Portland cement.On the other hand, seven different steel fibers were used for experiments. The two main geometric parameters considered in steel fibers are: aspect ratio (ℓ/d) and type (straight and hooked-end).Four fiber types were straight with aspect ratios ranging between 40 to 65 and three fibers were hookend-end (DRAMIX© 3D series from BekaertTMCompany) with aspect ratios between 37 and 67 approximately (See a code to distinguish the fibers during the tests was applied, by indicating first the length of the fiber, its aspect ratio and the shape of the fiber: Straight (S) or Hooked (H). shows the fiber types tested in this research.The mortar mixer used for every mortar/paste probe was a Ibertest IB32-040 C2000, the mixing steps for every test follows the standard procedure defined on UNE 196-1. All mixes were prepared following the same shear-history procedures, previous to be incorporated into the rheometer vessel.To measure the induced torque T(ω) a rotational rheometer suitable for fine-grained building materials (Model: ViskomatTM NT) was used. This rheometer can realize operative measurements on mortars up to a maximum particle size (Dmax) of 2 mm. Every test was executed filling the 370 ml rheometer vessel volume with fresh mortar/paste to introduce the system fiber-rheometer probe inside. The rotational rheometer has an accuracy able to resolve an angle of 10-4 degrees, it allows also ramping from 0.001 rpm to maximum 400 rpm in a speed-controlled mode. The measurement of torque induced over the rheometer probe can range between −250 to +250 N·mm, measured by a transducer. The torque resolution measurement is 0.05 N·mm, the accuracy is 2 N·mm.The rheometer probe (Probe model-V0011) was modified drilling a hole of 1 mm diameter to attach a steel fiber perpendicular oriented to the rotation axis (See ), the fiber was perpendicular to the probe. Every experiment was executed using first the reference probe (values obtained are shown in ) and after with each fiber mechanically fixed to the rheometer probe. The fibers used are shown by . Every fiber type is used to conduct a sequence of rheological tests immersed into the fresh mortar/paste. The mixed mortars and paste was filled into the rheometer vessel resting for five minutes prior to execute the two rheometer tests (as indicated by Two different tests were sequentially conducted with the rheometer for every mortar/paste and steel fiber aspect ratio (See ). Every test was repeated at least three times set up, the computed mean are taken to be the representative value. The standard deviation was taken, in every executed test as a value of experimental uncertainty. The sampling rate to measure the induced torque, by the rheometer probe, was set to 0.1 s. The first test is called a stress growth test (SGT) and the second one a flow control test (FCT). Five minutes of rest after mixing and two minutes between the two rheological tests were always applied (The rheometer in the SGT mode operates with an angular speed control, measuring the torque induced by the fresh mortar/paste (T(ω)) on the probe/fiber system from rest. Induced torque over a defined angular speed profile is measured starting with a controlled signal of rotation speed of 1.5 rpm (0.025 rps) during 70 s (short period), measuring the change of the induced torque. Plotting the recorded torques from the SGT test vs time submitted to a rotational value, the maximum torque value can be taken as a To(s) (static yield torque), one of the three rheological parameters assessed in the present study. This yield torque is associated to a state before the fresh cementitious structure is broken down, so To(s) is the torque necessary to initiate flow, corresponding to a previous well-connected undisturbed internal micro-structure The FCT test is also a angular speed-controlled test with a speed profile defined as a sequence of constant angular speeds during a fixed time interval, called patches: starting at 100 rpm during a 30 s interval, 90 rpm during five seconds, 80, 70 and so forth decreasing until the test is stopped. A total of ten patches using the same set of rotation speeds (ωi), per test. At every patch of controlled speed the FCT test it takes the mean torque measurement during an interval of five seconds, a set of T(ωi) values are obtained. The FCT test give us a set of tuples is recorded (ωi,T(ωi)) as result, these values are represented as straight line (following the Bingham law) using a previous least square approximation, following Eq. ). All the results from FCT experiments have a coefficient of determination R2 value with an average value of 0.97 and standard deviation of 0.05, which is acceptable for a linear relationship, such as:The relationship between the torque and angular velocity is plotted and the intercept at zero-torque rate considered is the dynamic yield torqueTo(d) (N·mm), while the slope S (N·mm·min) is the viscoplastic torque. Both are parameters corresponding to Binghams yield stress and plastic viscosity. The yield torque measured through flow curve is regarded as the dynamic yield shear stress To(d) when shear rate is zero, so this is the minimum stress to sustain or terminate the flow of the material. The established relationship (Bingham formula), what other researchers already previously presented The torque needed to rotate the fiber is considered from its edges to its center of gravity (CG), so the CG is the pivot point. Static yield torque To(s) is the macroscopic result of momentum of inter-granular friction with the steel fiber during initial paste/mortar shear, and must not be the value for the SGT and FCT tests. Regarding viscoplastic torque S, this rheological value is considered as the macroscopic effect of dynamic resistive torque caused onto steel fiber by flow around, like water, passing through the contour of the fiber A laminar flow regime around the steel fiber is considered, because the computed Reynolds number is still low even at greater angular velocities (100 rpm) in the rheological experiments The dynamical yield torque (To(d)) and the viscoplastic torque of a fiber from its center of gravity were determined for every batch with the probe alone and with the probe and a fiber. As explained before, T is related to the shear stress, τ and S with the plastic viscosity . The viscosity and the dynamic yield stress are obtained for each mix with the Viskomat™ NT probe. Considering these initial ideas, it is possible to affirm in every rheological test that the viscous torque T can be breakdown depending on their dynamical state in:A single fiber starting from a static position, or zero angular velocity (ω=0 rpm), immersed in pastes and mortars, must overcome first the static yield torque given by To(s) (N·mm), measured by the SGT rheological test.A single fiber in rotation, from 0-100 r.p.m and immersed in cementitious composites (paste and/or mortars) within rheometer vessel has a viscous torque following Eq. . The parameters values are given by: the viscoplastic torque S (N·mm·min) and dynamic yield torque To(d) (N·mm).The values obtained of dynamical yield torque To(d), and the viscoplastic torque S contributions, due to only the fiber are the difference between To(d)Ref and the SRef of the reference probe (without fiber as included into ) in each suspension and those obtained with the reference probe with each fiber. The equation obtained from the tests of a suspension with the is rheometer probe as follows, according to Eq. The values obtained from the FCT experiments, according to Eq. consider the rheometer measurements with the probe and a fiber together. The corresponding viscous torque due only the fiber (Tf) can be obtained as the difference between Eqs. . This difference can depicted algebraically as:where Tf is the viscous torque contribution of one fiber due rotation in alignment process. In the aforementioned process can be observed. Once the dynamical yield torque due a single fiber To(d)f is understood as a difference between dynamical yield torques: To(d)-To(d)Ref measured, and the viscoplastic Sf as: S-SRef for each fiber in the different suspensions are determined, dynamics of rotation to align fiber can be formulated accordingly. Similarly, using the differences between values obtained in the SGT rheological test, in such way that contribution of fiber to static yield torque is just the difference between observed values of TRef(s) (probe without fiber attached) and Tk(s) (probe with fiber innmersed in a specific mortar k).As the different suspensions present a different viscosity and dynamical and static yield stress, the effort of the same fiber in different suspensions can not be directly compared. Therefore, a lineal factor is applied for every batch as the suspensions follow the Bingham model, which attends to a lineal equation. To compare the results recorded in FCT rheological experiments, a procedure for data homogenization was established. Taking the FCT rheological value of cement paste (without fiber) as a reference for T(d)Paste equals to 7.990 N·mm) and for SPaste the value of 0.139 N·mm min. On the other hand, the five mortars has a dynamic yield torque represented as To(d)k and a viscoplastic torque Sk, where k is an index number from 1 to 5. A five adjustment constants ζTk has been defined for dynamic yield torques as a ratio To(d)k/T(d)Paste, and similarly the adjustment ratio for viscoplastic ζSk defined as a ratio Sk/SPaste, where k is equal to 1,2,3,4,5 mortars included in . The homogenized torques can be defined as:where Trefk and Srefk are the measured FCT torques without fiber per every five mortars (k = 1,2,3,4,5) indicated in are used to homogenize the FCT recorded data from torques to compare sand concentration and maximum particle size (Dmax) effects. Therefore, the results obtained of induced fiber torques have been analyzed and compared with mixtures with same viscosity and shear stress.Three rheological factors were considered to be measured by the experiments, two of them affecting the Bingham Eq. : dynamical yield (To(d)) and viscoplastic torque (S), and the third is the static yield torque To(s). The following figures show the torque needed to rotate a steel fiber surrounded by the fresh cement suspensions.The stress growth test (SGT) is commonly implemented to measure static yield torques Te(s), taken as an illustrative example for a cement paste.Two series of experiments using fibers types (straight and hooked-end) attached to the rheometer probe were made using the mortars and paste described in . Same experiments without fiber, taken as reference value for static yield torque were recorded in the as a reference values for dynamic yield torque To(d)Ref (4th column), static yield torque To(s)Ref (5th column) and viscoplastic SRef the last one. The uncertainty due the experimental SGT test procedure shows a dispersion greater in mortars than paste, the signal obtained from probe was noisy, and an a suitable data processing algorithm was used to filter the noise in measured torque signals prior to take the maximum value. The algorithm called Tikhonov-Phillips regularization was applied to SGT recorded torques with a standard prior deviation of 0.1 N·mm for pastes and 0.16 N·mm for mortars.a shows the recorded static yield torque versus the fiber aspect ratio for the straight fibers. It is possible to observe a transition of static yield torque up to 42 fiber aspect ratio. The b shows the static yield torque versus the fiber aspect ratio for the hooked-end fibers. The straight fibers have greater values of To(s) than hooked-end reaching a difference mean value of 5 N·mm approximately between both.Viscoplastic torques S (N·mm·min) for steel fibers within a range of angular rotations ω between 0 and 100 rpm are depicted considering all the tested paste/mortar and can be seen as a set of plots in a (straight fibers) and b (hooked-end). These results are given by fiber aspect ratio and the viscoplastic in rheometer units (N·mm min) for both type of fibers. Measured mean error due dispersion of experimental data falls in ±0.01 N·mm min in case of straight fibers, while the measured dispersion in case of hooked-end fibers give a ±0.016 N·mm min.Viscoplastic torque values are increasing aspect ratio from 37 to 47 fiber as pointed , about the viscoplastic torque S studied with straight fibers, shown comparable trends when the aspect ratios were higher than 50, but not lower than it., the effect caused by the concentration of sand aggregates, for straight fiber is shown. Curves in this represent the homogenized viscoplastic torque for every straight fiber type considered in . The curves in this figure present seems to show an initial plateau at low sand concentrations (0.0–0.4), and a progressive decrease of the viscoplastic torque needed for rotating the fiber at the increasing aggregate concentration. However, although fiber 1F40-09S(50.3) shows a decrease of S as the other fibers, the trend is different as it is more continuous. Nevertheless the range between 0% and 50% can be object of further experimentation to determine the fiber behavior more precisely. It should be mentioned that the lower the aspect ratio of fiber the lower the viscoplastic torque necessary for the fiber to initiate rotation (). Comparing 1F40-11S(41.4) and 1F40-09S(50.3) in (both with 40 mm length), it can be noticed that the first with 1.1 mm diameter can rotate more easily than the latter with 0.9 mm diameter. seems to have constant slope in all the fibers aspect ratios at low sand concentration, but it is necessary to determine values near to the 0.2 sand ratio in future experiments. It can be observed that viscoplastic torque decreases when the fine aggregate concentration is more than 0.5 ratio. Fiber rotates more easily in concentrated cementitious composites when aggregates are 50% of the volume fraction., the evaluation of S for hooked-end fibers in relation with the aggregate concentration has been studied. As in , hooked-end fibers seems also to have a similar plateau response in the viscoplastic torque diagram (See ) considering constant value at low aggregate concentration below to 0.5 ratio cement/aggregate. Similar viscoplastic torque behaviour with hooked-end fibers can be noticed showing a general tendency to decrease the viscoplastic torque over the 0.5 ratio cement/aggregate. It can be observed a different trend in the homogenized viscoplastic torque when 1F50-11H fiber is tested. At sand ratios over 0.6, the values are quite similar for all hooked-end fibers studied.On other hand, the variation of viscoplastic torque S for straight fibers depending on the maximum aggregate size is shown in . The lower values obtained can be observed when the maximum aggregate size is 0.5 mm. However, higher values are presented with lower and higher grain sizes than 0.5 mm. The higher viscoplastic torques were observed in straight fibers immersed in mixtures with lower grain size than 0.5 mm, except for 1F40-11S(41.4), which presents a different trend. When aggregate diameter increased up to 0.5 mm the viscoplatic torque to rotate a straight fiber increased also, except for 1F40-11S(41.4).Considering the maximum size aggregate of the cement-based composite mixture with hooked-end fibers is plotted. Similar increasing tendency of viscoplastic torque is observed in viscoplastic torque for both types of fibers. However, the hooked-end fibers show higher S maximum values to rotate at 0.12 N·mm·min.Considering dynamic yield torque (To(d)) values, obtained through FCT tests, a set of plots is presented. Computed mean error due dispersion measurement of experimental data falls in ±0.2 N·mm considering the case of straight fibers, while the computed dispersion in case of hooked-end fibers give a ±0.3 N·mm.The static yield torque To(s) is expected to be higher than dynamic yield stress To(d) considering the corresponding internal structural states of fresh paste/mortars a. This figure reveals a peak value close to an aspect ratio of 50. Viscoplastic torque S shown in a seems to have a similar qualitative behaviour than dynamic yield torque (To(d)) at this aspect ratio of 50, showing a change of tendency close to this value.Values of dynamic yield torque To(d) for a hooked-end fibers shown in b are in the domain range of 1 to 15 N·mm, except for mortar 1/2 and maximum aggregate diameter 1 mm. The trends are similar also for every mixture studied, although mortar1/2D 1 mm presents different behaviour depending of the aspect ratio of the fiber studied.The dynamic yield torque measurements obtained for straight fibers versus the aggregate concentration are represented in . All straight fibers seems to have same shape (inverted bathtub), with exception for fiber code 1F40-09S (aspect ratio 50.3).The dynamic yield torque (To(d)) needed to stop turning a single fibre seems to be constant for aggregate concentrations within a range 0.2 to 0.5 ratios, as shown before for cementitious pastes under dynamic conditions (viscoplastic torque). shows also a descent of dynamic yield torque value at values larger than 0.5 ratio of sand concentration where a maximum To is observed.It has been also observed that the fiber with higher diameter start rotating easily, confirming the asseveration commented before: the lower the aspect ratio the lower the torque required for stop rotating a single straight fiber. For a given aspect ratio and fiber volume concentration, an increase in diameter means the increase in fiber length and hence subsequent the increase in effective mechanical interlocking. Some authors, like Laskar and Talukdar Using dynamic yield torque measurements obtained for hooked-end fiber at different sand concentrations, the is plotted. This Figure shows different behaviours of dynamical yield torque To(d) have been observed. However, yield torque what seems to increase when the aggregate concentration is increased. At 0.7 ratio of sand concentration seems to decrease quickly. The fiber with the lower aspect ratio present the lower yield torque values. the To(d) variation for straight fibers with the maximum grain size of the cementitious composites has been shown. Yield torque of straight fibers has a maximum value between 0.3 and 0.35 ratio of sand concentration, this effect does not appears in for hooked-end fibers. In both cases, the yield torque To(d) necessary to stop rotating the hooked-end, and straight fibers, seems to increase more pronounced with sand concentration, but this increase is greater with long fibers (up to 50 aspect ratio) than with shorter ones.The dynamic yield torque increases with the maximum size of the aggregates (Dmax). However, the value of To(d) is nearly constant for mixtures with an aggregate maximum size under 0.5 mm. The increase of maximum aggregate size from 1 mm to 2 mm in cement-based composites also increased To(d), but pronounced than from 0.5 mm to 1 mm. considers the maximum grain size (Dmax) for hooked-end fibers. This figure is quite similar to the equivalent for straight fibers (See The static yield torque is expected to be higher than dynamic yield torque, as other authors pointed a for static yield stresses compared with the dynamic torques represented in b. In terms of fiber alignment, that means one fiber need more external torque to overcome the static yield torque than to maintain rotating a certain speed. It can be also observed this inequality in the 5th and 6th columns of measurements of reference probe without fiber.Regarding the different values found of static/dynamic yield torque in a and b (dynamic yield torque), can be seen the influence of particle size distribution (PSD) of aggregates (showed in ) on rheological properties, pointed also by other authors like Bentz et al. The fiber geometry has a strong effect on the viscoplastic torque response as expected It has been also noticed that hooked fibers increase dynamical yield torque values when the aspect ratio is reduced (ranging between 40 and 45). This behaviour differs from that pointed out for straight fibers, because of the differences in fiber geometry. Hooked-end geometry of fibers can increase the area or volume of fluid that the fiber has to slice when it rotates. This fact is interesting because the amount of oriented fibers can be lower when hooked-end fibers are used instead of straight ones. To avoid this, FRCC with lower shear stress and lower viscosity must be designed when hooked-end fibers are used It can be concluded that the geometry clearly modifies the flow around the fiber in the fresh cement mass. This fact requires a different model of stress distribution in the fiber depending on the geometry. A research considering different geometries immersed into viscoplastic fluids is reported However, it has been observed in other research, that plastic viscosity of cement based suspension increases with the volume fraction of inclusions Moreover, the volume of cement paste in a mixture must be studied as a parameter in terms of mixture design, to increase fiber alignment. Concrete with a higher cementitious paste content, such SCC, may need a lower viscosity to achieve same fiber orientation than other with higher aggregate volume fraction. In the it can be also observed that the torque necessary to rotate dynamically the fiber S in cementitious composites is lower in those batches containing larger aggregates than cement pastes Viscoplastic torque can be considered as a macroscopic drag causing on fiber rotation due to the friction between small particles assembling in cement-based suspension that contains more inter-particle contacts than a large particle packing. Thus, the friction generated is higher, for a given maximum packing fraction (MPF) The behaviour shown in paste, with the lowest Dmax in can be considered as a granular suspension in which small sand grains assemblies result in more inter-particle contacts than large particles packing. This situation can increase the opposite torque needed to rotate the fiber, as can be contrasted also in Taking into account the results shown in the , it can observed that incorporated sand to the composite reduces the torque in a first moment with Dmax 0.5 mm. However, this behaviour varies with other volumetric fractions as can be observed. The packing fraction obtained with several sizes is higher than with two sizes of aggregate, and the S also increases again The parameters regarding cementitious mixture rheology, like yield torque seems to correlate with packing density. The packing density is increased with the maximum size of the aggregate and with the concentration or volume fraction of aggregates The increase of the packing density of the mixtures increase the torque necessary to align the fibers, as the strength of flocculated network is increased with the number of particles in contact yield torque and viscoplastic of the mixture from a and b, where it can observed the plot of MOR-12-2MM-050 located under of MOR-12-1MM-050 with lower To(d)f and Sf. The volume of fibers reduces the packing density of a fiber reinforced composite Dynamic yield torque (To(d)) needed to rotate a fiber is decreased with aggregate concentration, as shown with the same fibers under dynamic load (). This Figure shows how an increment of the torque happens from 0 to 0.5 mm of Dmax.Although an increase of fiber aspect ratio increases the torque necessary for fiber rotation, a change it has been observed in trend when ℓ/d ratio was higher than 45. This behaviour can be explained because some elastic deformation causes a flexion of the fiber. The fiber inserted perpendicular to the probe could absorb some strain energy due to elastic bending deformation. This effect can be seen amplified into yield torque figures (like a) because this elastic deformation could be performed firstly during the initial yield stages and increasing later the torque to initiate the induced rotation.Fiber alignment in FRC can be obtained in different ways, and to reach it each fiber must shear the fresh mass where it is immersed. This shear generates also a load causing the fiber to bend. From the STG and FCT tests, the torque necessary to rotate a fiber have been obtained, which is the total momentum of the load caused during shearing. To understand the load chart along the fiber several facts have to be considered, and discussed as follows.A steel fiber during rotation ω has a different linear speed v(x) along its own length ℓ according to equation v(x)=ω·x. Where ω is the rotational speed, v is the linear speed from x = 0 to ℓ/2, the fiber outermost extreme. This rotation generates a different shear load in each section of the fiber, from the V = 0 in the rotation axis (in the center of mass or centroid of the fiber) to maximum speed in its edge.Moreover, this stress chart along the fiber can be modified depending on thixotropy. During a FCT test with a rotational rheometer, the microstructure of particle-particle network is affected This rheological behaviour of the fresh mass can show several load patterns that can be different depending on the angular velocity of the fiber during rotation, which are drawn in . When a static fiber initiates the rotation, it must overcome the To(s) considering velocities near to zero, and as its velocity is increased from the axis to the outermost edge (plot 1 in the )). Viscosity increases the load due to shearing with the velocity, and according to this the stress of the fiber will be increased along its length, from its centroid to the edge.On the other hand, when the fiber is rotating, is possible observe in plot 2 in , that in the axis the torque is To(d) due to thixotropy and is increased with rotation velocity due to S along its length. At very low velocity, the fresh cementitious composite can recover the initial network and the values can be next to To(s)Where Tf is the torque obtained in the rheological test, E is the elastic modulus of the fiber, Iz is the moment of inertia of the steel fiber. The expression Tfxdx can be obtained from the moment diagram (), although the centroid of the load plotted in the diagram can be displaced as shown in the figure, depending on the speed and thixotropy of the mixture.In order to discuss the behavior of the fiber during rotation, the deflections (mm) of the fibers from the axis to the edge during rotation in cement mixture MOR-11-2MM-050 (See ) have been summarized. This mixture has been selected as it shows higher values of Tf and Sf considering the load of a fiber from static, corresponding to plot 1 from . The calculations have followed the previously shown equations considering the fiber as a beam.It can be observed from the results shown in that some fibers can have a maximum deflection that can modify also the load chart estimated. As a high fraction of the span can be observed, over 1/5 in some cases, this deflection in many cases can produce second grade efforts and even larger deformations. All these results shown a higher energy absorption in the fiber when is deflected. ()) This point is important because it indicates that those fibers, which are able to keep a relation of deformation according to elastic behavior the values, are predictable. However up to this point, those fibers with lengths that allow them to deflect extremely, can reduce the torque necessary as shown in fiber 1F50-09S.This change of trend can been observed in , where over the value of aspect ratio 50 the fibers reduce their torque. This behavior can be only explained according to the aforementioned, as if we compare the fibers 1F50-09S and 1F40-09S with same diameter, shape but different length, the shorter has higher deflection under same load conditions, 4.40 mm and 3.32 mm respectively (). The deflection for a cantilever beam with constant load along its length view can be simplified as:Where δ is the deflection in the edge, q is the load due to shear according , ℓ is the length of the fiber, E is the elastic modulus, and Iz is the inertia of steel fibers. Considering fibers mentioned above, the only factor changing is the length, but according to this the deflection should increase. If the torque is reduced it can be caused to a higher deflection that reduce the load on the fiber, which under high deformations reduces the area of shearing. The shortest fibers and with highest diameters and indeed highest inertia moment, are more rigid and they are submitted to less deformation when shearing the fresh suspension. Hence, they rotate more effectively and the process to align them is easier, especially when the To(s) and S of the composite is higher. However, longer fibers, if are flexible,can also reduce their torque to be aligned when they overdue a certain aspect ratio. Although this geometric ratio has not been determined here it can be studied.The elastic deformation of steel fibers, and their effect into the yield torque and viscoplastic torque will be developed in further studies and tests. The study be can also be extended to other steel fiber geometries like crimped fibers The induced torque applied to a steel fiber immersed into a controlled rotating fresh cement-water-aggregate system was measured. The Bingham equivalence parameter: yield torque To(d) and viscoplastic torque S together with the static yiel torque Tos were determined in this study, some conclusions were stated according to bilinear Bingham expression when a single steel fiber is used attached to the rotational rheometer. Significant variations and parameters into the torque needed to rotate a steel fiber have been assessed considering only the geometry of the steel fiber: aspect ratio and shape (hooked-end and straight). The following conclusions can be drawn:The geometry of a fiber has a strong effect on the rotational viscoplastic torque response, and straight fibers (cylindrical geometry) have a more lineal behaviour against sand concentration than hooked-end fibers and they rotate more easily. Hooked-end fibers need up two times to obtain a higher torque to rotate than straight fibers. The values depend on the cement-based mixture. This fact highlights the different rheology parameters and alignment of FRCC.A range of steel fiber aspect ratios (30–70) reveals different behaviours in the torque response considering different ratios aggregate/cement. Some exposed results reveals a steel fiber elastic deformation over 45 aspect ratio for some aggregate concentration. This elastic deformation facilitates the alignment of the fibers, with a reduction of torque value needed to rotate them. The use of this rheological parameters exposed here as results, considering one fiber alignment, will address the future uses of precise studies of concrete simulation flows using the complete Bingham constitutive model considering both parameters (To(d) and S) as input.Moreover, the cement-based design parameters also affect the fiber alignment process. Both the Dmax and the aggregate volume fraction modify the fiber torque and hence the fiber alignment. The S and To(d) are modified with the Dmax. of the cement-based composite for the same rheological parameters. Particles under 0.063 mm can reduce fiber alignment. Dmax over 2 mm also increases the torque to rotate a fiber. On the other hand, higher aggregate volume fractions decrease the torque necessary for fiber rotation because the fraction of cement paste and fine particles under 0.063 mm is decreased. The cement paste volume hinders the fiber alignment.Mixtures with higher packing fraction increase the torque necessary to align successfully the fiber, as fine aggregates increase the area of contact with the fiber.Future research and considerations can be include focusing on steel fiber geometry and yield and viscoplastic behaviour associate with this characteristic. Regarding the elastic deformation of steel fibers under a induced torque gradient considering fresh concrete, some additional research can also consider larger fiber aspect ratios to the already studied interval to be compared.Special acknowledgment, appreciation and recognition to the IETcc-CSIC collaboration using the Viskomat™ NT rheometer within the framework of the Excellence Project MINECO BIA2013-47876-C2-1P. The authors want also acknowledge the laboratory of Materials of Architecture, Universidad Poiltécnica de Madrid.An inverse method for the abrasive jet micro-machining of high aspect ratio channels of desired topography – Part II, experimentsPart I of this two-part paper presented an inverse technique to sculpt high aspect ratio (AR) micro-channel cross-sections of desired topography. In this paper, the methodology is experimentally verified for a variety of topographies machined in both brittle and ductile erosive materials. Micro-channels with trapezoidal and semi-circular cross-sections, and semi-circular protrusions were machined in borosilicate glass. Micro-channels with symmetric and asymmetric wedge-shaped cross sections were machined in poly-methyl-methacrylate PMMA. The chosen topographies represent the most challenging cases because they run counter to the natural surface evolution tendency for these two materials. Overall, the average error between the machined and desired profiles was 6.4% in borosilicate glass and 9% in PMMA. The methodology opens up new possibilities for the micro-fabrication of higher efficiency devices containing high-aspect ratio micro-features of virtually any desired shape.Part I of this two-part paper demonstrated that an inverse technique could be used to predict the required erosive efficacy Eᵣ(x) to machine high AR micro-channels with particular desired cross-sectional topographies, D(x). The most challenging geometries were identified to be channels with a curved cross-sectional sidewall in brittle targets (e.g., borosilicate glass) and channels with linear sidewalls in a ductile target (e.g., PMMA). This paper experimentally validates the inverse method by comparing the measured cross-sectional profiles resulting from machining, using the predictions of the method, to those originally desired, for a variety of these more challenging geometries.AJM experiments were performed in order to machine the following desired micro-channel cross-sectional shapes in borosilicate glass: a 500 μm deep rectangular pocket, an 1100 μm wide and 300 μm deep trapezoid, 500 μm–900 μm radius semi-circular, and protruding semicircles of radii 600 μm and 800 μm. To demonstrate that the methodology could also be used to machine recessed protrusions, it was applied to a 600 μm radius protrusion etched within an 800 μm deep trapezoid, such that the protrusion was 200 μ below the surface at its highest point. In PMMA, the desired cross-sectional shapes were: a symmetric wedge of width 1600 μm and depth 1200 μm, and asymmetric wedges having slopes of 30° and 45° up to depths of 800 μm and 1000 μm, respectively.The experimental setup was identical to that described by Sookhak Lari et al. []. An AccuFlo AF10 Micro-Abrasive Blaster (Comco, Inc. Burbank, CA, USA) was used at a pressure of 400 kPa to blast 25 μm Al2O3 powder through a rectangular 0.2 mm × 2 mm nozzle (MB1500-20 Comco, Inc., Burbank, CA, USA). To improve the uniformity of the abrasive mass flow rate [], the powder was mixed in the hopper using a rotary blade (Arrow Model 850, Arrow Engineering Co., Inc., Hillside, NJ, USA) and the air was dried using desiccant and a refrigeration air drier. The abrasive mass flow rate was recorded as the average of that measured a before and after machining the channels by collecting and weighing (Sartorious CP224S, Mississauga, ON, Canada) the particles blasted into a can sealed with P100 filter for 100 s. Consistent with earlier unmasked AJM studies [], the target was placed at a very low 130 μm standoff distance. All machined channels, as well as the scars created by individual sources, were scanned using a non-contact profilometer (ST400, Nanovea, Irvine, CA, USA). The extracted footprint left by a single jet was previously presented in Part I of this paper and repeated here for clarity in The target movement was controlled by two linear actuators (Aerotech Inc., Pittsburgh, PA, USA) with a 0.5 μm positioning accuracy in two perpendicular directions. During each machining experiment, the abrasive was sprayed on the target while the stage moved it under the jet in a raster motion. The targets were 3.2 mm thick borosilicate glass (Swift Glass, Elmira, NY, USA) and 3 mm thick Poly(methyl methacrylate) (McMaster Carr, Aurora, OH, USA) plates, which erode in typically brittle and ductile fashions, respectively [For each of the desired shapes of Section 3, the inverse algorithm of Part I was used to predict the scaled erosive efficacies, Eᵣ(x) and the number of repeats nf, required to evolve the surface to approximate the desired surface D(x). Then, the machining procedure required to produce an approximation, S(x) to the required Eᵣ(x) was determined using methods described in Part I. These procedures involved machining adjacent passes at various offsets (x₀)κ and scan speeds, (vₛ)κ and then repeating them nf times to obtain the final measured profile. The machining procedures (offsets, scan speeds and the required number of repeats) to produce S(x) for each desired shape are provided in the appendices of the supplementary information.Glass tends to erode in a brittle manner, such that the erosion is maximized when particles are incident perpendicular, and minimized when they are incident at oblique angles, as shown in , which also shows the typically ductile behavior of PMMA that maximizes erosion at oblique impact. The changing topography of the channels as they become deeper results in changes in the instantaneous particle strike angles along the cross-sections. As will be seen, this interplay between local impact angle and differing erosion behavior largely determines the predicted scaled erosive efficacy required to produce a given shape in these materials.In the below sections, the predicted Eᵣ(x) and S(x) required to produce the various desired D(x) cross-sectional shapes will be presented, together with the predicted evolved surface ξ(x) (i.e. using S(x) in the surface evolution equations), and the measured micro-channel profiles. As mentioned in Section , the machining parameters required to produce S(x) and thus machine an approximation to D(x) are in the Appendices of the supplementary information. For every feature, the relative error was calculated using the absolute average difference as.AbsoluteAverageDifference=∫|ξ(x)−D(x)|dx∫|D(x)|dx×100%It was initially desired to machine a 500 μm deep rectangular pocket in glass. However, the inverse algorithm yielded a scaled erosive efficacy (a) which, when used in the surface evolution equation, yielded a more trapezoidal shape (b). It was not possible to create a vertical sidewall in glass using an adjacent pass raster technique because the maximum slope at the periphery of the feature was limited by the finite slope of the source's scaled erosive efficacy itself, and the nature of the brittle erosion process which meant (The desired trapezoidal shape is shown in a, together with the predicted approximated scaled erosive efficacy, S(x), required to machine it. The profile of the resulting measured channel is shown in b. A scanning electron micrograph (SEM) of the machined channel is also shown in a shows that the Eᵣ predicted by the inverse algorithm was higher towards the periphery than at the center. The differences in Eᵣ and S reflect the finite width of the source's scaled erosive efficacy Eⱼ used in approximating Eᵣ. Nevertheless, Channels with semi-circular cross sections having radii of 500, 600, 800, 700, and 900 μm were machined. As an example, shows an SEM of the successfully machined channel for the 800 μm radius case.) will tend to accelerate the erosion in the channel center (where particle impacts are near perpendicular) and decrease that on the sloped sidewalls (oblique particle impacts), so that a relatively high scaled erosive efficacy is required off-center to ensure a constant radius of curvature.The first specimen was a semicircle of 500 μm radius with rounded edges. The distribution of the scaled erosive efficacy created by 5 adjacent sources (a) may be compared to the required scaled erosive efficacy which was achieved after iterating the algorithm 51 times. The required number of machining repeats was 18. The average difference between ξ(x) and D(x) was 1%.b for the 500 μm radius semi-circle shows that the use of the scaled erosive efficacy of only 5 sources, creating S(x), (i.e., 5 adjacent offset passes) resulted in a reasonably good fit of machined (measured) to desired profile (the average difference between the desired and the machined was about 10%). The larger deviations in depth in the mid-section of the channel (51 μm on average) could be attributed to the number of adjacent sources being limited by the relative width of the source (450 μm) which was on the same order as that of the desired channel (500 μm). The number of sources was thus increased for the larger radius circles described below.The required scaled erosive efficacy for the 600 μm semicircle with rounded edges and the superimposed combination of 9 sources are presented in a after iterating the algorithm 44 times. It was predicted that the scaled erosive efficacy needed to be administered in 20 repeats. The average difference between ξ(x) and D(x) in The profile of the 600 μm radius circle machined with 9 sources did indeed significantly improve the agreement between ξ(x) and D(x) compared to the predictions made for the 500 μm radius semicircle. Overall, the average difference in depth between the desired target and the experiment was below 5.6%. shows the results for the 800 μm radius circle machined using 10 sources using machining parameter found by iterating the inverse algorithm 72 times. The machining procedure was repeated 24 times. The average difference between ξ(x) and D (x) was 1.1%.b demonstrates that increasing the radius of the desired semi-circle to 800 μm resulted in a very good fit between machined and desired (the average difference was less than 5.5% of the semicircle's depth). In this case, the channel was sufficiently wide to accommodate the 10 sources necessary to achieve a good machined resolution.An additional set of algorithm runs and experiments was undertaken to more fully understand the effect of increasing the number of adjacent sources. The algorithm, after iterating the scaled erosive efficacy 55 times, predicted that the 700 μm radius semicircle could be machined after 20 repeats, given the Eᵣ(x) seen in a, resulting in only 1% relative error between ξ(x) and D(x). The predicted Eᵣ(x) was produced, primarily, using 10 sources and later, after observing what appeared to be the second-strike effects (see below), 8 sources, resulting in S₁(x) and S₂(x), respectively (both are included in The two results using S₁(x) and S₂(x), are presented in b and 10c respectively. The channel machined using 10 sources seen in b was found to dramatically deviate from both the desired and predicted at the center. However, although the absolute average difference in depth between desired and measured profiles was 37%, the difference was much smaller at the periphery. For example, it was only 1.6% between x = −900 μm and x = −500 μm in b. This, and the fact that the predicted and desired final profiles show fairly good agreement, points to an experimental phenomenon, rather than any problem with the modeling. It is likely that this misfit is due to increased particle ricochets from the sidewalls to strike the channel center when a larger number of sources was used. Such second-strike effects have been noted by a number of authors in the machining of micro-channels using AJM []. This hypothesis was strengthened by the 8-source case (c) which shows that the agreement was much better (9.3%) in this case. The effect of these particle second strikes is discussed further in Section 3.3.Further evidence of the second-strike effect can be seen in the results for the semicircle of 900 μm radius machined using the predictions of the algorithm for 8 and 10 sources (). The required scaled erosive efficacy was predicted by the algorithm after 100 iterations such that the predicted average difference between D(x) and ξ(x) evolved using Eᵣ(x) was only 1.2%, if repeated 22 times.b and c show that reducing the number of sources from 10 to 8 drastically increased the agreement between measured and desired profiles (from 42% absolute average difference to only 10.9%).In summary, despite the tendency for profiles to evolve to have shallow sloped walls in brittle materials (), sections 3.1.2 and 3.1.3 demonstrated that the presented algorithm allows curved surfaces to be machined in such materials provided that significant amounts of second-strikes did not occur.In addition to machining recessed features, it was of interest to determine whether the inverse algorithm could also be used to machine protrusions. As an illustrative example, a semicircular protrusion was chosen as the desired target. An SEM image of the cross-section of a semicircle protrusion of 600 μm radius in a trapezoid of 800 μm depth (200 μm below the free surface) can be seen in a, was predicted by the algorithm after 100 iterations and resulted in an absolute average difference between ξ(x) and D(x) of 0.7%. The predicted Eᵣ(x) was simulated using 22 sources with 18 repeats. As expected, the brittle glass required a higher erosive efficacy closer to the edges of the semicircle where the oblique angle of attack reduced the erosion rate.The experimental, predicted, and desired profiles are shown in b. The resulting error between ξ(x) and D(x) was only 4.5% of the semicircle's radius. The significantly improved agreement between measured and desired profiles for protrusions compared to the semicircular channels of Section 3.1.2. suggests that, either the accuracy for the semi-circular channels was limited by the sidewalls of the channel approaching one other, or more likely, that the ability to use a much larger number of sources improved the accuracy.a depicts S(x) and Eᵣ(x) which resulted in an absolute average difference between D(x) and ξ(x) evolved by Eᵣ(x) of 0.5% of the semicircle's radius after 100 iterations, using 18 machining repeats.b shows close agreement between the measured profile and D(x) or ξ(x) (the average absolute difference in depth was only 3.3% in the range of x = −1000 μm to x = 1000 μm).Finally, a semicircle protrusion of radius 600 μm was machined within a trapezoid of depth 800 μm and width 5.6 mm. The results can be seen in a after 18 repeats using 24 sources. Eᵣ(x) was extracted after iterating the algorithm 199 times, such that the relative deviation of ξ(x) from D(x) at the final iteration was only 1.8%.The resulting absolute average difference between D(x) and ξ(x) was only 8.2% of the semicircle's radius.In summary, the inverse method can be used to control the radius of curvature, slope, and depth of machined protruding features. These predictions were more accurate compared to semi-circles, probably because more sources could be used.The approximated required superimposed scaled erosive efficacy, S(x), to machine a symmetric wedge in PMMA shown in a. It was produced using the 5 adjacent passes, and the machining procedure was repeated nf = 24 times to produce the measured channel shown in b. The general shape of the scaled erosive efficacy in a reflects the ductile erosive nature of PMMA i.e., a much higher scaled erosive efficacy is required at the center, where particle impacts occur perpendicular to the surface and erosion is relatively low (), than at the periphery, where particles strike at shallower angles, and the erosion is much higher.The average difference between the measured and desired profiles in b was 11.2%. The discrepancy is likely mainly due to the fluctuations in the mass flow rate delivered to the wedge's centerline. Since the erosion rate of PMMA is much lower than in glass [], a large number (24) of passes was required, and the level of the abrasive powder in the abrasive hopper significantly reduced, and, as noted in Ref. [], this significantly decreased the mass flow rate of the abrasive. The cross-section of the final machined channel is shown in Overall, the relatively good fit of the measured to the desired final profiles demonstrates that the present technique allows sloped symmetric features to be machined in PMMA, despite the natural tendency for very steep walls to form rapidly when machining with one source, as 's depiction of its erosion rate with increasing slope suggests [As mentioned previously, channels machined using a single AJM source in ductile materials such as PMMA evolve to be U-shaped [] with very steep sidewalls. The slope can be to an extent controlled by superposition of sources with varying scan speeds, however, the steep slope immediately after the edge could not be avoided, since only a single source pass is used at the periphery. In this case, the smallest contribution of the peripheral source to erosion at the periphery was limited by the maximum speed of the positioning stages. Hence, each desired profile was offset from the un-eroded surface by more than 200 μm, as discussed in Part I.An asymmetric wedge with the slope of 20°, which was offset in depth by 230 μm and its edges rounded by a minimum radius of 200 μm, was selected as the desired profile, and the inverse algorithm was used in combination with the surface evolution equation for a ductile target (Part I). Eᵣ(x) is presented in a, found after 73 iterations resulting in 0.5% absolute average difference between D(x) and ξ(x) evolved by Eᵣ(x). In addition, a includes the profile made by the superposition of 10 sources which was predicted to erode the surface to the desired shape after 20 repeats.The result of erosion under the specified scaled erosive efficacy is displayed in a. Eᵣ(x) was derived after 40 iterations, requiring 22 repeats. The average difference between D(x) and ξ(x) evolved using Eᵣ(x) was 10.3%.b, demonstrated agreement with both the predicted and the desired profile (the average error between the measured profile and the target was only 8.3% of the target's maximum depth). c shows an SEM of the machined channel's cross-section.a includes Eᵣ(x), created by applying the algorithm through 100 iterations, and S(x) which was the approximate scaled erosive efficacy of 9 sources.b only deviated by 6.2% average in depth from the desired profile. The limitations of the surface evolution model, and not the algorithm, caused the overestimation and formation of the sharp cusps near the edges of the channel. The slight change from Eᵣ(x) to S(x), resulted in presence of sharp cusps in ξ(x) and overestimation of depth, which can be seen in As mentioned in Section 3.1.2, particle second-strikes can deleteriously affect the predictions of the algorithm. As seen in section 3.1.2, the two S(x) profiles with smaller widths for both the 700 μm radius semicircle and the 900 μm semicircle were distributed such that the number of sources and their offsets from the center were reduced. Doing so reduced the possibility of particles ricocheting from the steep edges of each sidewall, impacting the deepest locations in the channel's profile and contributing to erosion via a second-strike. Therefore, it seems plausible that the algorithm's accuracy would improve if a modified surface evolution model was used which considered the erosion due to second-strike. Although using them in the present iterative technique would come at a considerable computational cost, ray-tracing algorithms have been previously used to track such second strikes, and their associated secondary erosion [Decreasing the source footprint size would also improve the resolution since it would allow a more flexible optimization of S(x) (i.e. the use of more adjacent passes within the narrow confines of the feature), and the feature's shape would be more controllable []. This could be achieved using a shadow mask of proper thickness and small enough stand-off [The inverse algorithm of Part I of this two-part paper predicted the required scaled erosive efficacy required to abrasive jet micro-machine high aspect ratio features with prescribed (desired) geometries. This paper used the algorithm to machine channels and protrusions with a variety of prescribed shapes in borosilicate glass and PMMA. The choices of semicircular channels and protrusions to be eroded in glass, and wedges in PMMA, were made to demonstrate the inverse algorithm's capability in applying the adjacent pass method to machine high AR features in both brittle and ductile targets. Each chosen feature was one that eroded contrary to its natural tendency.Overall, the algorithm's application was successfully verified through experiments. In glass, a typically brittle erosive system, the maximum average difference in depth between the desired and machined features was only 10.9%, for aspect ratios up to 0.5, thus demonstrating the usefulness of the algorithm. The accuracy of the features improved far from the edges of the channel since the shape at the edge was always limited by the shape of the source erosive efficacy at its edge. An increase in the desired profile's width improved the resolution since the optimization process could more flexibly distribute the scaled erosive efficacies.The algorithm is likely to find use in the machining of high AR channels used in heatsinks (e.g., trapezoidal and rectangular profiles []). They also have shown promising applications in medical studies requiring high flow rates for depleting blood cells [] and isolating circulating tumor cells []. An extension of the algorithm to 3D AJM might also find application in optimizing the AJM of 3D microfluidic devices such as ball valves in a multi-level microfluidic chip [The following is the supplementary data to this article:Supplementary data to this article can be found online at A quasi-static nonlinear analysis for assessing the fire resistance of reinforced concrete 3D frames exploiting time-dependent yield surfacesIn this work an automatic procedure for evaluating the axial force-biaxial bending yield surface of reinforced concrete sections in fire is proposed. It provides an accurate time-dependent expression of the yield condition by a section analysis carried out once and for all, accounting for the strength reduction of the materials, which is a function of the fire duration. The equilibrium state of 3D frames with such yield conditions, once discretized using beam finite elements, is formulated as a nonlinear vectorial equation defining a curve in the hyperspace of the discrete variables and the fire duration. A generalized path-following strategy is proposed for tracing this curve and evaluating, if it exists, the limit fire duration, that is the time of exposure which leads to structural collapse. Compared to the previous proposals on the topic, which are limited to local sectional checks, this work is the first to present a global analysis for assessing the fire resistance of 3D frames, providing a time history of the fire event and taking account of the stress redistribution. Numerical examples are given to illustrate and validate the proposal.The evaluation of the carrying capacity of a structure has always been a major concern to any design engineer. This implies not only situations of normal service conditions but also exceptional loadings. For reinforced concrete (RC) frames, an important aspect is to ensure the overall structural integrity during fire events.Usually, frame structures exhibit a relevant overstrength, that is their ultimate capacity can be significantly higher than the elastic limit, especially in the multi-story multi-span ones. For this reason, the material nonlinear analysis is a necessary tool for designing new buildings as well as for assessing existing structures. The plastic deformations are mainly due to normal stresses Concerning the yield surface construction, different strategies have been proposed over the years For well-confined RC sections, as proposed in many building standards The yield points have to then be interpolated in order to handle the yield criteria in structural analysis codes. A widely employed interpolation technique is the use of a multi-surface representation of the yield function usually by means of a piecewise linearization In this work, we use a different approach for constructing the Minkowski sum. It consists in giving a mechanical interpretation to each term of the sum, which corresponds to the contribute of a portion of the cross section to the overall yield surface. As such, after subdividing the cross-section in multiple sub-domains, we approximate the yield surface of each sub-domain as a single ellipsoid. Their Minkowski sum represents the yield surface of the whole cross-section. This strategy is simple, efficient and leads to a good approximation of the yield surface with a low number of ellipsoids The time-dependent yield criteria can be easily used to check the building safety by means of local strength checks of the sections. However, the confinement effects and the increase in ductility at high temperature, allow a stress redistribution over the frame, making the sectional check extremely conservative. Although this fact is well known, a global fire analysis accounting for the stress redistribution and the structural overstrength has never been proposed to our knowledge.To deal with this lack, in this work we propose a quasi-static nonlinear analysis for assessing the global safety of 3D RC frames in conditions of fire. It consists in a particular strain-driven incremental strategy which evaluates a sequence of safe states for an increasing fire duration. The time-dependent yield surface together with a finite element beam model allows us to formulate the equilibrium condition of the structure as a nonlinear system of equations defining a curve in the hyperspace of the discrete variables and the fire duration. The evaluation of this curve provides a time history of the fire event taking account of the stress redistribution and, if it exists, the fire duration limit, that is the time of exposure which leads to structural collapse. At each time step of the analysis the nonlinear internal forces are obtained by an elastic predictor-return mapping process based on the closest point projection (CPP) scheme The work is organized as follows: Section recalls the mechanical behavior of RC sections in fire in terms of temperature distribution, strength reduction of the materials and yield surface definition; Section describes a new approach for evaluating the time-dependent yield surface of RC sections in fire as a Minkowski sum of ellipsoids; Section introduces the mixed 3D beam finite element and the evaluation of its nonlinear internal forces with the strategy for solving the CPP problem at a given fire duration; Section proposes a generalized path-following strategy for tracing the equilibrium curve in the hyperspace of the discrete variables and the fire duration, deriving the algorithmic tangent operators of the iterative process; Section considers a series of analysis of 3D RC frames in conditions of fire that highlights the performance of the proposed tool; finally, conclusions are drawn in Section In this section, we describe the mechanical model for reinforced concrete sections in fire. In particular, we define the section yield surface in terms of axial force and bending moments corresponding to an assigned fire duration, taking account of the temperature distribution within the section which reduces the strength of the materials.For a generic solid body with thermal boundary conditions, the heat transfer equations can be solved using the finite element method The fire temperature (Tf) in Celsius is first calculated at a specific fire duration t expressed in hours using an assumed fire temperature-time relationship.An equivalent ISO 834 fire duration t∗=Γt is then calculated, that is the corresponding time of exposure to the standard ISO 834 fire to have a temperature of Tf, where Γ is the dimensionless compartment time factor. The ISO 834 standard fire can be described by temperature-fire duration lawChoosing a reference system with origin at the centroid, the temperature rise at any point (x2,x3), with x2 and x3 expressed in meters, within the section due to heating can then be estimated aswhere the dimensionless coefficients nw,nx,ny are evaluated by superimposing the effects of the heated sidesnw=1-0.0616(Γt)-0.88⩾0nx=0.18logt(0.5b+x2)2-0.81left+0.18logt(0.5b-x2)2-0.81right⩾0ny=0.18logt(0.5h+x3)2-0.81bottom+0.18logt(0.5h-x3)2-0.81top⩾0with b and h in meters being the section width and height respectively.The concrete compressive strength experiences significant degradation at elevated temperatures. The reduced compressive strength for concretes fcT can be estimated from its ambient value fcwhere the dimensionless reduction factor iswith T in Celsius. The concrete tensile strength, as usual, is assumed to be negligible. Lie et al.’s model ks[T]=1+T900log(T1750)0<T⩽600°C340-0.34TT-240600°C<T⩽1000°C0T>1000°Cwith T in Celsius. The reduction factors kc and ks in Eqs. are functions of the temperature, which depends on the fire duration and on the point (x2,x3) within the section, that is we have kc[x2,x3,t] and ks[x2,x3,t].Let us consider a cylinder occupying a reference configuration B of length ℓ confined by the lateral boundary denoted by ∂B and two terminal bases Ω0 and Ωℓ. The cylinder is referred to a Cartesian frame (O,x1≡s,x2,x3) with unit vectors {e1,e2,e3} and e1 aligned with the cylinder axis. In this system (see ), we denote with X=se1+x the position of a point P, where s is an abscissa which identifies the generic cross-section Ωs of the beam, while x=x2e2+x3e3 is the position of P inside Ωs.The displacement field u[X] of the model is expressed, as usual, as a rigid motion of the sectionwhere u0[s] and φ[s] are the mean translation and rotation of the section and the operator × denotes the cross product. The kinematics assumed in Eq. allows us to evaluate, using a linear Cauchy continuum, the stress-strain work W in terms of the generalized strains and stresses on the section aswhere the generalized strains ε[s]=[∊,γ2,γ3]T and χ[s]=[χ1,χ2,χ3]T are defined as are the resultant force and moment. Finally, the elastic constitutive law is expressed aswhere the coefficients of the cross-section compliance matrix F can be obtained as in As usual in practical applications involving slender beams from the point coordinates over the section and fire duration t.In the following the dependence on s is omitted for a clearer exposition. In accordance with which defines the position and orientation of the neutral axis for the collapse state from the conditionwhere ε̇11 is the axial strain of the collapse mechanism.Denoting with Ω the concrete beam section domain, Ai (see ) the steel rebar area and (x2i,x3i) its coordinates, the yield stress vector τy collecting the generalized section resultants associated with n by the Drucker condition, at a given fire duration t, isτy[n,t]=NyMy2My3withNy=fy∑i=1nsaiks[x2i,x3i,t]Ai-fc∫Ωckc[x2,x3,t]dΩcMy2=fy∑i=1nsaix3iks[x2i,x3i,t]Ai-fc∫Ωcx3kc[x2,x3,t]dΩcMy3=-fy∑i=1nsaix2iks[x2i,x3i,t]Ai+fc∫Ωcx2kc[x2,x3,t]dΩcwhere ns is the number of rebars, Ωc is the area of the compressed portion of the section according to Eq. allows the evaluation, for an assigned fire duration t, of the set of generalized yield stress τy[nk,t] associated to the mechanism nk, simply by assuming uniaxial stress fields reaching their maximum strength capacity in each region, either in tension or in compression.A suitable interpolation or approximation In this section a new approach for constructing the yield surface of RC sections in conditions of fire in terms of the Minkowski sum of ellipsoids From now on, for a more clear notation, the dependence on the fire duration will be omitted to denote the quantities at ambient temperature. The domain of the composite cross section Ωs=Ω∪iAi is subdivided into a grid of sub-domains Ωs=∪IΩI as shown in with the rebars collected in groups, one for each edge. Exploiting the properties of the integral in Eq. , the true yield stress τy[nk] at ambient temperature can be obtained aswhere τyI[nk] is the contribution of the Ith subdomain evaluated for concrete aswhere ΩcI is the compressed part of the sub-domain ΩI. The integrals can easily be evaluated by the numerical procedure described in τyI[nk]=fy∑i=1NsIaiAify∑i=1NsIaix3iAi-fy∑i=1NsIaix2iAiThe yield surface of each sub-domain I, that is the cloud points τyI[nk] for all the mechanisms nk, is approximated using a single ellipsoid aswith the stress on the ellipsoid surface which assumes the following expression in terms of a generic normal vector nThe ellipsoidal center cI and shape matrix CI are obtained, as in min(cI,CI)∑krk2withrk=nkT(τIy[nk]-τI[nk]).Finally, the stress points on the yield surface expressed as a Minkowski sum of ellipsoids can be parametrized in a closed form in terms of the normal vector n (see The reduction factors kc and ks in Eqs. depend on the fire duration and on the point (x2,x3) within the section. It is possible to approximate them with a mean value k¯I[t] within each sub-domain I. This value is chosen as the one which provides an exact axial force, but it furnishes accurate results also for the bending moments when multiple sub-domains are used. For the concrete sub-domains, letting kI[x2,x3,t]=kc[x2,x3,t], this meanswhere the integral can be evaluated analytically as in The points belonging to the time-dependent yield surface can then be easily expressed in a closed parametric form, for any t, asThis means we do not need to re-compute the yield surface at a given fire duration t, because it is automatically available by simply scaling the ellipsoidal contributions of the yield surface at ambient temperature. In other words, the cross-section analysis is carried out once and for all and no further calculations on the cross-section are needed. Furthermore, the account of the strength reduction is quite easy and inexpensive because it just requires the evaluation of some scalar quantities.The proposed strategy for the evaluation of the time-dependent yield surface is now tested for two RC cross-sections, called RS1 and RS2, with steel reinforcements of diameter ϕ typical of columns and beams respectively and reported in . The accuracy is tested varying the number of sub-domains of the concrete part, while one sub-domain is used for each edge. The reference solution is obtained by evaluating the yield points numerically according to Eq. using a very fine discretization of the concrete area and considering the contribution of each rebar separately. The yield surfaces are illustrated in the space of the generalized stresses τ=[N,M2,M3]T.The RS1 section is analyzed considering a fire exposure all along its perimeter. The temperature distributions within the section predicted by Wickstrom’s formulas are reported in for 1 and 2 h of fire. Clearly, they are symmetric with respect to the principal axes of the section because of the symmetry in the geometry and thermal boundary conditions. shows how the proposed Minkowski approximation fits the yield points of the reference solution for different fire durations. It is possible to observe how the 2×2 approximation of the concrete domain provides an excellent fit of the true yield points at ambient temperature, but the solution gets worse as the time of exposure to fire increases. A 4×4 approximation on the other hand is able to capture the contraction of the yield surfaces for increasing fire durations more correctly. The error is due to the assumption of constant strength reduction within each sub-domain, but it is quite low even for coarse discretizations because of the use of a suitable average of the strength reduction.The evolution of yield surface is better illustrated in for the 4×4 approximation. We can note the symmetry with respect to the M2-M3 plane as well as the non-null position of the center along the N axis, due to the zero concrete tensile strength, of the ambient temperature domain. These features are preserved also for the section in fire because of the bi-symmetric temperature distribution. Furthermore, we can note that the admissible domains are quite significantly reduced by the thermal loading.The RS2 section is analyzed considering a fire exposure along three edges: left, bottom and right. shows the temperature distributions within the section predicted by Wickstrom’s formulas for 1 and 2 h of fire. They are not symmetric with respect to the x3 axis of the section because of the asymmetric thermal boundary conditions. we can observe the quality of the proposed Minkowski approximation in fitting the yield points of the reference solution at various fire durations. Again, the 2×2 approximation of the concrete domain provides an excellent fit of the true yield points at ambient temperature, but the solution gets worse increasing the time of exposure to fire. A 4×4 approximation is able to capture the contraction of the yield surfaces more correctly also for increasing fire durations.The evolution of yield surface is better illustrated in for the 4×4 approximation. We can note that, in contrast to the section previously analyzed, the symmetry with respect to the M2-M3 plane of the ambient temperature domain is no longer preserved for the section in fire as soon as the heating is non-symmetric. Similar results are obtained for one-face heated rectangular sections In the following the finite element beam model for the incremental fire analysis is described. A specialized stress update strategy for the Minkowski representation of the yield condition is also illustrated., where the interpolation matrix Dt[s] is obtained satisfying the equilibrium equations on the element for zero body forces exactly, that isBody load effects are then included exactly as a “particular solution”. and the torsional moment component M1 are constant, while the two flexural components M2[s] and M3[s] of are linear with s and linked to the shear resultants so that V2ℓ=-(M3[ℓ]-M3[0]) and V3ℓ=(M2[ℓ]-M2[0]). The internal work becomesallowing us to directly obtain the discrete form of W without any FEM interpolation for the kinematic variables. The vectors collecting the kinematics de and static β finite element generalized parameters and the compatibility operator Qe are defined asβ=NM2[0]M3[0]M2[ℓ]M3[ℓ]M1,de=u0[0]φ[0]u0[ℓ]φ[ℓ],Qe=1ℓ-ℓe1T0ℓe1T0e3T-ℓe2T-e3T0-e2T-ℓe3e2T0-e3T0e3Tℓe2Te2T0-e2Tℓe3T0-ℓe1T0ℓe1T.The linear elastic problem can be formulated as the stationarity of the Hellinger-Reissner functional ΠHR that at the element level can be written aswhere pe is the element contribution of the external loads and the elastic compliance matrix of the element Fe is obtained from the equivalenceThe stationarity of ΠHR with respect to the stress variables furnishes the discrete elastic constitutive lawwhich allows us to express the elastic problem in terms of displacement variables only. The stationarity condition with respect to de furnishes the equilibrium equations on the element aswhere se[de] and pe are the internal force vector and the external load vector of the element respectively. Eq. Denoting with a subscript s the quantities related to the cross-section at abscissa s, the yield function fs[t,τs] is defined in a 3D space involving axial force N and bending moments M2[s] and M3[s] collected in vector τs=[N,M2[s],M3[s]]T. The plastic admissibility condition isThe update of the stress is obtained, in a strain-driven way, by means of a closest point projection (CPP) which corresponds to a backward Euler scheme for integrating the constitutive law. Starting from a known state de0,β0 at time t0, the stress parameters β at time t for an assigned displacement increment Δde=de-de0 are obtained by solving, for each element, the optimization problemminimize12(β-β∗)TFe(β-β∗)subject tof0[τ0,t]⩽0fℓ[τℓ,t]⩽0where β∗=β0+EeQeΔde is the elastic predictor. The admissibility condition is checked only on the end nodes of the beam, as done in . Note that, the stresses at both end sections are coupled with each other by the equilibrated interpolation and, then, the CPP has to be performed at the element level. Moreover Eq. defines the constitutive law with the stresses uniquely defined by their initial values, the time of exposure and the displacement increment. In the following, to simplify the notation, we write β=β[de,t] omitting the dependence from the known quantity β0. corresponds to an elastic predictor-return mapping scheme.If the stress predictor is admissible for the two sections, this is the solution of the CPP problem in Eq. , otherwise a return mapping process is needed. The return mapping consists in solving the constrained optimization problem Eq. . Two cases are possible: only one active constraint or two active constraints. The full solution algorithm for the CPP, for a standard incremental elasto-plastic law, is reported in , they are reformulated using the normal vector n as primal unknown. In this way, the dimension of the problems is fixed and it is independent of the number of ellipsoids used in the approximation.Omitting the subscript s to simplify the notation, the problem now addressed is how to check if a given stress state τ∗=Psβ∗ of a generic section s, extracted from β∗, is inside or outside the admissible domain at a given fire duration t bounded by a yield surface expressed in terms of Minkowski sum, and then not explicitly available in terms of stress variables. To this end, we adopt the algorithm illustrated in , which is based on the parametrization of the stress states belonging to the yield surface τ[n,t] in terms of the cross-section collapse mechanism n (see Eq. The intersection of the straight line passing through the center of the Minkowski approximation and the stress point τs∗ with the yield surface parametrization τs[n,t] is defined asrn≡τ[n,t]-c[t]-α(τ∗-c[t])=∑Ik¯I[t]CInnTCIn-α(τ∗-c[t])=0where c[t]=∑Ik¯I[t]cI is the center of the Minkowski sum of ellipsoid at fire duration t and α is the admissibility factor associated to τ∗ with respect to the yield condition: α⩾1 means τ∗ is admissible. of 3 equations in 4 unknowns needs a further equation which defines the normalization condition for n. Furthermore, there are two possible intersection points while only the one with positive value of α is of interest. Exploiting the convexity of the yield surface, the following normalization can be adopted to complete the equations and assure the convergence to the sought solutionThe nonlinear system r≡{rnT,rα}T=0 in the unknowns z≡{nT,α}T can be solved using a Newton schemeJk=H[nk,t]-(τ∗-c[t])-(τ∗-c[t])T0,H[n,t]=∑IkI[t]CInTCIn-CInnTCI(nTCIn)3/2This iterative process converges very quickly in the smooth regions of the yield surface, but often diverges in the regions with a quasi-discontinuity of the normal vector (corners and edges), that is when τ[n] is almost constant under large changes in n. In this last case Jk tends to become singular compromising the convergence of the iterative process. An easy way to avoid the singularity problem is to modify matrix H[n,t] with a penalization factor on its second part, as proposed and validated in The first order condition of the CPP problem in the hypothesis of one active constraint for a generic section s can be writtenwith me=Psns the increment of plastic strain in the finite element., regardless of the number of ellipsoids which defines τs[ns], can be rewritten as a nonlinear system of 3 equations as followsand the unknowns are the components of ns, that is the plastic strain increment.The solution can be obtained iteratively using the following Newton schemewith Aj≡H[nsj,t]+Ess. Again a modified iteration matrix H[nsj,t] can be used in order to improve the robustness of the iterative process (see . Note that, contrary to the classical return mapping scheme, in this case the stress point τs[ns,t] belongs to the yield surface during the iterative process.In the case of active constraint for both the end sections, the first order conditions of the CPP problem areβ-β∗+Eeme=0P0Tβ-τ0[n0,t]=0PℓTβ-τℓ[nℓ,t]=0with, now, me=(P0n0+Pℓnℓ) the increment of plastic strain. in the other ones the CPP problem is defined by a nonlinear system of 6 equations in 6 unknowns as followsr0[n0,nℓ]≡τ0∗-τ0[n0,t]-E00n0-E0ℓnℓ=0rℓ[n0,nℓ]≡τℓ∗-τℓ[nℓ,t]-E0ℓTn0-Eℓℓnℓ=0The following Newton iteration is adoptedA00A0ℓA0ℓTAℓℓδn0δnℓ=-r0jrℓjn0j+1nℓj+1=n0jnℓj+δn0δnℓA00=E00+H0[n0,t]Aℓℓ=Eℓℓ+Hℓ[nℓ,t]A0ℓ=E0ℓ.Also in this case a modified iteration matrix In this section, the equilibrium condition of 3D frames with time-dependent yield conditions, once discretized using beam finite elements, is formulated as a nonlinear vectorial equation defining a curve in the hyperspace of the discrete variables and the fire duration. A strain-driven incremental strategy is proposed for tracing this curve in a path-following manner and for evaluating, if it exists, the fire duration limit, that is the time of exposure which leads to the structural collapse. The algorithmic tangent stiffness operators for the beam finite element with yield condition expressed as Minkowski sum are also derived for an efficient incremental analysis.Once the finite element assemblage has been carried out, the equilibrium condition of a RC building subjected to fire can be written aswhere p and s are the load vector and the internal force vector of the structure respectively, obtained assembling the finite element contributions in Eq. , and d is the vector collecting the overall kinematic degrees of freedom. This system of nonlinear equations represents a curve in the hyperspace d-t, which can be traced in a path-following manner.The curve can exhibit a limit fire duration, that is the time of exposure which leads to structural collapse. For this reason it is not convenient to use a time controlled scheme since Eq. could not have a solution, that is no equilibrium state, for a given fire duration. We propose instead the use of a generalized arc-length method defines a sequence of points (steps) z(k)≡{d(k),t(k)} belonging to the equilibrium path. Starting from a known equilibrium point z0≡z(k), the new one z(k+1) is evaluated correcting a first extrapolationz1={d1,t1} by a sequence of estimates zj by a Newton–Raphson iterationwhere Rj≡R[zj] and J is the Jacobian of the non-linear system at zj or its suitable estimate. Also if other choices are possible vdT(d-d1)+vt(t-t1)=ξ-ξ(k)wherevd≡M(d1-d(k))vt≡μ(t1-t(k))M and μ being some suitable metric factors J≡∂R[z]∂zzj=KtstvdTvtwithKt=∂s[d,t]∂dzj,st=∂s[d,t]∂tzj.The choice of an adaptive constraint makes the Jacobian matrix in Eq. non singular also when Kt is singular. The solution of Eq. is conveniently performed in a partitioned way as followsin order to exploit the symmetry and the band structure of the tangent stiffness matrix Kt. The tangent operators Kt and st are obtained assembling the element contributions derived in the next subsection.Omitting the dependence of the quantities on t and n to simplify the notation, the finite element contribution to the Jacobian , when the yield conditions are expressed as a Minkowski sum, can be derived by writing the return mapping Eqs. in the incremental form. For the two active constraints case, we haveδβ=Eeδρe-δmeP0Tδβ-H0δn0-τ0,tδt=0PℓTδβ-Hℓδnℓ-τℓ,tδt=0where δρe=QeTδde is the element strain increment and a comma denotes partial derivative. Remembering that δme=P0δn0+Pℓδnℓ and substituting the first of Eqs. in the other ones, we obtain δn0 and δnℓ asδn0δnℓ=B00B0ℓB0ℓTBℓℓP0TEeδρePℓTEeδρe+δtτ0,tτℓ,tBy substituting the expression of δme in the first of Eqs. δβ=Eteδρe+δtyt,withEte≡Ee-Ee(B̃00+B̃0ℓ+B̃0ℓT+B̃ℓℓ)EeIn order to make the evaluation of k¯I,t more efficient, the exact law which links k¯I[t] to the fire duration t can be approximated by a Lagrangian polynomial law based on its values at assigned time durations, belonging to the range of interest for practical applications.In the single constraint case, following the same approach, the algorithmic tangent moduli of the element Ete simply becomesIn both cases the symmetry of Ete is preserved. The finite element tangent stiffness matrix is then evaluated in both cases aswithout the need for a Gauss numerical integration. Similarly, the derivative of the internal force vector with respect to the fire duration can be computed as set=QeTyt. In order to make the partitioned solution in Eq. possible, the exact singularity of the tangent stiffness matrix is avoided by adding a small quantity 10-4Ee to Ete.The points z(n) evaluated by the scheme are, by definition, equilibrated and plastically admissible at time t(n). In other words, they satisfy the hypotheses of the lower bound theorem of the limit analysis and, then, the structure is safe for this fire duration. Furthermore, we have that z(n) is plastically admissible also for the yield conditions at time tk<tn if we assume that the temperature, and then the strength reduction, is a nondecreasing function of the fire duration as stated in Eq. . We now demonstrate that when the curve exhibits a limit fire duration, that is Δt≡t(n)-t(n-1)=0, a kinematically admissible mechanism develops and we are in a situation of incipient collapse.Since the Riks constraint approximates a curvilinear abscissa along the fire duration-displacement path and the tangent matrix in Eqs. along this curve is positive semi-definite, the scheme produces t(n)⩾t(n-1). At each step of the analysis the total strain increment QeΔde of each finite element is decomposed into an elastic part FeΔβ and a plastic one me according to Eqs. where Δ denotes the difference of quantity between the two steps tn and tn-1. Subtracting the equilibrium Eqs. Multiplying the result by the displacements increment Δd and summing the contribution of each element, we haveIf we consider the case Δt=0 and QeΔde≠0 we note that the elastic domain, for each section, remains unchanged. Since the first term on the right hand side of Eq. is not negative due the positiveness of Fe and the second is not negative due to the Drucker condition being, for Δt=0,β(n-1) contained in the elastic domain at time t(n), we have that both terms have to be null and this proves that the kinematically compatible strain increment is purely plastic and, then, the structure is just at the point of failure because the hypotheses of the upper and lower bound theorems of the limit analysis are satisfied simultaneously.The time-dependent yield surfaces and the incremental strategy are employed for assessing the safety of RC structures exposed to fire. Three examples are given with an increasing complexity: a beam fixed at both ends, a simple 3D frame and a multi-story multi-span building. The same sections as previously analyzed are employed. In particular, the RS1 section is used for the columns, while the RS2 one is adopted for the beams. A single finite element is used for the columns, while two finite elements are used for the beams. An ISO 834 standard fire is considered. The maximum structural deflection, denoted as umax, is chosen as control variable and monitored in the numerical tests.The results provided by our fire analysis in terms of limit fire duration are assessed by means of a comparison with a standard elasto-plastic analysis where the yield surfaces are kept constant and the load is amplified by a factor λ. In particular, we show that the limit load provided by the elasto-plastic analysis coincides with the applied one (λ=1) when the yield surface of the fire exposed sections is evaluated at the limit fire duration.The first test regards the clamped beam depicted in the fire duration-displacement curve for the assigned distributed load is reported. It is possible to note that, even if plastic deformation also occurs for a low fire duration, the structure does not fail until a limit fire duration equal to 2.3 h. It is possible to observe that both the 2×2 and 4×4 discretizations provide similar results. In the structure is analyzed using a standard path-following elasto-plastic analysis, where the load is amplified by a factor λ. In order to validate the proposal, the analysis is carried out for different yield surfaces evaluated at assigned fire durations. It is possible to observe how the collapse load factor decreases with the fire duration and, in particular, it is equal to one for the yield surface corresponding to the limit fire duration evaluated with the proposed incremental strategy.The second example regards the simple 3D frame reported in . The load over the floor is uniformly distributed over the four beams. The fire scenario considered is the columns exposed to fire at each edge while on the beams it is on the three edges excluding the top one. the fire duration-displacement curve for the assigned distributed load is reported. The curve is characterized by a significant initial portion with zero displacements. This means that the load is largely inside the initial domain at ambient temperature. Two hours are required to observe the first plastic deformations while the limit fire duration is equal to 2.6h. Different cross-section discretizations are employed. All of them provide similar results and the 3×3 practically coincides with the 4×4 one. Also in this case the structure is analyzed using the standard incremental elasto-plastic analysis with constant yield surfaces corresponding to different fire durations. The load-displacement paths are reported in for different times of exposure. It is possible to observe how the collapse load factor is equal to one for the yield surface corresponding to the limit fire duration evaluated with the proposed incremental strategy.The collapse mechanism of this simple 3D frame is shown in . As expected, it is symmetric with respect to a vertical axis passing trough the midpoint of the floor. We can observe how plastic deformations occur at the midspan of the beams and at the top and the bottom sections of the columns, as highlighted in by blue dots. The evolution in time of N,M2,M3 is reported in for some of these sections in order to show the stress redistribution and the interaction between the stress resultants. In particular, the midspan of the beams is characterized by a decreasing value of the non-null bending moment M2 due to the contraction of the admissible domain. This is associated to an increase in the axial force due to the non-symmetric shape of the yield surface, which however remains quite low. Conversely, the top section of the columns shows a constant value of the axial force, imposed by the axial equilibrium equation, and the variation of both the bending moments up to collapse as a consequence of the stress redistribution occurring after the plasticization of the beams.The last test regards the real scale building reported in . The vertical story load p of the one way ribbed slab as depicted in is distributed on the beams. For each floor area, 90% of weight is assigned to the beams orthogonal to the ribs, while the other 10% is applied on the parallel ones. The fire event involves the ground floor only. the fire duration-displacement curve for the assigned distributed load is reported. The curve is characterized by an initial portion with zero displacement. This means that the load is sufficiently safe at ambient temperature. 1.3 h of fire exposure are required for the first plastic deformations, while the limit fire duration is equal to 2.7 h. We can note that in this case, due the high hyperstaticity of multi-storey multi-span frames, the commonly employed sectional check underestimates the structural safety by about twice the one predicted by our model, which accounts for the redistribution of the stresses and the consequent structural overstrength. Different cross-section discretizations are employed, all of them providing similar results. The 3×3 practically coincides with the 4×4 one also in this more complex test. Again, the structure is analyzed using the standard path-following elasto-plastic analysis and the corresponding load-displacement paths are reported in for different fire durations. It is possible to observe how the collapse load factor is equal to one for the yield surface corresponding to the fire duration limit evaluated with the proposed incremental strategy. In both kinds of analysis, the equilibrium paths are traced up to a limit displacement. At this point, the slope of the different curves is very small, even if not exactly zero, and this means that the actual collapse state occurs for large displacements. The collapse mechanism is reported in where the sections with generalized stresses lying on the contracted yield surface are highlighted with blue dots. One can note that, even if the fire event involves the ground floor only, the plastic deformation spreads to the upper floors as a consequence of the stress redistribution. The time history has been reconstructed also using finer meshes for the beams and reported in . No relevant difference on the maximum displacement-fire duration curve can be observed.In this work, we proposed a numerical framework for the global assessment of the fire resistance of RC 3D frames. First of all, a simple, accurate and efficient numerical procedure for constructing the axial force-biaxial bending yield surface of RC sections in fire was derived. This is based on a particular Minkowski sum of ellipsoids, where each ellipsoid represents the contribution of a sub-domain of the cross-section to the overall surface. The yield conditions so obtained are time-dependent, in the sense that the yield surfaces corresponding to different fire durations are directly available from the one at ambient temperature, with no need to reanalyze the cross-section. These yield criteria can be easily used to assess the building safety simply checking the local strength of the cross-sections. However, the overstrength of the structure and the ductility due to confinement and temperature increase, allow a stress redistribution over the frame, making the sectional check extremely conservative. For these reasons, we proposed a novel global fire analysis. Once the structure is discretized using 3D beam mixed finite elements which check the admissibility condition on the end sections, the equilibrium condition of 3D frames is formulated as a nonlinear system of equations defining a curve in the hyperspace of the discrete variables and the fire duration. A strain-driven incremental strategy was employed for solving these global equilibrium equations in a path-following quasi-static manner. The nonlinear internal forces are obtained by a closest point projection problem on yield surfaces at the current fire duration which is solved, exploiting the properties of the Minkowski sum, using the cross-section collapse mechanisms as unknowns. The tangent operators of the global iterative process were derived in order to trace the fire duration-displacements curve using a restricted number of Newton iterations. This kind of analysis provides a time history of the fire event taking account of the stress redistribution and, if it exists, the limit duration, that is the time of exposure which leads to the structural collapse. In particular, it furnishes a sequence of safe states at increasing fire durations according to the lower bound theorem of the limit analysis. Numerical tests showed that the proposed formulation is suited for real scale buildings.Future developments will focus on accounting for the other effects, as large deformations and ductility limit, in the global fire analysis for more accurate and general simulations. Trans. Nonferrous Met. Soc. China 24(2014) 3070í3075 Microstructures and mechanical properties of extruded and aged MgíZníMníSníY alloys Guang-shan HU 1,2 , Ding-fei ZHANG 1,2 , Ding-zang ZHAO 1,2 , Xia SHEN 1,2 , Lu-yao JIANG 1,2 , Fu-sheng PAN 1,2 1. College of Materials Science and Engineering, Chongqing University, Chongqing 400045, China; 2. National Engineering Research Center for Magnesium Alloys, Chongqing University, Chongqing 400044, China Received 29 September 2013; accepted 20 January 2014 Abstract: The microstructures and mechanical properties of Mgí6Zní1Mní4Sn and Mgí6Zní1Mní4Sní0.5Y alloys under extrusion and T6 aging conditions were investigated by optical microscopy (OM), X-ray diffraction (XRD), scanning electron microscopy (SEM) and tensile test. The results show that Y element refines the grains and improves the comprehensive mechanical properties of ZMT614í0.5Y both in as-extruded and T6 states. The phase compositions of Mgí6Zní1Mní4Sní0.5Y are Ä®-Mg, MgZn 2 , Mn, Mg 2 Sn and MgSnY phases. After T6 treatment, the ultimate tensile strength (UTS) and yield strength (YS) increase while the elongation decreases severely. For both of these alloys, the theoretical results combined with the experimental values demonstrate that the grain boundary strengthening and solid solution strengthening play an important role in enhancing the YS in the as-extruded state, while the precipitation strengthening is the key factor for the enhancement of YS in the T6 state. Key words: MgíZníMníSníY alloy; yttrium; extrusion; T6; microstructure; strengthening mechanism 1 Introduction As the lightest green metallic structural materials, magnesium (Mg) alloys have great potential for applications in the fields of automobile, aerospace, electronic and telecommunication industries [1í3]. However, the low strength and poor ductility limit their applications [4]. Therefore, strong interests have been focused on the development of new wrought Mg alloys. Previous investigations have shown that rare earths (RE) could improve the comprehensive mechanical properties of Mg alloys by means of fine-grain strengthening, solid-solution strengthening and precipitation strengthening [5,6]. Yttrium (Y), as one of RE elements, has been widely used in improving the mechanical properties of Mg alloys. For Mg alloys, the solid solubility of Y element decreasing exponentially depends on the temperature decreasing, which indicates that the precipitation strengthening capability of Y-containing Mg is excellent [7]. The MgíSn alloy has been known as a precipitation hardenable system. Sn has a high solubility (3.35%, mole fraction) at 834 K and low solubility at ambient temperature [8í10]. Recent researches have indicated that the addition of cost-effective Sn to Mg alloys could enhance the comprehensive mechanical properties since the formation of Mg 2 Sn phase [11í13]. Combined addition of Y and Sn to Mg alloys could develop a new low cost high strength wrought Mg alloys. Therefore, many Y- and Sn-containing Mg alloys are researched, such as MgíSníY [14], MgíAlíSníYíNd [15] and Mgí10Gdí 3Yí1Sní0.5Zr [16] alloys. But up to now, the investigations of MgíZníMníSníY alloys are not carried out and the scientific understanding of the influence of Y on the microstructures and mechanical properties of this alloy is not clear. The present work studied the effects of Sn and Y on the microstructures and mechanical properties of MgíZníMníSníY alloys in extrusion and T6 treated conditions. 2 Experimental Commercial high-purity Mg (>99.9%, mass fraction), Zn(>99.95%), Sn(>99.9%) and two master Foundation item: Project (2013CB632200) supported by National Basic Research Program of China; Project (2010DFR50010) supported by International Scientific and Technological Cooperation Program of Ministry of Science and Technology of China; Project supported by Sharing Fund of Chongqing University’s Large-scale Equipment, China Corresponding author: Ding-fei ZHANG; Tel: +86-23-65112491; E-mail: [email protected] DOI: 10.1016/S1003-6326(14)63444-0 Guang-shan HU, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3070í3075 3071 alloys Mgí30.0%Y and Mgí5.01%Mn were used to prepare the experimental alloys. All alloys were melted at about 750 °C in a vacuum induction melting furnace under Ar atmosphere. Then the melts were poured into a steel mold with an ingot diameter of 90 mm. The chemical compositions were analyzed by XRFí1800 CCDE sequential X-ray fluorescence spectrometer, which were Mgí6.01Zní0.88Mní4.20Sn for ZMT614 and Mgí6.14Zní0.91Mní4.38Sní0.50Y for ZMT614í 0.5Y. The ingots were homogenized at 420 °C for 12 h and then under a controlled constant force by XJí500 horizontal extrusion machine. The homogenized ingots were hot extruded to bars of 16 mm in diameter at 360 °C with the extrusion ratio of 25. After extrusion, the alloys were cooled in the open air. The extruded samples were solid-solution treated at 440 °C for 2 h followed by water quenching. Subsequently, the samples were age treated at 180 °C for 12 h followed by water quenching (T6). Tensile tests were performed using tensile specimens with gauge length of 50 mm and gauge diameter of 5 mm. The tensile directions were parallel to the extrusion direction (ED). The tensile tests were performed on a SANS CMTí5105 electronic universal testing machine in air at a speed of 2 mm/min at room temperature. Tensile properties under each condition were obtained as the average values of three tests. The microstructures of specimens were observed with LEXT 2000 laser metallographic microscope and TESCAN VEGAÄŠ scanning electron microscope equipped with an INCA Energy 350 energy dispersive X-ray spectrometer (EDS). Phase components were characterized with a Rigaku D/max 2500PC X-ray diffractometer using Cu K Ä® . 3 Results and discussion 3.1 Microstructure of as-extruded alloys Figure 1 shows the XRD patterns of as-cast and as-extruded ZMT614 and ZMT614-0.5Y alloys, which reveals that the phase compositions of both alloys are remained whether in as-cast or as-extruded conditions. The ZMT614 alloy is composed of Ä®-Mg, MgZn 2 , Mn and Mg 2 Sn phases. After adding 0.5% Y, a new ternary phase MgSnY is formed. Therefore, the phase compositions of ZMT614-0.5Y alloy are Ä®-Mg, MgZn 2 , Mn, Mg 2 Sn and MgSnY phases. Figure 2 shows the optical micrographs in longitudinal extrusion direction of as-extruded samples. The fine grains in the longitudinal direction indicating that dynamic recrystallization (DRX) occurred during extrusion at 360 °C. The average grain sizes of these samples are 6 and 5 È�m, respectively. A small number Fig. 1 XRD patterns of ZMT614 (a, b) and ZMT614-0.5Y (c, d) alloys at different states: (a, c) As-cast state; (b, d) As-extruded state Fig. 2 Optical micrographs of as-extruded samples: (a) ZMT614; (b) ZMT614-0.5Y of oval and rod shaped compounds lie in the as-extruded ZMT614 alloys, whose lengths are 5í10 È�m. However, for ZMT614í0.5Y alloy, a mass of irregular blocky compounds disperse in the matrix with a non-uniform manner. The size of these compounds reaches more than 10 È�m. Extrusion streamlines which consist of MgZn 2 , Mn, Mg 2 Sn and MgSnY phases parallel the extrusion Guang-shan HU, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3070í3075 3072 direction in the alloys. Some unDRX grains around the extrusion streamlines reflect that the irregular blocky compounds restrain the DRX process. Figure 3 and Table 1 show the SEM and corresponding EDS analysis of longitudinal extrusion direction of as-extruded samples. From Fig. 3(a), EDS analysis demonstrates that the fine oval and rod shaped compounds both are Mg 2 Sn phase. From Fig. 3(b), a small quantity of oval shaped compound exists, and EDS analysis indicates that they are Mg 2 Sn phase. The aspect ratio of Mg 2 Sn phase in ZMT614í0.5Y is smaller than that of ZMT614 alloy. Based on the XRD and EDS analyses, the irregular blocky compounds are MgSnY Fig. 3 SEM images of as-extruded samples: (a) ZMT614; (b) ZMT614í0.5Y Table 1 Corresponding EDS results of Fig. 3 Mass fraction/% Region Mg Zn Mn Sn Y A 85.96 8.93 0.96 4.15 í B 50.18 3.18 í 46.64 í C 32.91 í í 67.09 í D 87.54 7.52 0.78 4.43 í E 77.26 7.78 1.25 8.61 5.10 F 62.46 2.83 í 34.72 í phase. It is obvious that the volume fraction of the Mg 2 Sn phase in the ZMT614í0.5Y alloy is lower than that in the ZMT614 alloy. This is mainly due to the fact that the formation of MgSnY phase consumes a certain amount of Sn element. In addition, EDS analysis reveals that the MgSnY phase contains Mn element. According the calculated MgíMníSn and MgíMníY phase diagrams [17], a solid-solution reaction LĺL+Ä®-Mn occurs at about 650 °C at the first stage of solidification. Then at the later stage, formed primarily Mn phase may act as heterogeneity nucleus of MgSnY phase, consequently promotes the formation of MgSnY phase. However, more details need further study. 3.2 Microstructure of T6 treated alloys Figure 4 shows the optical micrographs in vertical section of T6 treated samples. The average grain sizes of ZMT614 and ZMT614í0.5Y alloys are 60.8 and 52.8 È�m, respectively. A mass of tiny precipitations dispersed in the matrix. EDS analysis indicates that they are Mg 2 Sn and MgZn 2 phases. However, the density of the precipitations in ZMT614í0.5Y is much higher than that in ZMT614, explaining that the Y elements or its intermetallic could promote the precipitates nucleation and growth. Some big irregular blocky compounds disperse at triple points of the grain boundaries. EDS Fig. 4 Optical micrographs of T6 treated samples: (a) ZMT614; (b) ZMT614í0.5Y Guang-shan HU, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3070í3075 3073 analysis reveals that they are MgSnY phase. The MgSnY ternary phase may act as crack source during deformation. The XRD patterns of solid-solution and T6 treated samples are shown in Fig. 5. After being solution treated, the diffraction peaks of MgZn 2 disappear, indicating that the phase dissolved into the matrix completely. Due to the fact that the melting temperature of MgSnY phase is much higher than the solution temperature, the phase cannot dissolve into the matrix during solution treatment and precipitate in the following T6 treated process [18]. The solid solubility of Zn and Sn declines dramatically as the temperature decreases [19]. As a result, large amount of Mg 2 Sn and MgZn 2 precipitate during the aging. Fig. 5 XRD patterns of ZMT614 (a, b) and ZMT614-0.5Y (c, d) alloys at different states: (a, c) Solid-solution treated state; (b, d) T6 treated state Figure 6 shows the SEM micrographs in vertical section of T6 treated samples. The extremely fine MgZn 2 and Mg 2 Sn precipitates dispersed in the grains and at boundaries. The T6 treated sample has been not changed in the macro-morphology of the MgZn 2 and Mg 2 Sn phase obviously. Nevertheless, the macro-morphology of MgSnY phase changes obviously, transforming from irregular blocky to petal shape. The MgSnY phases are much bigger than the others. 3.3 Mechanical properties Table 2 shows the tensile results of as-extruded and T6 treated ZMT614 and ZMT614í0.5Y alloys. It is interesting to note that the ultimate tensile strength (UYS) and elongation (EL) of as-extruded ZMT614í 0.5Y increased obviously compared with ZMT614. While the yield strengths (YS) of both alloys are almost the same. The UTS and YS of T6 treated sample increase, while the EL decreases obviously. Under T6 treatment, the EL of ZMT614í0.5Y alloy increases by 1.68% compared with ZMT614 alloy. In conclusion, the YS, UTS and EL of ZMT614í0.5Y alloy are improved by adding Y element both in as-extruded and T6 states. Fig. 6 SEM micrographs of T6 treated samples: (a) ZMT614; (b) ZMT614í0.5Y Table 2 Tensile properties of as-extruded and T6 treated ZMT614 and ZMT614í0.5Y alloys Alloy State UTS/MPa YS/MPa EL/% As-extruded 338 254 15.7 ZMT614 T6 367 353 5.27 As-extruded 350 259 18.3 ZMT614í0.5Y T6 372 367 6.93 For the as-extruded alloys, the YS improvement consists of grain boundary strengthening and solid solution strengthening. Therefore, the YS of as-extruded alloy is expressed as [16] ys Mg gb ss VVVV (1) where ı Mg =21 MPa [16] for a pure Mg; ı gb and ı ss are grain boundary strengthening and solid solution strengthening, respectively. The grain boundary strengthening ı gb can be estimated by the HallíPetch law: 1/2 gb Mg kdVV (2) where k is a parameter determined by the polycrystalline materials, and k=220 MPa·È�m 1/2 for Mg alloys [16]; and d is the average grain size. Then, ı gb is calculated to be 110 and 119 MPa for ZMT614 and ZMT614í0.5Y alloys, respectively. Guang-shan HU, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3070í3075 3074 Considering that Zn and Sn are the main solid solution strengthening elements in the alloys, the solid solution strengthening ı ss can be described by 3/2 3/2 3/2 2/3 ss Zn Zn Mn Mn Sn Sn ()kC kC kCV (3) where k Zn , k Mn and k Sn are the strengthening constants, k Zn = 905 MPa/% 2/3 and k Mn =196 MPa/% 2/3 [20] in the alloys. It is linear combination of the atomic size, shear modulus and valency difference. The atomic size, shear modulus and valency difference of Sn are almost to Zn, thus, k Sn =905 MPa/% 2/3 is estimated. The C Zn and C Sn are the concentration of the solution in mole fraction (%). The assumption is that no interaction exists between Zn and Sn. Substituting k and C (see Fig. 3) into Eq. (3), the calculative solid solution strengthening values of ZMT614 and ZMT614í0.5Y alloys are 117 and 105 MPa, respectively. The theoretical calculation values of YS of ZMT614 and ZMT614í0.5Y alloys are 248 and 245 MPa, respectively, which are quite close to the experimental values of the as-extruded alloys. The discrepancy may be concerned with the inaccurate parameters and simplified solid solution elements interaction models used for prediction. However, the theoretical calculated values combined with experimental values state that the YS enhancement of as-extruded alloys originates from grain boundary strengthening and solid solution strengthening. Under T6 treated state, most of Zn, Mn, Sn and Y elements are consumed to form precipitates. Consequently, the solid solution strengthening is substituted by the precipitation strengthening. The YS of T6 treated alloys is expressed as ys Mg gb ppt VVVV (4) where ı ppt is the contribution of precipitation strengthening. The ı gb values of ZMT614 and ZMT614í0.5Y treated by T6 are 49 and 51 MPa, respectively. The Orowan mechanism is operative for precipitation strengthening, so ı ppt is described by ppt tt v t t 2 1- 0.825 ( 0.393 0.886 ) Gb dt f d t V Q u ± tt 0.886 ln dt b (5) where G is the shear modulus of the pure Mg; b is the magnitude of the Burgers vector; È£ is the Poisson ratio; d t is the mean diameter of the precipitations; t t is the average thickness of the precipitations; and f v is the volume fraction of the precipitates. As shown above, the precipitation values of d t , t t and f v in ZMT614í0.5Y alloy are higher than those of ZMT614 alloy. And the ı ppt is proportional to d t , t t and f v . So, the YS of ZMT614í0.5Y alloy is much higher than that of ZMT614 alloy. The YS of T6 treated ZMT614 alloy is ı ppt +70 MPa and the ZMT614í0.5Y is ı ppt + 72 MPa. As a result, the precipitation strengthening exerts the dominating effects on YS enhancement of these alloys in T6 treated state. Figure 7 shows the fracture surface morphologies of the T6 treated samples. Some deep cracks are observed (marked by arrows in Fig. 6). Furthermore, there are a quite large number of cleavage facets on the surface of ZMT614 alloy, the fracture of the alloy belongs to cleavage regime. Many cleavage facets besides small-sized dimples are on the surface of ZMT614í0.5Y alloy, which reflects that the fracture of the alloy belongs to quasi-cleavage regime. The cleavage facets of ZMT614í0.5Y alloy are much smaller than those of ZMT614 alloy. This indicates that a large amount of dispersed precipitations inhibit the dislocation motion and cracks propagation. In consequence, adding Y element can change the fracture mode and improve the comprehensive mechanical properties. Fig. 7 SEM micrographs of fracture surface of T6 treated samples: (a) ZMT614; (b) ZMT614í0.5Y 4 Conclusions 1) After adding Y element to ZMT614 alloy, a new MgSnY ternary phase is formed. The T6 treated sample cannot change the phase compositions. The phase compositions of ZMT614í0.5Y in as-extruded and T6 Guang-shan HU, et al/Trans. Nonferrous Met. Soc. China 24(2014) 3070í3075 3075 states both are Ä®-Mg, MgZn 2 , Mn, Mg 2 Sn and MgSnY phases. 2) The Y element refines the grains of ZMT614í0.5Y alloy in as-extruded and T6 treated states. Compared with ZMT614 alloy, the UTS, YS and EL of ZMT614í0.5Y alloy in as-extruded and T6 states are improved. 3) For the ZMT614 and ZMT614í0.5Y alloys, the grain boundary strengthening and solid solution strengthening make the same contribution to the YS enhancement in as-extruded state. However, the precipitation strengthening exerts the dominating effect on the YS enhancement in T6 treated state. References [1] MAO Ping-li, YU Jin-cheng, LIU Zeng, DONG Yang. Microstructure evolution of MgíGdíYíZr magnesium alloy under dynamic compression [J]. Journal of Magnesium and Alloys, 2013, 1(1): 64í75. [2] XU D K, LIU L, XU Y B, HAN E H. The influence of element Y on the mechanical properties of the as-extruded MgíZníYíZr alloys [J]. Journal of Alloys and Compounds, 2006, 426(1í2): 155í161. [3] ZHANG Ding-fei, QI Fu-gang, LAN Wei, SHI Guo -liang, ZHAO Xia-bing. Effects of Ce addition on microstructure and mechanical properties of Mgí6Zní1Mn alloy [J]. Transactions of Nonferrous Metals Society of China, 2011, 21(4): 703í710. [4] BAE D H, KIM S H, KIM D H, KIM W T. Deformation behavior of MgíZníY alloys reinforced by icosahedral quasicrystalline particles [J]. Acta Mater, 2002, 50(9): 2343í2356. [5] WU Guo-hua, ZHANG Yang, LIU Wen-cai, DING Wen-jiang. Microstructure evolution of semi-solid Mgí10Gdí3Yí0.5Zr alloy during isothermal heat treatment [J]. Journal of Magnesium and Alloys, 2013, 1(1): 39í46. [6] FANG Xi-ya, YI Dan-qing, WANG Bing, LUO Wen-hai, GU Wei. Microstructure and mechanical properties of Mgí6Alí1ZníY alloys [J]. Chinese Journal of Rare Metals, 2006, 6(30): 724í728. (in Chinese) [7] WU Yu-juan, DING Wen-jiang, PENG Li-ming, ZENG Xiao-qing, LIN Dong-liang. Research progress of advanced magnesium rare-earths alloys [J]. Materials China, 2011, 2(30): 1í9. (in Chinese) [8] SASAKI T T, OH-ISHI K, OHKUBO T, HONON K. Effect of double aging and microalloying on the age hardening behavior of a MgíSníZn alloy [J]. Materials Science and Engineering A, 2011, 530: 1í8. [9] YANG Ming-bo, CHENG Liang, PAN Fu-sheng. Effect of calcium addition on as-cast microstructure and mechanical properties of Mgí5Sní5Zn alloys [J]. Transactions of Nonferrous Metals Society of China, 2011, 5(20): 769í775. [10] SON H, LEE J, JONG H, KONNO T J. Effects of Al and Zn additions on mechanical properties and precipitation behaviors of MgíSn alloy system [J]. Mater Letters, 2011, 12(65): 1966í1969. [11] ZHAO Hao-feng, WANG Ling, YAN Kai, SUN Lei, ZHANG Shuai, LI Qing-fang, LEI Yong. Effect of Zn on the morphology and properties of magnesiumítin alloys [J]. Rare Metal Materials and Engineering, 2010, 39(S1): 86í88. (in Chinese) [12] LIU Bing. The microstructure and mechanical properties of MgíSn alloys [D]. Shenyang: Shenyang University of Technology, 2012: 8í10. (in Chinese) [13] CHENG Wei-li, PARK S S, TANG Wei-neng, YOU B S, KOO B H. Influence of rare earth on the microstructure and age hardening response of indirect-extruded Mgí5Sní4Zn alloy [J]. Journal of Rare Earth, 2010, 5(28): 785í789. [14] ZHAO Hong-da, QIN Gao-wu, REN Yu-ping, PEI Wei-li, CHEN Dong, GUO Yun. Microstructure and tensile properties of as-extruded MgíSníY alloys [J]. Transactions of Nonferrous Metals Society of China, 2011, 21(S2): s493ís497. [15] WANG J, FU J, DONG X, YANG Y. Microstructure and mechanical properties of as-cast MgíAlíSníYíNd alloy [J]. Mater Design, 2012, 36: 432í437. [16] LIU Chu-ming, ZHU Xiu-rong, ZHOU Hai-tao. The magnesium alloys phase diagram [M]. Changsha: Central South University Press, 2006: 287í291. (in Chinese) [17] ZHANG L, GONG M, PENG L M. Microstructure and strengthening mechanism of a thermomechanically treatment Mgí10Gdí3Yí 1Sní0.5Zr alloy [J]. Materials Science and Engineering A, 2013, 565: 262í268. [18] LIU H, CHEN Y, TANG Y, WEI S, NIU G. The microstructure, tensile properties, and creep behavior of as-cast Mgí(1í10)%Sn alloys [J]. Journal of Alloys and Compounds, 2007, 440(1í2): 122í126. [19] OH-ISHI K, MENDIS C L, HOMMA T, KAMADO S, OHKUBO T, HONNO K. Bimodally grained microstructure development during hot extrusion of Mgí2.4Zní0.1Agí0.1Caí0.16 Zr (at.%) alloys [J]. Acta Mater, 2009, 18(57): 5593í5604. [20] GAO L, CHEN R S, HAN E H. Effects of rare-earth elements Gd and Y on the solid solution strengthening of Mg alloys [J]. Journal Alloys and Compounds, 2009, 481(1í2): 379í384. ᣸य़ᗕ੠ᯊᬜᗕMgíZníMníSníYড়䞥ⱘ㒘㒛ᗻ㛑 Ü‘à±–Ú› 1,2 ē჆Հׄ 1,2 ēვՀϿ 1,2 ēኚ ຑ 1,2 ēߠឪ྇ 1,2 ē૬Ø�ಓ 1,2 1. 䞡ᑚ໻ᄺ ᴤ᭭⾥ᄺϢᎹ⿟ᄺ䰶ˈ䞡ᑚ 400045Ë—2. 䞡ᑚ໻ᄺ ೑ᆊ䬕ড়䞥ᴤ᭭Ꮉ⿟ᡔᴃⷨã�ŠÐ�ᖗˈ䞡ᑚ 400044 ᨬ 㽕˖Ü�⫼߽ᄺᰒᖂ䬰ǃX ᇘ㒓㸡ᇘ੠ᠿᦣ⬉䬰ã„�á‡�᣸य़ᗕ੠ᯊᬜᗕ Mgí6Zní1Mní4Sn à©  Mgí6Zní1Mní 4Sní0.5Y䬕ড়䞥ⱘᖂ㾖㒘㒛੠࡯ᄺᗻ㛑䖯㸠ⷨã�ŠÇ„㒧ᵰ㸼ᯢ Ϣ˖ ZMT614䬕ড়䞥Ⳍ↨ â��ˈࡴ Yܗ㋴ৢ ZˈMT614í 0.5Y᱊㉦ᕫࠄ㒚࣪ ã“�ˈড়࡯ᄺᗻ㛑ᕫࠄᦤ催DŽMgí6Zní1Mní4Sní0.5Yড়䞥ⱘⳌ㒘៤Ў Ä®-MgǃMgZn 2 ǃMnǃMg 2 Sn à© MgSnYⳌDŽ㒣䖛 T6â›�໘⧚ৢ ড়ˈ䞥ⱘᡫá¢�ᔎᑺ੠ሜ᳡ᔎᑺᯢᰒᕫࠄᦤ催 Ԍˈ䭓⥛ᯢᰒ㹿䰡ԢDŽ⧚䆎䅵ㅫ㸼ᯢˈ ೼᣸य़ᗕড়䞥Ð�ˈ㒚᱊ᔎ࣪੠೎⒊ᔎ࣪ѻ⫳䞡㽕ⱘ԰⫼ˈ㗠೼ T6â›�໘⧚ᗕড়䞥Ð�ˈᵤߎᔎ࣪ѻ⫳އᅮ԰⫼DŽ ݇䬂䆡˖MgíZníMníSníYড়䞥˗Y˗᣸य़˗T6˗ᰒᖂ㒘㒛˗ᔎ࣪ᴎࠊ (Edited by Xiang-qun LI) 013, 1(1): 39í46. [6] FANG Xi-ya, YI Dan-qing, WANG Bing, LUO Wen-hai, GU Wei. Microstructure and mechanical properties of Mgí6Alí1ZníY alloys [J]. Chinese Journal of Rare Metals, 2006, 6(30): 724í728. (in Chinese) [7] WU Yu-juan, DING Wen-jiang, PENG Li-ming, ZENG Xiao-qing, LIN Dong-liang. Research progress of advanced magnesium rare-earths alloys [J]. Materials China, 2011, 2(30): 1í9. (in Chinese) [8] SASAKI T T, OH-ISHI K, OHKUBO T, HONON K. Effect of double aging and microalloying on the age hardening behavior of a MgíSníZn alloy [J]. Materials Science and Engineering A, 2011, 530: 1í8. [9] YANG Ming-bo, CHENG Liang, PAN Fu-sheng. Effect of calcium addition on as-cast microstructure and mechanical properties of Mgí5Sní5Zn alloys [J]. Transactions of Nonferrous Metals Society of China, 2011, 5(20): 769í775. [10] SON H, LEE J, JONG H, KONNO T J. Effects of Al and Zn additions on mechanical properties and precipitation behaviors of MgíSn alloy system [J]. Mater Letters, 2011, 12(65): 1966í1969. [11] ZHAO Hao-feng, WANG Ling, YAN Kai, SUN Lei, ZHANG Shuai, LI Qing-fang, LEI Yong. Effect of Zn on the morphology and properties of magnesiumítin alloys [J]. Rare Metal Materials and Engineering, 2010, 39(S1): 86í88. (in Chinese) [12] LIU BiMicrostructures and mechanical properties of extruded and aged Mg–Zn–Mn–Sn–Y alloysThe microstructures and mechanical properties of Mg–6Zn–1Mn–4Sn and Mg–6Zn–1Mn–4Sn–0.5Y alloys under extrusion and T6 aging conditions were investigated by optical microscopy (OM), X-ray diffraction (XRD), scanning electron microscopy (SEM) and tensile test. The results show that Y element refines the grains and improves the comprehensive mechanical properties of ZMT614–0.5Y both in as-extruded and T6 states. The phase compositions of Mg–6Zn–1Mn–4Sn–0.5Y are α-Mg, MgZn2, Mn, Mg2Sn and MgSnY phases. After T6 treatment, the ultimate tensile strength (UTS) and yield strength (YS) increase while the elongation decreases severely. For both of these alloys, the theoretical results combined with the experimental values demonstrate that the grain boundary strengthening and solid solution strengthening play an important role in enhancing the YS in the as-extruded state, while the precipitation strengthening is the key factor for the enhancement of YS in the T6 state.Shear capacity of steel plate girders with large web openings, Part I: Modeling and simulationsNumerical simulations are carried out in order to provide data for the development of a design model for the shear capacity of steel girders with web openings, with and without transverse stiffeners and opening reinforcements. The numerical model is designed such that the girder is in a state of pure shear at the opening center. Results are presented in terms of ultimate shear capacity and distribution of transverse web deformations and von Mises stresses. Based on the numerical data, a design model is presented that accounts for the reduction in web shear area, shear buckling of the web and the effect of opening position, vertical stiffeners and opening reinforcements.Plate girders with large web openings are commonly used in offshore platforms for oil and gas exploration and production. Often production and drilling of wells take place simultaneously, requiring the processing of oil and gas, drilling mud and various chemicals. Due to space limitations, it is inevitable that process pipes, electrical and instrumentation cables and ventilation ducts have to be routed through the girder webs. Beams and girders with web openings are also common in land based industry, and the topic has been extensively covered in literature.Distinction is commonly made between stocky web, i.e. webs where the yield shear strength can be developed over the full web height, and slender webs where buckling will limit the shear capacity. In the former case reference is made to the contributions of Bower et al. The rotated stress field method for slender web developed by Höglund However, many of these methods may not always satisfy the need of the practicing engineers for a simple estimation of girder strengths at an early design stage. Simplicity of method is highly desirable because the value of any calculation decreases sharply if it is not completed before the design is frozen. Maybe 80% of all web openings are of a relatively small size, or they are located in positions where the shear capacity is far from fully utilized. It would be more convenient to check girders with such openings based on design guidelines in combination with a simple formula, than on comprehensive calculations.The present study is motivated by this need for simple guidelines that can be used in practical design of girders in building and offshore structures. The response of 260 girder and opening configurations were carried out by means of the non-linear finite element program ABAQUS. Results from previous experiments for large plate girders were used to calibrate the finite element models in order to ensure that reliable models are used in the simulations. The simulations comprise girders with webs of h/t ratios from 63 to 333. The openings were circular, elongated circular, square and rectangular, with and without sleeves, doubler plates, transverse stiffeners and horizontal reinforcement. The opening size varied from 0.25h to 0.50h, and both single and closely spaced openings were considered. depicts some of the opening configurations considered.The starting point of the proposed design model for girders with openings is the shear buckling capacity of slender girder webs given by EN 1993-1-5  Here h and t are the web height and thickness respectively, and fdw=fyw/γM1 is the design stress for the web. χw is the buckling reduction factor and γM1 is the material factor.When designing girders with web openings, it is tempting to use the same design format as for girders without openings. All effects on the shear capacity from web openings should preferably be included in a modified reduction factor χw,mod. In addition to buckling, this reduction factor, or function, should also account for the effect of the reduced shear area of the web and of all secondary and tertiary effects of the presence of the opening. Hence, according to Hagen  It should be emphasized that this is not a new load-carrying model; it is a system of organizing experimental data, theoretical methods and numerical simulations. The results can be used directly for design purposes, and various effects and theories can be compared. The presentation of the shear capacity is similar to that of the rotated stress field method and the modified Vierendeel method. The results from such methods can be included directly in the design procedure. For openings not covered by these methods, numerical simulations may be sufficient to establish the functions χw,mod without the need for supporting load-carrying theories.A similar approach may be taken for the moment capacity, and the resulting shear and primary moment capacities may be used in interaction equations, derived from moment-shear interaction equations for girders without openings.The reduction factor χw,mod may be given by diagrams, tables, equations or spread-sheets. In principle, one diagram is needed for each opening configuration. The term “opening configuration” defines an opening shape, size and location, as well as possible stiffeners and reinforcement. Each such diagram or table may cover several opening shapes and dimensions. However, the total number of diagrams would soon be more confusing than informative. To limit the number of diagrams, it is necessary to split χw,mod into factors depending on primary, secondary and tertiary effects of the presence of the opening: Here, the factors c1,c2 and c3 depend on the primary, secondary and tertiary parameters, respectively.Of the 260 simulations performed, the first 41 simulations were related to verification of the ABAQUS models as explained in Section . Most of the remaining simulations aimed at finding the factors c1,c2andc3. For the interpretation of the results, it was necessary to design a simulation program that allowed the effects of the various parameters to be separated. For this purpose a basic set of 24 girder configurations comprising a single circular opening at the center of girder with two D/h ratios, three h/t ratios, and four spacings of transverse web stiffeners were chosen. By means of the simulated ultimate load and Eq. , a basic set of reduction factors χw,mod,basic was determined: c1=χw,mod,basic≡χw,modwhen c2=1 and c3=1. The effect of the secondary parameters was determined by varying the vertical position of the single opening, the horizontal and vertical spacing of multiple openings, the spacing of transverse web stiffeners and adding sleeves and doubler plates. Also elongated circular, square and rectangular openings were included, with and without horizontal reinforcement. This allowed the secondary reduction factors χw,mod,sec to be determined. The adjustment factor c2 is by definition given by In any simulation, it is imperative that the numerical models to be used are verified against analytical or experimental data. Here, experimental data from a previous investigation These five factors were studied by means of numerical simulations and half-fractional factorial design at two levels. The factors give 32 combinations for each girder, but assuming that higher order interaction is negligible the number of combinations was reduced to 16 for each girder. From this study it was concluded that the two most important factors are the imperfection shape and amplitude, which could be represented by the first eigenmode with an amplitude of 0.75% of the web height.The experimental and simulated response curves for the two girders are shown in . As seen, the simulations agree quite well with the experiments both in term of ultimate capacity and ductility. It was thus deemed that the FE models used were sufficiently accurate.In another nine FE-models, elastic stress and plastification around openings were studied, as well as the effect of two versions of the ABAQUS program.The main objective of the subsequent 219 FE simulations was to provide a basis for the determination of the factors c1 and c2 of the proposed design procedure. With various aspect ratios, web thicknesses, opening shapes and configurations many different models were required, as each simulation requires a new model. However, it was considered important to use one “fundamental” girder for all these simulations. This in order not to introduce more uncertainties from shift between two or more girders than from those connected to the variables themselves. It was also evident from the verification study that the length of the girder on either side of the opening should be long enough to ensure that the stiffness of the web corners is not overestimated. Further, it should be possible to investigate aspect ratios up to 4, as well as two openings horizontally spaced. Hence, the starting point for the modeling was simple girders with dimensions 1.0×4.0 m without openings. Typical web thicknesses were 4, 8 and 16 mm. Subsequently, single and multiple openings and reinforcement in the form of stiffeners, sleeves and doubler plates were introduced.Whereas the girders of the experimental investigation were subjected to a combination of shear and moment at the opening, it was decided to use a model that gave shear only at the opening center in the simulations. This was done in order to be consistent with the design model in EN 1993-1-5, which uncouples the shear and moment behavior.A state of pure shear at the opening center is difficult to achieve both in physical and numerical models of girders. In the present study the loading and boundary conditions were chosen such that the bending moment at this location was zero. The chosen static system is depicted in . At the left (clamped) end of the girder all nodal translations were restrained, while the nodes at the right (free) end were coupled to a lever arm with large bending stiffness EI. The lever arm extended to the center of the opening. The “load” was applied in the form of a vertical displacement at the tip of the lever arm, resulting in a state of shear only at the center of opening.A typical mesh for a girder with a circular opening of diameter D=0.50h is shown in . The lever arm has a trapezoidal/rectangular shape and is attached to the web at the right end of the girder.The choice of initial web imperfections was guided by the verification study, and was based on the eigenmodes that gave the largest buckle at the opening. The imperfection amplitude was taken as 7.5 mm for all girders, except for those with aspect ratio 0.5, where an amplitude of 4.05 mm was used.Two geometrically linear simulations, i.e. with the transverse displacement of the web restrained, were carried out in order to determine if the element models described in Section Three nonlinear simulations were carried out for girders without openings in order to check simulated ultimate capacity against the design rules in EN 1993-1-5 assuming rigid end posts. For h/t ratios equal 125 and 250 the results agreed very well, while the simulated capacity was slightly lower for h/t=63.Furthermore, the results from nine FE models were compared with those from Höglund’s rotated stress field method . The girders are identified by the legend HxxxCyy. Here, H denotes the girders studied by Höglund, xxx is the web slenderness and Cyy indicates a circular opening with diameter equal yy% of the web height. As seen from the rotated stress field method overestimates the capacities by up to 21% for girders without openings, whereas the discrepancy is at most 9% for girders with openings. Compared to the rotated stress field method the results from the simulations can therefore be considered to be conservative.All the response curves showed a ductility similar to the curves for girders S1 and S3 in , and no sudden loss of strength was observed. For the parameter study, only the ultimate shear force V in terms of the reduction factor χw,mod was directly used, and is presented in the following tables. As only the spatial distribution of the transverse web displacements and web stresses at ultimate shear are of interest, no numerical values are attributed to the plots. In order to make comparison between many plots easier, a limit of 5 mm is set for all plots of displacements and a limit of the yield stress is set for all plots of von Mises stress. See for instance (a) where the grey region in the center part of web and the dark regions at the ends had displacements exceeding 5 mm. In (b) the grey areas depict where the yield stress is exceeded. Because of the elastic-plastic material assumed in the analyses, the stress never exceeded the yield stress more than 1% at any point in any model.(a) shows the distributions of the transverse web displacement at ultimate shear are for girders H125, H125C25 and H125C50, i.e. the girders used in the comparison with the rotated stress field model. The maximum transverse displacements at ultimate shear are 20 mm, 23 mm and 24 mm for H125, H125C25 and H125C50, respectively. This indicates that the opening dimensions have relatively little influence on the transverse displacements at maximum shear.The corresponding von Mises stress on the web surface at ultimate shear is depicted in (b). Due to the variation in the curvature across the diagonal buckle, three plastified diagonal stress bands form.In order to organize and ease the interpretation of the numerical results, a set of 24 basic web configurations were chosen. These encompass three web slendernesses, two circular opening diameters and four spacings between transverse web stiffeners. The geometric data for the girders are given in The girder legends are as defined in Section , but with “I” denoting a girder with material properties as given in Section . The presence of transverse stiffeners is indicated by the label “T” followed by a digit defining the spacing; T2 for aspect ratio 2, T1 for aspect ratio 1 and T0 for ratio 0.5. All transverse stiffeners had dimensions hst/tst=8 and satisfy the EC3 stiffness requirement for plain girders.Based on the simulated ultimate loads and Eq. the reduction factor χw,mod was determined for all 24 girder configurations of the basic set, and for the 12 corresponding girders without openings. The values of χw,mod are plotted as a function of the relative slenderness λ̄w in . In the figure, the values for D/h=0 (no opening) are represented by the crosses, and those for opening sizes D/h=0.25 and D/h=0.50 by small and large circles, respectively. λ̄w is determined with a shear buckling factor kτ=5.59 for girders with aspect ratio 4, kτ=6.59 for ratio 2, and kτ=9.34 and kτ=25.36, respectively, for ratios 1 and 0.5. The shear buckling curve of EN 1993-1-5 for girders with rigid end posts and η=1,0 is also plotted in the figure.As can be seen, four of the twelve χw,mod values for girders without openings deviate significantly from the EC3 curve. These are the girders I125T1, I250T0, I250T1 and I250T2, i.e. slender girders with closely spaced transverse stiffeners. For these girders the tension field effect is prominent, an effect that is not fully accounted for in EC3. The tension field action is also present for girders with openings, but the relative contribution of the tension field decreases with increasing opening size. For D/h=0.50 the simulated values agree quite well with the EC3 curve scaled to 50%, which is in accordance with the theory of Narayanan et al. The effect of vertical stiffeners is also shown in . Here the transverse web deformations at ultimate shear are depicted for four of the basic girders. The three girders I125C50T1, I125C50T2 and I125C50T0 are developed from girder I125C50 by adding transverse stiffeners. As expected the inclination of the tension field increases with decreasing spacing. Also, the presence of closely spaced stiffeners restricts the buckled part of the web to the panels next to the opening.For small values of the relative slenderness λ̄w it may be assumed that the primary effects can be represented simply by scaling the shear capacity of the full web by the ratio between the net and gross area web area. This suggests a reduction factor in the form This gives a scaling factor of 75% and 50% respectively for D/h=0.25 and D/h=0.50, and the corresponding scaled shear buckling curves are plotted in the figure. As can be seen, the simulated values for D/h=0.25 and D/h=0.50 agree quite well with Eq. for small values of λ̄w, while the equation underestimates the capacity for larger values. Again, the agreement is poorest for the girders with closely spaced vertical stiffeners. For design purposes it is deemed that the accuracy of Eq. As previously noted, the secondary effects are due to the shape and vertical position of the opening, the distance between two openings and the amount of reinforcement around the opening. The adjustment factor c2 is intended to account for the effect of all these parameters. Of these only the effects on circular openings are described here. Adjustment factors for non-circular openings are presented in By definition c1=1.0 for the basic set of girders, and c2 is simply given as the ratio between the reduction factors for the modified girders and those for the basic girders, as given by Eq. The transverse web deformation is given in for girders I125C50 and M125C50 at ultimate shear. Clearly, the shift has changed the load carrying mechanism completely, as the shape and the inclination of the diagonal tension band have changed. It was observed that the maximum transverse web displacement at maximum shear increased from 38 mm for I125C50 to 61 mm for M125C50.The reduction factors χw,mod,basic and χw,mod,vert, as well as the factor c2 are presented in The effects of local stiffening of the openings by means of sleeves were also investigated. In the strict sense a sleeve means a ring-shaped stiffener that goes through the opening, such that the stiffener is symmetric with regard to the web plane. However, to simplify fabrication it may be preferred to weld ring-shaped stiffeners on one side of web only. In this case stiffeners are often placed 10–20 mm from the edge of opening to allow fillet welds all around. For the girders considered the sleeve dimensions were chosen such that the weight of the sleeve was equal to the weight of the removed plate in the opening. The width/thickness ratios of sleeves were 6 and 8.A total of 24 girders with sleeves were studied, of which only the six girders without vertical stiffeners are discussed here. The girders are identified by labels starting with the letter “SL” for sleeve. This implies that girder SL63C50 is identical to I63C50, except for the presence of the sleeve. shows the reduction factors χw,mod,basic and χw,mod,sl and the adjustment factor c2 for these girders. As can be seen, the effect of the sleeve is less than 7% for girders with D/h=0.25, while the capacity has increased by up to 50% for girders with D/h=0.50. This is to be expected as the sleeve contributes more to the “global” stiffening for the largest opening.The reduction factor χw,mod for all girders with sleeves are plotted in . The EC3 curve for χw is also plotted, but with an upper limit of 0.75 and 0.50 for D/h=0.25 and D/h=0.50 respectively. For the former case the sleeves increase the capacity to that of girders without openings for λ̄w>1, while the slenderness limit is 2.0 for the latter case.Doubler plates are commonly welded to one or both sides of the web to increase the capacity. The plates have an outer diameter Do and an inner diameter Di, both larger than the opening diameter. It has been recommended in the literature that heavy plate dimension should be used in order to restore the full capacity.Six simulations of girders with doubler plates were performed. The results are included in . Two alternative dimensions were considered for the doubler plates; small plates with Do/Di=384/280 mm and large plates with Do/Di=530/280 mm. The thickness td varied between 4 and 16 mm. The prefix of the label for these girders is “D” for doubler and the trailing label is “S” for small and “L” for large plates. The small plates have the same weight as the weight of the removed web material, while the weight ratio is 3 for the large ones. The small plates increase the shear capacity by at most 9%, while an increase of up to 14% is achieved with the large plates.Two or more adjacent openings spaced along the web are common in practical design of girders, but scarcely described in the literature. Here, simulations were carried out both for girders with two openings horizontally and vertically spaced. depicts the transverse web deformation at maximum shear for the former case. Using the girders I63C50 and I125C50 as reference, four values of the opening spacing in horizontal direction were studied, and the prefix R,S,T and U in the girder labels refer to the horizontal c/c distance ca between the openings. In the present study ca was chosen as 1.04D,1.5D,2D and 3D respectively. In all girders the webs had an aspect ratio equal 4.The reduction factor χw,mod and the adjustment factor c2 are listed in for the eight girders with two horizontally spaced openings. Sa is the clear distance between the openings.The adjustment factor, c2, is plotted as a function of the spacing in . As seen, c2 increases smoothly with increasing values of the spacing. For the thickest web there is no interaction effect between the two openings when Sa≥2D. In order to ensure that a plastic mechanisms involving interaction between the openings will not appear, AISC Two or more openings in the same vertical section of girder occur infrequently in practice, and this situation is not covered in literature. Eight such girders were analyzed, using girders I63C25 and I125C25 as references. shows the transverse web deformation for variations of girder I125C25. The vertical c/c distance ch between the openings was chosen as 1.08D, 1.5D, 2D and 3D. In order to identify the girders the labels were given the prefixes RH,SH,TH and UH respectively.The reduction factor χw,mod and the adjustment factor c2 are listed in for the girders with vertically spaced openings, and c2 is also plotted as a function of the spacing in . Sh is the clear distance between the openings. It is observed that the vertical spacing has little effect on the shear capacity.Numerical simulations have been carried out to determine the ultimate shear capacity of steel girders with web openings. The opening configurations considered encompassed single and multiple openings with rectangular and circular shape, as well as openings with stiffeners and doubler plates. The objective of simulations was to establish a data base that could be used to derive a simple model suited for practical design purposes.The simulations were carried out by means of the FE program ABAQUS, using a model that gave a state of pure shear at the center of the opening. The element models were verified against experimental data from a previous investigation. Both element meshes and representation of initial deformations were considered. Results are given for single circular openings with various diameters, single circular opening in the lower part of a web, single circular opening with vertical stiffeners and two circular openings horizontally or vertically spaced. Similar results for elongated circular openings, square and rectangular openings are presented in Hagen The simulations confirmed that the main reduction in shear capacity for girders with openings could be given by the factor (1−Dh/h). Reduction due to buckling can be covered by χw, i.e. the same reduction factor as for plain webs provided that the adjustment factor c2 is assigned an appropriate value.Hence, the shear capacity of girders with openings may, in general, be given by The adjustment factor, c2, must account for a wide range of design situations. Based on Eq. design guidelines have been developed that cover the most common opening configurations, interaction between moment and shear and requirement for stiffeners and doubler plates Influence of hot isostatic pressing temperature on microstructure and tensile properties of a nickel-based superalloy powderA high strength high γ′ fraction nickel-based superalloy powder RR 1000 has been hot isotatically pressed (HIPed) at different temperatures. Microstructural analysis and assessment of the tensile properties were performed on these samples. It was found that HIP led to the formation of (Hf,Zr)O2 particles on prior particle boundaries (PPBs) which were not present in the as-received powder. It is suggested that the oxides are formed by the diffusion of Hf and Zr from the interior of powder particles to the particle surfaces where oxygen level is usually high. When different HIP temperatures were used, no obvious effect on oxide size and distribution was observed but there was an effect on the microstructure and tensile properties. Thus, HIPing at super-solvus temperatures reduced the density of PPBs over the density observed in samples HIPed at sub-solvus temperatures by making grains within the original powder particles grow beyond the precipitates on PPBs, resulting in larger grains with serrated boundaries. Slow cooling from HIPing temperatures also led to the formation of irregular-shaped γ′. The 0.2% yield strengths at room temperature and at 700 °C were found to decrease with increase of HIP temperature but the high temperature ultimate tensile strengths and elongation increased considerably. Increasing HIPing temperature from sub-solvus to super-solvus temperatures also led to the transition of fracture mode from interparticle debonding to transgranular fracture mode.The demand for improved jet engine efficiency and performance has resulted in the continued development of high strength polycrystalline superalloys. Concurrent with the increase in strength is a significant decrease in conventional hot workability complicated by extensive segregation in the cast ingots. The decrease in workability adversely affects the overall component cost and the ability to achieve the desired properties. This has spurred the development of powder metallurgy (PM) techniques for producing components of highly alloyed compositions to achieve the desired microstructures, properties, and cost effectiveness. One of the most common PM techniques is hot isostatic pressing (HIPing) which enables production of fully consolidated product with homogeneous microstructure. So far, HIPing has been used to consolidate advanced nickel-based powder superalloys such as Rene 95 Many attempts have been made to reduce or eliminate PPBs. Decreasing either oxygen or carbon level was reported to decrease PPBs by reducing PPB precipitate decoration The powder used in this study is an argon-atomized nickel-based superalloy powder and has a size range below 53 μm in diameter. The nickel-based superalloy used in this study is RR 1000 which contains alloying elements such as 6.6 wt% (Al+Ti), 2.5 wt% (Hf+Ta), 38.5 wt% (Co+Cr+Mo) and 0.048 wt% (C+B+Zr). The gamma prime solvus of this alloy is 1160 °C and the oxygen level of the as-received powder is around 200 ppm.Heat treatment was conducted on some powder to study their thermal response. The powder was first loaded into stainless steel 316L tubes which were then outgassed at room temperature for 20 h to achieve a vacuum level of 10−2

Pa before being sealed by closing the evacuation tubes by welding. Some were then heat treated at temperatures below or above gamma prime solvus (S) such as (S-310)°C, (S-260)°C, (S-53)°C and (S+40)°C, for 2 h and others were HIPed at S, (S-53)°C, (S-30)°C, (S+20)°C and at a pressure of 100 MPa for 4 h, followed by cooling at 5 °C/min to room temperature. The particle surfaces and sections of as-received and heat treated powders as well as the as-HIPed samples were then examined using scanning electron microscopy (SEM) in a JEOL 7000 FEG-SEM microscope. For observation of PPB precipitates, the samples were polished and/or chemically etched in activated colloidal silica solution and examined under SEM using back scattered electrons. For observation of gamma prime, the as-HIPed samples were electrolytically etched in 10% H3PO4 in H2O at 5 V for 2–5 s and observed using secondary electrons. The grain size and orientation of the as-HIPed materials were investigated using electron back scattered diffraction (EBSD). TEM examination together with EDX analysis was also conducted to analyse the precipitates at PPBs. Discs for TEM examination were cut from the as-HIPed samples and subsequently ground and electro-polished at −10 °C and 25 V in 10% perchloric acid in methanol. TEM analysis was carried out in an FEI TecnaiF20 FEG TEM microscope fitted with EDX facility. An accelerating voltage of 200 kV was used for the TEM analysis.Tensile tests were performed using a computer controlled electric screw driven Zwick/Z100 tensile testing machine on as-HIPed samples. The tests were conducted under strain control mode with an initial strain rate of 5×10−4

s−1. Tests were performed at both room temperature and 700 °C. Tensile fracture surfaces were examined using SEM. shows the particle surfaces and section structure of as-received powder. It can be seen that the as-received powder particles generally show a dendritic surface and show no precipitates on the surfaces; (b). The dendritic microstructure could be also observed on the section of particles; see (c). The interdendritic regions of the as-received powder usually appear bright by virtue of atomic number contrast in the back scattered electron SEM image, which suggests the presence of a higher concentration of high atomic number elements such as Hf and Zr. This was further verified by EDX analysis on the interdendritic and matrix areas (see (c)–(f)). A distinct Hf peak is present in the EDX spectrum of the interdendritic region but is absent in that of the adjacent matrix, suggesting the interdendritic regions may be rich in Hf. The high atomic number contrast in the interdendritic regions is continuous suggesting that the Hf, which is giving rise to this contrast, is not present as discrete particles but may be in solution, having been rejected during the initial solidification. Occasionally, some spherical precipitates (>2 μm) were found in the as-received powder particles and were found to be rich in Hf and O by EDX; see When heat treatment was carried out on the as-received powder no obvious change of the particle surface could be observed until the powder was heat treated to (S-260)°C and above, at which temperature very fine precipitates were formed on the particle surface (as shown in (b)). At increased temperatures the precipitates coarsened and became more discrete (((c) and (d))). Meanwhile, the particle surface changed from discreet regions to much rougher and increasingly integrated regions. The segregation of high atomic number elements such as Hf at interdendritic regions visible in sectioned powder particles (shown in ) was not completely removed until the powders were heat treated to (S-53)°C or above; see . This obvious dispersion from the interdendritic regions of the original segregation of Hf may be associated with the formation of the Hf particles on the surfaces of heat treated powders as shown in shows the PPB precipitates in the samples that were HIPed at different temperatures. It can be seen that HIPing temperature generally shows no influence on the size and distribution of precipitates, which is different from the above observation of heat treated powder samples. This may be due to that with simultaneous high pressure and temperature in a HIP run, the powder would be consolidated quickly, which suppresses the surface diffusion of elements on powder particles and thus suppress the diffusion- or coalesce-induced coarsening of precipitates (it is noted that free surface diffusion is generally faster than boundary diffusion . The PPB precipitates observed were basically smaller than 100 nm and seemingly decorated the PPBs continuously. However, it is shown that increasing HIPing temperature seems to promote grain boundaries to move across PPBs and thus leave the precipitates in the interior of coarsened grains. This becomes most pronounced in the sample that was HIPed at the highest temperature (S+20)°C in the current study, which is in sharp contrast to the sample that was HIPed at the lowest temperature (S-53)°C where grains tend to be confined by PPBs and thus precipitates were still present at PPBs, see . Meanwhile, it is noted that pronounced grain boundary serrations were developed in the samples HIPed at (S+20)°C, see (c) and (d). Moreover, increasing HIPing temperature leads to considerable increase of grain size, as shown in . Irrespective of HIPing temperature, grains in all the samples studied are randomly orientated. shows the gamma prime distribution in the samples that were HIPed at (S-53)°C, (S-35)°C, S and (S+20)°C. A tri-modal gamma prime distribution, composed of primary, secondary and tertiary γ′ can be seen in all the samples. The coarse primary γ′ are usually formed at grain boundaries and show a big size range from 1 to 5 μm and can exist in either a blocky morphology or script or dendritic morphology. As for secondary γ′, both the size and morphology change significantly with increasing HIPing temperature. When HIPed at (S-53)°C, most of the secondary γ′ show a near-cuboidal morphology while others show a jagged morphology on one side and all show a size of 300–800 nm. When HIPed at (S-35)°C, the size of secondary γ′ does not change very much (around 300 nm–1 μm) but the morphology has become dendritic. HIPing at higher temperatures like S or (S+20)°C led to even more irregular and complicated γ′ morphology with a much bigger size, basically in the range of 800 nm–1.6 μm. Tertiary γ′ basically show a very small size (<100 nm) and a spherical morphology. Obviously, secondary γ′ seem to be most sensitive to the HIPing temperature. shows the tensile properties of samples that were tested at both room temperature and 700 °C. It can be seen that HIPing temperature shows a significant influence on the tensile properties of the HIPed samples. At room temperature, the samples HIPed at (S+20)°C show a 100 MPa reduction in 0.2% yield strength, but show similar ultimate tensile strength (UTS) and elongation, as compared with the samples HIPed at (S-53)°C. At 700 °C, the samples HIPed at (S+20)°C showed an even lower 0.2% yield strength but much higher UTS and elongation than the samples HIPed at (S-53)°C (around 250 MPa and above 20% higher in magnitude, respectively). show the fracture surfaces of samples obtained from different HIPing processes after tensile testing at room temperature and 700 °C. It can be seen that samples HIPed at (S-53)°C showed an interparticle debonding fracture mode whereas those HIPed at (S-53)°C generally showed a ductile transgranular fracture mode.The observations have shown that the as-received powder particles show a dendritic microstructure with high-atomic number elements such as Hf segregated at interdendritc regions. The Hf here seemed to be present in solid solution (given its continuous decoration at interdendritic regions) rather than as discrete Hf compound particles of the type shown in (c) (see the red arrow). This interpretation, that the continuous contrast arises from Hf in solution, is also supported by the fact that the interdendritic enrichment of Hf was removed by high temperature heat treatment, which would not be expected if the Hf were in the form of oxides or carbides. As suggested from the data shown in this interdendritic Hf seemed to have diffused from the interior to particle surfaces to form Hf-rich oxides. This is further supported by the fact that Hf can be observed on the particle surface of heat treated powder (at (S-53)°C or above) by EDX but not on the surface of as-received powder particles (c)) or inclusion clusters during atomization The HIPing temperature shows a significant influence on both microstructure and tensile properties. Increasing HIPing temperature from sub-solvus to super-solvus made many grains grow beyond PPBs and left the precipitates in the interior of grains, which greatly reduced PPBs. Moreover, larger grains with serrated boundaries were produced and irregular-shaped secondary γ′ structures were formed during the slow cooling from super-solvus. The fracture mode was changed from interparticle debonding, for samples HIPed sub solvus, to a much more ductile transgranular fracture mode for samples HIPed super-solvus, for both room temperature and 700 °C tests.Interpretation of the influence of microstructure on the tensile properties and fracture-mode is complex and it is necessary to consider the different tensile properties at the two testing temperatures and for the two HIP conditions individually. Thus considering the 0.2% proof stress at room temperature it is reasonable that the coarser microstructure, obtained at the higher HIP temperature, has a slightly lower proof stress. When testing at 700 °C the situation is similar; the lower HIP temperature has a higher proof stress, but surprisingly its proof stress does not change with test temperature whereas that of the sample HIPed at the higher temperature decreases significantly so that there is now a bigger difference between the proof stresses. This suggests that a factor other than the coarser microstructure is influencing the proof stress at the higher test temperature and the most likely factor is the change observed in the distribution and morphology of the gamma prime. There is of course significant plastic deformation occurring at the 0.2% proof stress and it is reasonable that the coarser gamma prime formed after HIPing at (S+20)°C allows dislocations more degrees of freedom—including perhaps some climb, which results in a drop in proof stress.At room temperature the UTS was not influenced by the HIP temperature and reasonable elongation was obtained for both HIP temperatures, although it was slightly lower for the lower HIP temperature. These observations are surprising in view of the very different fracture modes and suggest that although HIPing at lower temperature had given perfect interparticle bonding, it was strong enough to resist stresses up to the UTS at room temperature.At 700 °C the UTS dropped significantly for samples HIPed at both temperatures, but the decrease was significantly greater for the sample HIPed at the lower temperature. The elongation to failure dropped very significantly at 700 °C for the sample HIPed at the lower temperature, but did not change significantly for the sample HIPed at the higher temperature. The fact that interparticle failure occurs in the sample HIPed at the lower temperature, whereas the failure is more ductile in the sample HIPed at the higher temperature is consistent with these observations at 700 °C where low ductility is associated with interparticle failure.Thus the tensile elongation and UTS found at 700 °C are consistent with the observed difference in fracture surface, but the values found at room temperature are not expected. It is suggested therefore that the interparticle failure is dominant at lower stresses at 700 °C because it is easier for cracks once initiated at the higher temperature to propagate. The current observation is consistent with the previous report where interparticle failure (along PPBs) at room temperature did not lead to degradation of strengths and elongation but caused significant decrease of ultimate tensile strength and elongations at elevated temperatures PPB precipitates were formed during HIPing of a nickel-based powder superalloy and probably attributed to the diffusion of Hf from interior of particles to particle surface.Increase of HIPing temperature reduced PPBs by grain boundaries’ migrating beyond PPBs, also leading to larger grains and serrated grain boundaries. This led to the transition of fracture mode of samples from interparticle debonding to transgranular fracture mode.The coarser microstructure was found to account for the reduction of 0.2% yield strengths of the samples HIPed at higher temperature but is good for ultimate tensile strengths and elongation at 700 °C.An experimental confirmation of thermal transitions in native and regenerated spider silksBiological structures such as spider silks are formed by proteins. The physical properties of such proteins are determined by environmental conditions such as temperature and humidity. In this paper, we confirm the thermal transitions that take place in spider silks using differential scanning calorimetry and study how the interaction of spider silk proteins with water affects the onset temperatures for these thermal processes. Native fibres and regenerated films of dragline silk and egg sac silk from Argiope argentata spiders were used to study thermal transitions of protein based structures. For the first time, differential scanning calorimetry (DSC) tests were carried out with spider silk samples of relatively large mass (10 mg). Previous attempts of DSC tests applied to spider silk samples failed to detect thermal transitions in a conclusive way. The tests reported here, however, show thermal transitions on both natural and regenerated samples that are in agreement with results from dynamic mechanical analysis (DMA) tests reported in the literature. The water content on spider silks seems to lower the temperatures at which such thermal transitions take place. The results also confirm that the amorphous regions of native and regenerated spider silk and silk worm silk give rise to similar thermal transitions.► Thermal transitions of spider silks were observed for the first time by DSC tests. ► DSC tests were carried out with spider silk samples of relatively large mass (10 mg). ► Thermal transitions found at around 200 °C are in agreement with DMA results. ► Water was found to act as a plasticizer in native and regenerated spider silks.Silk is a fibrous protein containing highly repetitive sequences of amino acids that are stored as a liquid and processed as fibres when sheared or spun at secretion Tubuliform and acinifom silk are used for the construction of protective egg cases. Spider egg cases have revealed a high serine and low glycine content Dragline silk which is secreted by the major ampullate gland is composed of glycine alanine (GA) and poly(A) entities and short repeats of GPGXn entities Experimental investigations of the structure of silk at a nanoscale revealed that there are two fundamental structural constituents: a highly organized antiparallel beta sheet nanocrystals and a semiamorphous phase that consists of less orderly protein structures As part of the quest to produce synthetic spider silk, several procedures have been studied in order to regenerate spider silk. Among these techniques, the use of ionic liquids as solvents has been reported The solubility of ionic liquids depends on the properties of cations and anions The excellent mechanical properties of spider silk have been studied extensively Differential scanning calorimetry is one of the most common techniques used for assessing the thermal transition of polymeric materials. DSC curves show thermal events that can be related to structural changes on polymers such as melting, crystallization and vitrification due to the fact that these changes are accompanied by transitions in the thermodynamic properties of polymers. However, DSC has not been successfully used to study the thermal transitions of spider silks. This is mainly due to the difficulties that arise when trying to find thermal transitions with low mass specimens. Osaki The aim of this paper is to provide an experimental confirmation of thermal transitions occurring in native and regenerated spider silk. Differential scanning calorimetry was used for this purpose since it probably is the most common technique used for determining glass transitions in the polymer field. To the best of our knowledge, this is the first time that spider silk samples of relatively large mass (10 mg) have been used to carry out DSC tests. The thermograms obtained clearly show thermal transitions that, in the past, had been only registered by means of other characterization techniques such as dynamic mechanical analysis (DMA). The effect of water content on these transitions, as well as the changes in thermal transitions that might arise when spider silk is regenerated has also been considered in this study.Silk fibres from Argiope argentata (Fabricius, 1775), an American species of the Araneidae family, were used in this study. Female adult spiders of 3.5–5 mm in prosoma width were collected in the vicinity of Lima outskirts, Peru. They were housed in 30 × 20 × 10 cm cages and were fed larval stage mealworms (Tenebrio molitor) three times per week.Whole egg sacs, including tubuliform and acinifom silks, were used in this study. The egg sacs produced by some of the spiders kept in captivity were collected from the cages. They were opened and spider eggs were removed. Then, the sacs were cleaned in distilled water with continuous stirring and dried in air for 1 day. Finally, the egg sacs were dried stored.Dragline fibres were retrieved directly from spider ampullate glands at a controlled speed (2 cm/s) by using a forced silking process described elsewhere Silkworm (B. mori) silk fibres (typical length 20 cm) were obtained by boiling cocoons in three 30 minute changes of a 0.5 % (w/v) Na2CO3 aqueous solution in order to extract the glue like sericin protein. The material recovered was then rinsed thoroughly with distilled water. The degummed silk was dried at ambient temperature for 1 day and finally, placed in dry storage.Both, dragline fibres and egg sacs were dissolved and used to prepare films. The spin dope was prepared from spider silk in ionic liquid 1-butyl-3-methylimidazolium chloride (BMIC). The stored silk fibres were chopped and mixed at 95 °C with BMIC to make a 5% (w/w) dope solution. After 1.5 h silk fibres were completely dissolved and distilled water was added in order to decrease the dope solution viscosity. The dope was cast on a glass substrate by using a syringe and let cool down for 1 h. The resulting film was then immersed on a methanol bath for 1 h in order to remove the ionic liquid from the film. Finally, the film was dried in air and stored.Differential scanning calorimetry (DSC) measurements were performed with a Perkin-Elmer DSC-4000 calorimeter. Samples of around 10 mg in mass were heated from 10 °C to 350 °C at a heating rate of 2 °C/min. The samples were prepared and moisturized in a thermogravimetric scale at room temperature. While the pans were still open, the samples were sprayed with distilled water. Once the right amount of water was obtained, the pans were sealed and the tests were carried out. The water contents of the samples were 10%, 20% and 30% (w/w). All measurements were carried out under a nitrogen atmosphere (20 mL/min). Hermetic stainless steel pans were used.Thermal gravimetric analysis (TGA) was performed in a Perkin-Elmer TGA-4000 instrument. Samples of around 10 mg were heated from 50 °C to 900 °C at a heating rate of 5 °C/min. The sample atmosphere was purged with a dry nitrogen gas flow of 20 mL/min.The morphology of the silk specimens was assessed with a Nanosurf Easyscan 2 Atomic Force Microscope (AFM) in the dynamic mode. A cantilever with a nominal spring constant of 42 Nm− 1, resonance frequency of 179 kHz and a tip radius lower than 10 nm was used.Native silk samples were prepared by grinding the silk with KBr, with the help of a mortar and a pestle. A fine powder was obtained, which was used to produce pressed pellets for the FTIR spectroscopy. Regenerated spidroin films were tested directly. FTIR spectra were recorded on a Perkin-Elmer 237 spectrophotometer at room temperature (26 °C), with a nominal resolution of 4 cm− 1 on the single-beam mode. An average of 500 scans at intervals of 1 cm− 1 was performed on a frequency range between 4000 cm− 1 and 400 cm− 1.Representative thermograms showing all samples tested at 10% of water content are depicted in . Each thermogram showed a step change associated to a thermal transition. shows the values of such transitions for all the samples tested at different water contents.For the sake of comparison, silkworm silk samples were also tested. The thermograms of silkworm silk are in agreement with previous DSC tests performed in the past In the case of native egg sac silk and regenerated egg sac film, these thermal transitions have not been previously reported in the literature. The difference between the thermal transition temperature found for egg sac silk samples and dragline samples could be due to the different composition of the amino acid on each type of fibre. In fact, tubuliform and acinifom silk are used for the construction of protective egg cases and are composed by glycine, alanine and high serine content shows the storage (E′) and loss (E″) moduli of spider silk obtained from DMA tests in the tension mode. As can be observed in the loss modulus curve the same thermal transition observed with DSC (at around 160–200 °C) occurs at around 200 °C in the DMA tests. Other studies have reported DMA tests on dragline spider silk and found two local transitions at around − 70 °C and 200 °C It is reasonable to consider that the thermal transitions obtained from our DSC tests correspond to a glass transition. Several authors DSC tests show that a glass transition is present on both native and regenerated dragline silk, egg sac silk and silkworm silk. Moreover, the temperature at which this glass transition takes place depends on the water content of the sample (). This suggests that water acts as a plasticizer and the glass transition temperature drops as the water content of the sample rises. The amorphous segments on spider and silkworm silk are held together by hydrogen bonds that are broken at the onset of the glass transition. The presence of water ncreases the molecular chain dynamics of the oligopeptide chains present in the amorphous region and, thus, the energy needed for the onset of the glass transition is lower than the value expected in the dry state The effect of water on the physical properties of spider silk has been reported in the past. It has been showed that water content has a major effect on spider silk It is worth noting that a similar thermal behaviour is observed for both, native and regenerated silks. They both present a glass transition and they are affected by water content in the same way. TGA tests show also a similar behaviour with regard to water loss for both native and regenerated spider silk (). The weight of the sample decreases remarkably with increasing temperature above 300 °C. At 800 °C the samples were completely degraded.The structure at the nano-level is shown in a shows a sample of native dragline silk. The diameter of the dragline fibres studied here was around 5 μm. b shows the same dragline sample at a higher magnification. Globular regions of around 200 nm can be observed in this picture, which are in agreement with similar globular regions have been reported in other silk morphology studies c and d show a native egg sac silk sample. The egg sac is formed by rather small fibres ranging 200–300 nm in diameter (d are around 200 nm in length by they seem to be more tightly packed when compared to those observed in dragline silk. Dragline silk was obtained by using a forced silking process. It has been reported somewhere else that forced silking might alter the morphology of spider silk changing the size and arrangement of the globular regions By contrast, egg sac and dragline regenerated films (e, f, g, h) display a different morphology. The globular regions are not clearly depicted in these samples. This difference could be due to the fact that nano-fibrils (formed by interlinked globular regions) are not present in regenerated films, although further studies on controlled morphological characterization would be needed to confirm this.Contamination due to the processing technique used to obtain the regenerated films could also affect the AFM images of such films. FTIR () was used to determine if the ionic liquid (BMIC) used for dissolving the silk was completely removed during the methanol bath. It has been reported Also, the FTIR tests show similar spectra for all the silk types studied (). The band at 1650 cm− 1 is associated to the CIt is clear that the thermal transitions of the different types of silk studied here are rather similar. Conversely, the mechanical properties reported in the literature such as Young's modulus, maximum stress and maximum strain are different for each type of silk. Dragline spider silk shows a maximum stress and Young's modulus of 1.7 GPa and 30 GPa The thermal transitions of native and regenerated spider silk and silkworm silk have been studied and documented for the first time by means of differential scanning calorimetry. The thermal transitions for forced dragline silk, egg sac film, silkworm silk and regenerated silk films occur at around 200 °C. This value is in agreement with reported values of thermal transitions of spider silk that are associated with a glass transition. Also, water was found to act as a plasticizer in native and regenerated spider and silkworm silks as it lowers the glass transition temperature. Morphological characterization assessed by means of AFM showed similar characteristics between the different types of native silk studied. Globular regions were not observed in the regenerated specimens. FTIR showed that the regeneration process had not left traces of contaminants, confirming that all types of silk studied displayed similar spectra. The fact that we have found similar glass transitions for the different types of silks studied here, while their mechanical properties remain quite different, leads us to believe that the mechanical behaviour might be controlled mainly by the ordered or crystalline region in spider silk Mechanisms of toughness improvement in Charpy impact and fracture toughness tests of non-heat-treating cold-drawn steel barIn this study, toughness properties of a non-heat-treating cold-drawn bar were examined by Charpy impact test and fracture toughness test, and the toughness enhancement mechanisms were clarified in relation with microstructure. As the thickness of pearlite bands decreased after the cold drawing, the Charpy impact energy of the cold-drawn bar was higher than that of the as-rolled bar, which could be reasonably explained by the thin sheet toughening. On the other hand, thin pearlite bands negatively affected the fracture toughness because of the decreased spacing between crack or void initiation sites inside the fracture process zone in front of the pre-fatigued crack tip. The Charpy impact test data could also be correlated with the absorbed energy of the dynamic compressive test specimen whose orientation was matched with the hammer impact direction of the Charpy impact test, although the Charpy impact and dynamic compressive test specimens had a notched body and a smooth body, respectively.Cold heading quality wires are structural steel products mainly used for connecting parts such as bolts, nuts, and threads in various industrial areas of automobiles, electronic, machineries, and constructions. These wire parts are mostly classified into two parts, i.e., heat-treating and non-heat-treating wire parts, and their kinds reach several tens of thousands as they are fabricated by various processes of forging, drawing, extrusion, and heat-treatment. Heat-treated wires are generally subjected to spheroidization or annealing treatments, but recently developed non-heat-treating wires meet with required mechanical property levels are by cold working without heat-treatment processes, thereby achieving economical merits of costs and productivity However, non-heat-treating wires cope with some disadvantage of low toughness in final products. In order to solve this problem, the formation of low-temperature transformation microstructures such as bainites or degenerated pearlites by raising the Mn content and by controlling cooling rates is recommended In the present study, a non-heat-treating cold heading quality bar was fabricated by cold drawing of a rolled bar, and their microstructures and tensile properties were evaluated. Toughness properties were examined by Charpy impact test and plane strain fracture toughness test, and dynamic compressive tests were performed at a strain rate of about 103

s−1 by a split Hopkinson's pressure bar to correlate with the toughness. In order to analyze work hardening and residual stress distributions in the cold-drawn bar, the cold drawing process was simulated by using a finite element method (FEM), which could explain the deformation behavior related to the microstructural evolution. Based on the results of microstructural modification and toughness properties, mechanisms of toughness improvement in the non-heat-treating cold-drawn bar were clarified.Chemical composition of the non-heat-treating cold heading quality steel bar used in this study was 0.25C–0.15Si–2.0Mn–0.08Al–0.004N–Fe (wt%). The bar contained 2 wt% of Mn to attain the solid solution hardening effect and to form some degenerated pearlite The as-rolled and cold-drawn bars were sectioned in parallel to the rolling direction, polished, and etched in a nital solution. The center and surface regions were observed by an optical microscope and a scanning electron microscope (SEM, model; JSM-6330F, JEOL, Japan). Five optical micrographs at least were taken at various magnifications, from which volume fractions of ferrite and pearlite and their band thickness were measured by an image analyzer (model; SigmaScan Pro ver. 4.0, Jandel Scientific Co.).Tensile specimens were obtained from the center and surface region of the as-rolled and cold-drawn bars. Plate-type specimens having a gage length of 12.6 mm, a gage width of 6.25 mm, and a gage thickness of 1 mm were prepared, and were tested at room temperature at a strain rate of 2×10−3

s−1 in accordance with the ASTM standard test method Plane strain fracture toughness was analyzed at room temperature in accordance with the ASTM E1921-05 standard test method where E is elastic modulus. The measured KJc was used after checking if it met the following condition:where bo and σys are initial ligament and yield strength at the test temperature, respectively. The number of valid KJc data measured at the same test temperature is more than six.A split Hopkinson's pressure bar was used for dynamic compressive tests . Cylindrical specimens (size; 5Φ×5 mm) were prepared in vertical to the rolling direction (or the alignment direction of ferrite-pearlite bands) so that their orientation could be matched with the hammer impact direction during the Charpy impact test. The specimen situated between incident and transmitter bars was compressed by a striker bar (diameter; 19 mm) projected at a high speed using an air pressure of 0.2 MPa (impact velocity; 26.7 m/s), and the strain rate could be controlled by varying the compressive pressure. During the dynamic compression, the incident wave, reflective wave, and transmitted wave were respectively detected at strain gages, and recorded at an oscilloscope. Among the recorded wave signals, average compressive strain rate expressed as a function of time was measured from the reflected wave, while compressive stress expressed as a function of time was measured from the transmitted wave. Dynamic compressive stress–strain curves were obtained from these two parameters by eliminating the time term. Compressive strain rate during the test was about 2.0–3.5×103

s−1. Detailed descriptions of the dynamic test are provided in references In order to investigate the deformation behavior during the cold-drawing of steel bars, the finite element method (FEM) analysis was employed by using an elasto-plastic commercial package ABAQUS (Dassault Systemes Simulia, Corp.) The FEM analysis results of effective strain and stress in the cold-drawn bar are shown in (a) and (b). The effective strain in the steady state region where the stress and strain contours are parallel to the axial direction increases almost linearly as a distance from the center to the surface increases, and reaches the peak in the surface region, as shown in the path plot of (a). This indicates the increased work hardening (about 40–55%) with increasing distance from the center. The effective stress increases as the distance from the center increases, and then reaches a saturation stress state near the surface region, as shown in (b). Since the effective stress cannot represent directionality of stresses, three axial stress components need to be examined.(a) through (c) shows the distribution of stress components of σ11, σ22, and σ33 along the radial, axial (longitudinal or drawing), and hoop (circumferential) directions, respectively, of the cold-drawn bar. It should be noted that the stress distributions are totally different in the deforming region and out of the die region. In the deforming region of the workpiece confined by the drawing dies is the compressive stress state, while in the center region is the tensile stress states due to the development of the secondary tensile stresses. After the workpiece came out of the drawing dies, the stress states are reversed. The stress distributions along the three directions are compared in (d). The compressive stress along the radial direction (σ11) is weakly formed in the center region, and increases as the distance from the center increases to reach the zero residual stress in the surface region. The residual stress along the axial direction (σ22) is strongly formed in a compressive mode in the center region, while it is formed in a tensile mode in the surface region. The residual stress along the hoop direction (σ33) is also formed in the same manner to the σ22, but its amount is somewhat lower than the σ22. According to the FEM results of , the high tensile residual stresses exist in the surface region where the work hardening occurs severely, which can result in different microstructures and mechanical properties in the center and surface regions. Thus, the detailed analyses of microstructures and mechanical properties in the center and surface regions are essentially needed.(a) through (d) shows optical micrographs of the center and surface regions of the as-rolled and cold-drawn bars. These bars consist of ferrite and pearlite, which are severely elongated along the rolling or drawing direction. Thus, band structures of ferrite and pearlite are well developed inside bars. In most of pearlite grains, degenerated pearlites are observed, as marked by arrows in , which indicates the effect of high Mn content (2 wt%) . Though the volume fractions of ferrite and pearlite are similar in the bars, the band thicknesses of ferrite and pearlite are smaller in the cold-drawn bar than in the as-rolled bar, which indicates that they are reduced after the drawing. It is also smaller in the surface region than in the center region because of the heavier deformation in the surface region.Room-temperature tensile stress–strain curves of the bars are presented in (a) and (b), from which yield strength, ultimate tensile strength, and elongation, together with hardness, are summarized in . The yield and tensile strengths of the cold-drawn bar are higher than those of the as-rolled bar because of work hardening of the cold-drawn bar, whereas the elongation is lower. The yield point occurring in the as-rolled bar disappears after the cold-drawing The room-temperature Charpy impact test results are shown in . The Charpy absorbed impact energy of the cold-drawn bar is higher by about 60–70% than that of the as-rolled bar, which shows the opposite trend of tensile elongation. (a) through (d) shows SEM fractographs of Charpy impact specimens. The cleavage fracture mode is mainly observed throughout the whole specimen, but some ductile dimpled fracture mode is also found in the cold-drawn bar, as indicated by dotted oval areas in (c) and (d). This supports the increased impact energy in the cold-drawn bar.The room-temperature fracture toughness data are provided in . All the fracture toughness values satisfy the plane strain condition. The fracture toughness of the cold-drawn bar is lower than that of the as-rolled bar. This shows the same trend of tensile elongation and the opposite trend of Charpy impact energy. (a) through (d) shows SEM fractographs of fracture toughness specimens. This observation area is located in front of the pre-fatigued crack tip as marked in (a) through (d). The stretched zone, at which the pre-fatigued crack tip is stretched or blunted prior to the crack propagation, exists in front of the pre-fatigued crack tip, as indicated by arrows in (a) through (d). The high magnification SEM fractographs of the stretched zone are shown in (a) through (d). This stretched zone is differentiated from the pre-fatigued crack area or the crack propagation area, and is mostly composed of ductile dimples. The width of the stretched zone was measured, and the results are shown in . The stretched zone width of the cold-drawn bar is narrower than that of the as-rolled bar, which is well correlated with the fracture toughness data. presents dynamic compressive stress–strain curves of the bars, from which yield strength, maximum compressive strength, strain at the maximum stress point, plastic strain, and area beneath the stress–strain curve (absorbed energy of the compressive specimen) are obtained as listed in . The yield compressive strength is lowest (881 MPa) in the surface region of the cold-drawn bar, while it is not varied much (1350–1410 MPa) in the other bars. The overall trend of the maximum compressive strength roughly follows the trend of the quasi-static tensile strength (), although the former is about twice higher than the latter because of the strain rate hardening effect. The strain at the maximum stress point is similar in the range of 28–30% in all the bars. The areas beneath the stress–strain curve of the cold-drawn bars are higher than those of the as-rolled bars, which tends to roughly match with the data of Charpy impact energy.When the cold-drawn bar is microstructurally compared with the as-rolled bar, the thickness of ferrite and pearlite bands decreases after the cold drawing, and the surface region is more strain-hardened than the center region, as shown in (a) through (d). According to these microstructural modifications, the Charpy impact energy of the cold-drawn bar is higher than that of the as-rolled bar, whereas its fracture toughness is lower. This is interesting because these two toughness properties show the opposite trend in the as-rolled and cold-drawn bars, which can be explained by toughness testing methods themselves as well as microstructural modifications. In the Charpy impact test method, the specimen is momentarily subjected to very high energy by the impact of a heavy hammer under a dynamic loading condition, and the energy absorbed in the specimen contains both initiation and propagation energies of a crack initiated from a V-shaped notch. On the other hand, the fracture toughness test method is quasi-statically performed, and shows the stress intensity at the time of initiation of crack growth at a sharp pre-fatigue-crack tip region Charpy impact energy is plotted as a function of pearlite band thickness in . The Charpy impact energy increases after the cold drawing of bars as pearlite bands are thinned. (a) through (d). In the as-rolled bar, the crack propagation profile is relatively linear as the crack initiated from the notch readily propagates against ferrite and pearlite bands ((a) and (b)). The crack profile of the cold-drawn bar shows a quite tortuous shape because thin ferrite and pearlite bands effectively block the crack propagation ((c) and (d)). When the crack propagation profiles is magnified, as shown in (g) and (h), the crack propagation sometimes changes its path along the pearlite band direction (vertical to the crack propagation direction) to leave deep steps of 50–200 μm in depth, as marked by yellow arrows. This observation implies that hard and brittle bands of pearlite are delaminated during the Charpy impact test, which can interrupt the rapid crack propagation.This delamination and the subsequent increase in impact energy in the cold-drawn bar can be explained by the thin sheet toughening phenomenon, which indicates the increased resistance to crack propagation in lamellar-structured materials It is interesting to note that the Charpy impact energy data can be correlated with the data obtained from the dynamic compressive test specimen whose orientation is matched with the hammer impact direction of the Charpy impact test ( shows the relationship between Charpy impact energy and absorbed energy of the dynamic compressive specimen (area beneath the stress–strain curve) (). Here, the absorbed energy of the dynamic compressive specimen means the toughness measured under the dynamic compressive loading condition. The Charpy impact energy tends to increase with increasing the absorbed energy of dynamic compressive test specimen. This indicates that the both energies show the close correlation because they are obtained under dynamic loading conditions, although the Charpy impact and dynamic compressive test specimens have a notched body and a smooth body, respectively. In addition, this tendency is interpreted by the thin sheet toughening effect because the dynamic compressive loading direction is matched with the hammer impact direction of the Charpy impact test.On the other hand, the fracture toughness decreases when the as-rolled bar is cold-drawn. shows the relationship between fracture toughness and pearlite band thickness, showing the opposite results to the Charpy impact test data (). Inside the fracture process zone in front of the pre-fatigued crack tip of the fracture toughness specimen (), pearlites play a role in initiating voids or cracks. As the thickness of ferrite and pearlite bands decreases after the cold drawing, the spacing between crack or void initiation sites decreases. Lee et al. The present study on the correlation of pearlite band thickness with Charpy impact properties and fracture toughness in non-heat-treating cold-drawn steel bars would prove a good way to find mechanisms of the toughness improvement. It can also be useful to understand the dynamic compressive deformation behavior and to suggest important microstructural parameters for improving toughness. In view of microstructural aspects, thin pearlite bands obtained after the cold drawing are desirable for improving Charpy impact toughness, which can be reasonably explained by the thin sheet toughening, whereas they negatively affect the fracture toughness because of the difference in testing methods. In view of mechanical aspects, considering that the Charpy impact test is performed under very fast strain rates, the impact energy absorbed should be analyzed under a dynamic loading condition such as dynamic compressive loading, instead of a quasi-static loading condition, in order to closely correlate with the Charpy impact fracture behavior. The present research idea using the dynamic compressive test can provide the reasonable explanation of improved Charpy impact energy in the cold-drawn steel bar. Since only dynamic compressive tests were conducted in this study, various dynamic deformation tests under tensile and torsional loading conditions are to be conducted and analyzed in the future, considering various dynamic loading conditions of a Charpy specimen impacted by a hammer.Toughness properties of a non-heat-treating cold-drawn bar were examined by Charpy impact test and fracture toughness test, and the toughness enhancement mechanisms were clarified in relation with microstructure.When the cold-drawn bar was microstructurally compared with the as-rolled bar, the thickness of ferrite and pearlite bands decreased after the cold drawing, and the surface region was more strain-hardened than the center region. According to these microstructural modifications, the Charpy impact energy of the cold-drawn bar was higher than that of the as-rolled bar, whereas its fracture toughness was lower.Thin pearlite bands obtained after the cold drawing were desirable for improving Charpy impact toughness, which could be reasonably explained by the thin sheet toughening. On the other hand, they negatively affected the fracture toughness because of the decreased spacing between crack or void initiation sites inside the fracture process zone in front of the pre-fatigued crack tip. Toughness properties obtained from these two toughness testing methods had different significations in view of fracture mechanics, and thus should be analyzed differently.The Charpy impact energy data could be correlated with the absorbed energy of the dynamic compressive test specimen whose orientation was matched with the hammer impact direction of the Charpy impact test, although the Charpy impact and dynamic compressive test specimens had a notched body and a smooth body, respectively.Consideration of plasticity within the design of timber structures due to connection ductilityThe plastic behavior of fasteners in timber structures has gained more and more interest within recent years. In particular, dowel type fasteners show a significant ductile behavior if a certain embedded length of the dowel is ensured. The embedded length is either found by using the formulas based on the design codes (DIN (2008) Most of the inherent material properties of timber, except the behavior in compression, do not allow a plastic design in pure timber structures. Connections accomplished with dowel type fasteners however enable to bridge that gap. The ability of forming plastic hinges by ductile joints within statically undetermined systems provides substantial advantages for a structure. First and foremost, the capability to dissipate energy provides some benefits, such as the integration to the earthquake analysis and in addition to increase the robustness of the structure. A load redistribution within statically undetermined systems can also be achieved, and thereby the possibility of a higher utilization of the structural system.Within this paper, the possibility to redistribute internal forces in timber structures is shown and some application criteria to form plastic hinges are given. Since timber is an inhomogeneous material and is characterized by the scattering of the material properties, the influence of the scattering of the modulus of elasticity to the required rotation of the joint is presented.In order to implement the ductility to timber structures, it is necessary to appraise the ductility as an interaction of the different types of fasteners within timber. Based on conducted experiments the evaluation of the displacement at the point of yielding with respect to existing appraisal models is discussed. Furthermore, different existing methods to evaluate the point of yielding and the ductile behavior of fasteners in timber structures are discussed.► The moment–rotation behavior with the focus on the ductility was examined. ► A very ductile behavior was observed. ► We showed the influence of the material scattering (E-modulus) on the beam-end rotation. ► The evaluation of the ductility in timber joints was discussed.The plastic behavior of connections in timber structures has gained more and more interest in recent time. The theory of Johansen  to develop plastic hinges within the connection.By increasing the in between distance (a1, The ability of forming plastic hinges within statically undetermined systems provides substantial advantages for a structure. First and foremost, to assess the desired behavior within the earthquake analysis, particularly to appraise the dissipative energy. Secondly, to redistribute internal forces within statically undetermined systems, which allows a rearrangement of internal forces in the case of unexpected loads. Thirdly, a higher utilization of the structure itself may be achieved.Timber is an inhomogeneous material and the properties themselves scatter within the material. In order to use the plastic behavior not only the joint characteristics, but also the materials properties need to be analyzed in detail.To introduce the ductility into timber structures it is unavoidable to define the ductility of connections in timber structures. Based on conducted experiments several different methods are discussed to define the point of yielding and to evaluate the ductility.Timber structures are in general designed by using elastic design methods. In this case, the elastic internal forces are compared with the elastic resistance of the cross-section. This leads to the fact, that a full utilization of the cross-section is only achieved within a limited area of the beam. In the case of a uniformly loaded two-span beam, only approximately 4% of the beam length is utilized by more than 80% of its strength (comp. ). By installing a plastic hinge at the location of the maximum bending moment (in this case at the mid support), it is possible to redistribute forces, and therefore to raise the utilization within the beam.In order to prove the capability to form a plastic hinge with typical fasteners, an investigation based on experiments conducted at the University of Stuttgart was accomplished The performed experiments were general divided into two parts. First, pure tension tests to obtain experiences about the general ductile behavior of the connection (comp. (a)), and secondly four-point bending moment test setups to achieve the moment–rotation capacity of the previous tested connection within a joint at mid-span (comp. (b)). The specimens had a cross-section of 180 mm×180 mm for the tension tests, and 180 mm×400 mm for experiments loaded in bending. The timber grade was for all experiments GL24h. Although in practical use a timber grade of GL24c is appropriated for members stressed in bending, a homogeneous setup was chosen in order to ensure, that all connectors nearly acting under the same conditions. Within this consideration, a dowel configuration of 3×3 dowels with a diameter of 12 mm and a flitch plate with a thickness of 8 mm (S355 JR) was used (comp. (b)). The mean value of the density for all of the processed lamellae within the manufactured glulam beams was 446 kg/m3. The ordered steel grade of the dowels was S235 JR. However, the stress–strain relationship showed a tensile strength of 581 N/mm2. Therefore the steel can be classified as S355 JR pertaining to DIN EN 10025-2 The configuration of the group of dowels was reinforced with self-drilling fully threaded screws in order to prevent a brittle failure of the connection by splitting of the timber (b)) in addition to the prevention of a timber splitting at the connection arrangement.With a slenderness λ of 7.1, all of the tested connections indicated a pronounced ductile behavior. shows the moment–rotation behavior as the mean value of the angle on the left (ϕl) and on the right (ϕr) of the connection of the three single experiments (comp. (a)). The rotation was measured with an inclinometer, the moment was calculated based on the measured force at the thirds of the beam length. Since the flitch plate remained almost horizontally during the experiments, the rotation on the left hand side (ϕl) and on the right hand side (ϕr) have been nearly identical. The slightly falling values of the moment–rotation behavior resulting from a performed relaxation of the connection at certain points (comp. ). The decline at a rotation of about 100 mrad is an effect of a complete unloading of the experiment due to reaching the maximum working movement of the hydraulic cylinder.The experiments show that reinforced connections behave in a ductile manner and dispose a sufficient rotation capacity.The verification of the moment–rotation capacity of a connection in timber structures is performed on a two-span beam.In general there are two different possibilities to determine the ultimate load within a system, either following the principle of superposition, or using the ultimate load design method ). The ultimate load is then calculated by using the Principle of Virtual Work.This is a rather quick solution with an important disadvantage. The method is based on the assumption, that the required rotation capacity of the joint is adequate. For joints in timber structures, however, the rotation of the hinge may not be sufficient to redistribute the internal forces until the ultimate load is reached or the second plastic hinge is formed and the structure turns into a mechanism. Given the previous arguments, the method based on the principle of superposition is chosen to determine the ultimate load. The moment–rotation behavior is approached as a tri-linear graph (comp. ). Each single load step is calculated based on a certain stiffness (Ki) of the joint. The ultimate load is obtained, either if the maximum rotation capacity is attained, or the maximum resistance of the cross-section is reached. The ultimate load and the appendant required rotation are found by adding the values of the single load steps Δq for every stiffness (Ki). shows the straight dependence of the joint stiffness on the moment distribution. For the initial stiffness K1 the moment at the joint increases until M1 is reached. Subsequently, the stiffness at the joint turns to K2 (comp. ). Hence a rising of the moment increase within the field and a lowering of the moment increase at the joint is achieved in the system until the joint turns at M2 into a plastic hinge (comp. ). In this stage the moment at the support remains constant whereas the moment within the field still increases to a higher degree, until the cross-section fails by reaching the ultimate bearing resistance within the field.Based on the previously introduced experiments (comp. Section ) the available rotation capacity was sufficient for the example on a two-span beam.Timber is, especially in tension, a brittle material; hence it is not able to form a plastic hinge. The general focus is to install the plastic hinge at the joint itself, at the location where the plastic hinge will occur. There are still open questions about the strength, the sufficient stiffness and the yield deformation. However, within the design of the joint a primary rule has to be considered: This general rule relies on the capacity based design method Dowel type connections in timber engineering are in general semi-rigid connections. That means, a joint does not fully accomplish neither the criteria of a rigid joint, nor the classification of a pinned joint (comp. ). The stiffness of the joint is a decisive value for the design of a structure. By using elastic design methods, the distributions of the internal forces for an undetermined structure differ from each other in dependence on the stiffness. If the stiffness of the joint is overestimated, the structure may fail at mid-span due to an increase of the bending moment and therefore of an exceedance of the bearing resistance. In this case, the joint may still be in the elastic stage, whereas the ultimate stresses of the timber member are reached at mid-span due to stress redistribution within the elastic stage. On the other hand, if a joint is too stiff without any rotation capacity, the cross-section fails next to the joint without any benefit. The key characteristic is therefore a certain initial stiffness and a rotation capacity of the joint. Introducing a semi-rigid joint at a two span beam, the actual stiffness of the joint has to fulfill a certain stiffness criterion, see Kjoint>3⋅EI⋅Mjointl⋅(2⋅Mcross-section−Mjoint)withEIStiffness of the beamlLength of the beamKjointStiffness of the jointMjointYield plateau of the jointMcross-sectionMaximum elastic moment resistanceof the cross-section based on fm,k, the connection is not stiff enough to reach Mjoint and therefore the yield plateau of the joint. A premature failure of the timber at mid-span may occur. This phenomenon is represented as hatched area in . If the joint stiffness corresponds to Eq. in dependence on the stiffness EI of the beam, a plastic design within a two span beam is in general possible, delineated as dashed hatched area in . The delimitation of the essential ratio of Mjoint/Mcross-section (comp. Eq. ) is gray colored backing. Again, in this case no activation of the ductility is possible, since the joint is not able to form a plastic hinge and the timber cross-section fails next to the joint. With respect to the capacity based design method and the first recommended overstrength factor of Jorissen and Fragiacomo ), the designed joint resistance should be less then 62,5% of the bearing resistance of the cross-section.Timber as a natural material has strongly variable material properties. Particularly, the scattering of the density, the modulus of elasticity or similar properties have a great influence on the behavior, not only within a certain section (e.g. joints, supports, etc.) but also within a complete structural system. For instance Werner geometrical properties of the connection andmechanical fixing of the fastener within the timber in dependence on the dispersive material properties.Within this section the influence of the scatter of the modulus of elasticity on the required end rotations of a beam element is discussed. by a numerical integration, the end rotations ϕi/k (comp. ) for the appropriate bending moment are determined. The required end rotations of a beam element based on a certain applied bending moment distribution vary with the scattering of the modulus of elasticity (comp. Eq. ). In order to achieve the intended bending moment distribution, the joints need to have the ability to provide at least the required rotation ϕreq at the joint (comp. Eq. The factor kmat represents a safety margin to cover the influence of the material scattering. A computer model has been developed based on Ehlbeck et al. ). The lamella of each glulam beam has been divided into 150 mm long cells, with a reference thickness of 40 mm. A statistically assigned modulus of elasticity is allocated to each cell. The different moduli of elasticity of each cell is shown in in corresponding grayscale. It is assumed, that each lamella is running along the complete beam length. Based on the material properties displayed in the modulus of elasticity is changing within each board and of each board itself.The statistical distribution model of each board is lognormal EI(eff)=∑(Ei⋅Ii)+∑(Ei⋅Ai⋅ai2)withEI(eff)Effective stiffness within the load stepEiModulus of elasticity of each cellIiMoment of inertia of each cellAiArea of each cellaiLeaver arm of each cell to the centroid have been used in order to run the program.The influence of the material properties have a remarkable effect on the required rotation of a beam element. shows a first result of the required end rotations depending on the beam length. Within this study, the intended bending moment distribution is equal for all beam lengths. Hence the uniformly distributed load was recalculated for every step to achieve the specified bending moment distribution. Therefore the behavior of the beam length to the required rotation has a linear dependency (comp. ). The mean value of the required rotation based on the computer program follows the averaging process with a constant mean of DIN 1052 ). This has an important effect on the design of a joint. The calculation with respect to the mean value according to DIN 1052 A similar but subtly different required rotation arises if the intended bending moment in the beam element is changed. The rotations at the supports depend on the internal forces and therefore on the uniformly distributed load which is applied to a beam member. Hence, the beam element was loaded with varying types of uniformly distributed loads, in order to analyze the influence of different load configurations on the required rotations. For a uniformly distributed load on a beam with a constant cross-section of 180 mm×400 mm the required rotation varies from 7.7% to 8% (comp. The influence of the height of the beam itself follows the equation Within this study the thickness of the lamellae remains constant for every height. The increase of the height leads directly to a decrease of the required rotation (comp. A decrease of the height of the lamella with a constant beam height, however, leads only to a decrease of the required rotation (comp. (b)). For a higher number of statistically determined cells, the mean values of the cells within a length step tend to the mean value itself. Therefore the required rotation decreases with a thinner lamella, if the height of the beam keeps constant.Based on the conducted analysis the parameter kmat to consider the scattering of the modulus of elasticity on the required rotation of a joint is recommended according to Eq. In order to operate with ductility in timber structures it is inevitable to specify the ductile behavior of commonly used fasteners. Within this study a large number of tests conducted by Jorissen To evaluate the experiments in consideration of ductility, the mean graphs were determined of several test series. The number of experiments for the different test arrangements vary from 10 to 20 single experiments, some of them were loaded in tension and some in compression (comp. ). The type of loading has a marginal influence on the brittle failure mode, and no influence on the ductile failure mode (comp. ). The experiments showed in general a load–slip behavior depending on the thickness of the timber members and the in between distance of the dowels (comp. ). A failure due to splitting occurred for thin timber members (t1=12mm/t2=24mm)An important component to appraise ductility, is the point of yielding of a connection. Muñoz et al. The results of the different types of evaluation methods are presented in ). For specimens with thin timber elements the failure mode was mostly brittle, except the experiments conducted with a single fastener or with three fasteners in a row and an in between distance of 11 times the diameter. Although these types of connections behave brittle, some of the methods give a point of yielding and therefore a displacement at yielding (K&C, CSIRIO and Y&K) (comp. On the other hand, the method based on the EN 12512 The driving parameter within those definitions is the slope of the tangent following the initial stiffness. If the defined slope of 1/6 of the initial stiffness is lowered to 1/8 or 1/10 Given the previous discussion with some applicable methods it seems not reasonable to apply an approach which achieves a yield displacement although the connection behaves brittle.The large variation (up to 5 times) of the displacement at yielding between the six methods (comp. ) is due to the remarkably high value of the method using a 5% offset of the diameter Within the consideration of the ductility, it is indispensable to define the ductile behavior. Smith et al. ) to classify fasteners in timber structures based on the ductility ratio Di which is calculated by: Di=uu,fuywithuu,fUltimate displacement or in some cases thedisplacement at failureuyDisplacement at yielding describes the area underneath the graph which represents the energy which is needed to perform the experiment. Since the shape of the graph is not taken into account, Ef represents an absolute value with no correlation to the load–slip behavior. shows two different test results, whereby the area underneath the graph is almost equal and therefore Ef as well. The study demonstrates that no classification of the ductility based on Ef is possible. A further possibility to define the ductility is given by Jorissen and Fragiacomo De=EdEpywithEd=Energy dissipated per half cycleEpy=12⋅Fy⋅uyFy=Force at yieldinguy=Displacement at yieldingSince this definition is only applicable to quasi static experiments, this definition is not further discussed.DEu=EuFu⋅uuwithEuCharged energy till ultimateFuForce at ultimateuuDisplacement at ultimateThis approach describes the degree of concordance with an ideal elastic–plastic behavior. A value of 1.0 reflects an ideally elastic–plastic behavior, whereby a ratio of 0.5 displays an ideal-elastic behavior. Experiment A in achieves a ratio of 0.65, whilst experiment B obtains a ratio of 0.78. This approach enables to describe the ductility within a narrow range.Besides the energy based appraisal methods, there are furthermore two general principles based on reference displacements to evaluate the ductility ratio D. On one hand the relative definitions (Eqs. ) on the other. Within both procedures the essential question of the ductility reference number arises. Some of the approaches define uf (displacement at collapse) as reference others uu (displacement at the ultimate load). This definition has a significant influence on the ductility ratio which is described in The elegance of the absolute definition lies in the fact, that by the value Dfy the magnitude Ds/f=K0F1⋅ufF1:Fmax(0≤u≤5mm)Ko:Initial stiffness of the displacement due to yielding is shown. On the other hand, no attention is given to the initial stiffness of the joint. In order to consider the plasticity in timber structures, this is an important information (comp. Section  gives the ductile displacement as a percentage of the displacement at failure. The ductility criteria according to Smith et al. . Depending on the yielding displacement, both Eqs. give reasonable results based on the classification given by Smith et al.  describes the ductility factor Ds/f as the ratio of the initial stiffness to an imaginary stiffness depending on the displacement at failure and the maximum load till 5 mm (comp. For the load–slip behavior displayed in the different ductility ratios are calculated based on Eqs. and compared to the original definition (comp. . The primarily definition overestimates the ductile behavior, therefore a rather brittle behavior might be classified as low or moderate ductile. The deviation to the original definition in Eq. increases with an increase of the load after a displacement of 5 mm. Therefore it is recommended to discuss the use of Ku respectively Kf instead of the imaginary stiffness for this method.The discussion of the appropriate definitions of the point of yielding and the assessment of the ductility is still open. Both discussed definitions are crucial for the implementation of the ductility in timber structures.This paper shows the plastic behavior of a reinforced doweled connection, not only as load–deformation but also as a moment–rotation behavior. Based on a two-span beam the applicability of the plastic design in timber structures is demonstrated. The influence of the joint requirements is discussed. Timber with its inherent material properties is not able to form plastic hinges, therefore the plastic hinge is formed due to the ductile behavior of dowel type fasteners. These types of fasteners show a significant plastic behavior if the connection is not exposed to the risk of splitting. This can either be achieved by enlarging the in between distance of the fasteners or by reinforcing the connection with for instance self-drilling screws. Since timber has a high scattering of the material properties, the influence of a scattered modulus of elasticity on the required rotation is discussed. Not only the experiments, but also some first analytical investigations show, that an implementation of the desired ductility of fasteners within timber structures is possible.To consider the ductility of commonly used fasteners within timber structures it is indispensable to evaluate fasteners concerning the ductile behavior. Thereby the displacement at yielding is of significant importance. Based on experiments conducted at the University of Delft, some of the existing methods to appraise the displacement at yielding are discussed (compare ). Within the discussion it is pointed out, that some methods tend to be unsuitable, whereas the method based on DIN EN 12512 General solution of the problem of design of laminated plates possessing the given stiffnessesThe paper deals with the problem of design laminated plates possessing the given stiffnesses. The following two design problems are considered: (1) the continuous design problem (when one can use materials with any elastic characteristics to manufacture the plate); (2) the discrete design problem (when one can use a finite set of materials). It is known that design problems are closely related with convex analysis problems. It is shown that the laminated plate design problems are related with the convex combinations problem (CCP).Using the CCP technique, one can analyze the laminated plate design problems in detail. This paper is concentrated on the general solution of the design problem (i.e. the set of all solutions of the problem). The general solutions are constructed for both the continuous and the discrete design problems. The methods developed in the paper can be used to solve the design problem numerically.Laminated plates are widely used in the modern structures. In many cases the plate can be effectively used if it has prescribed properties. It leads to design problem. In its engineering arrangement, this problem has the following form: the material characteristics of laminas and distribution of laminas must be specified so that a plate formed from them will have a given set of stiffnesses.Numerous investigators analyzed the design problem for laminated plate. It is impossible to give a full list of the papers devoted to this problem here (see the book by giving an introduction into the modern state of the problem and references). The most part of the papers was devoted to the optimal design problem formulated as follows: Find a design giving to the plate an optimal property (for example, the minimal weight or the maximal stiffness). The design problem considered in this paper is formulated as follows: Find a design giving to the plate the required property (in particular, the optimal one).Generally, the design problem may not have a unique solution. This means that a plate, which possesses a given set of stiffnesses, can be designed in many ways. This paper is concentrated on description of all possible designs.The relationship between the overall properties of an inhomogeneous plate and the properties of the materials forming the plate is established by the homogenization theory (see ). In the general case this relationship is very complex. For a laminated plate the local material characteristics depend on only one spatial variable. This makes it possible to obtain explicit formulas for calculation of the stiffnesses of laminated plates and to reduce the design problem to an integral equation of first order.For laminated solids the design problem was solved by using the convex combinations problem (CCP) technique. The laminated plate design problem involves the coordinate across the plate. It changes the problem drastically. For the case when there are no restrictions on the constitutive materials (materials with any characteristics are available to manufacture the plate) the plate design problem can be analyzed on the basis of Pontraygin’s extremal principle (see ) and the set of possible values of stiffnesses can be described. In the present paper this problem is analyzed on the basis of the CCP technique. This approach provides information not only about the stiffnesses but also about the general solutions of the problem.In many cases one can use a finite set of materials to manufacture the plate. It leads to the mathematical formulation of the problem in the form of a discrete problem (some analog of an integer-programming problem). The problem arising is called below the discrete CCP. A method for solution of the discrete CCP is developed. The method can be used to solve the discrete design problem numerically. the statement of the problem is given. In some results concerning the CCP are presented. deal with the continuous design problem. is devoted to plates of symmetrical structure. In the discrete design problem is formulated and reduced to a discrete CCP. In a method solution of the discrete CCP is described. are devoted to the case when the stiffnesses are given of non-exactly or a combination of stiffnesses is given.Let us consider a laminated plate formed from layers of homogeneous isotropic materials parallel to the Ox1x2 plane (Denote by z=x3/h the undimensional coordinate transverse to plate (h means the total thickness of the plate). The material characteristics of the plate (Young’s modulus E(z) and Poisson ratio ν(z)) are functions of the variable z. The stiffnesses of the plate (the in-plane stiffnesses S0ijkl, the coupling stiffnesses S1ijkl and the bending stiffnesses S2ijkl, ijkl=1,2) are related with the variable z and the functions E(z), ν(z) by the following formulas (see e.g. The other stiffnesses are equal to zero.With regard to the formulas (2.1)–(2.3) the design problem may be formulated as follows: Solve the for (ν,i,j,k,l)∈S with respect to the functions E(z) and ν(z). Here S means the indices of the given stiffnesses (all or only some of the stiffnesses may be included in the set S of the given stiffnesses).Let us consider the case ν=const. In this case the problems (2.1)–(2.3) may be reduced to the problem of the formwith respect to the unique function E(z). The quantities Sμ in (2.4) are expressed through the given stiffnesses Sμijkl.Note 2.1: If the number of layers is large (the thickness of layer is small compared with the thickness of plate) the stiffnesses may be calculated using the classical formulas (S21111=Eh3/(1−ν2) and so on) where the Young’s modulus E and the Poisson’s ratio ν are calculated in accordance with the homogenization procedure for 3-D body (see for details ). If the number of layers is not large this method can lead to incorrect results.Note 2.2: If ν≠const, we can solve the problems (2.1)–(2.3) with respect the functions I1(z)=E(z)/(1−ν2(z)), I2(z)=E(z)/(1+ν(z)), I3(z)=E(z)ν(z)/(1−ν2(z)) and then construct the general solution, (see Analyzing the design problem, we will use the methods based on the CCP technique developed by ), which will be used in the next sections. be given vectors. Consider the following problem with respect to the real numbers It is the so-called CCP. It is known (see ) that the set Λ(v) of all the solutions of the problems (3.1) and (3.2) (the so-called general solution) is given by the following formula is a finite set of solutions of CCP; M is the total number of these solutions; and are arbitrary real numbers satisfying the conditionsor, that is the same, the set Λ(v) can be represented asNote 3.1: An algorithm for calculation the solutions The bending stiffness S21111 of the laminated plate is calculated as (see The design problem is formulated as follows: Find all distributions of Young’s modulus E(z) which satisfy is not a CCP. Nevertheless, we can transform it into a CCP. Introduce the new measure μ determined by the equation: For a plate formed of m homogeneous materials we can rewrite where C=12S21111(1−ν2)/h3. Introducing the variables xi=12μi, we can write the problem (4.3) in the forms (3.1) and (3.2). we can write down the general solution of the problem (4.3) in the formConsider the domain Mp={μ: E(μ)=Ep} corresponding to the pth material (p=1,…,m). Note that Mp is not the domain occupied by the pth material and measure μp of Mp is not the volume ratio of the pth material. In order to find the design we must return to the initial coordinate z. This procedure is illustrated in for the case of a plate made of two materials. The curve in is the graph of the function μ(z)=(z3/3)+(1/8). The solutions presented in and (c) are corresponding to the maximal and the minimal volume ratio of phase in composite.The in-plane stiffness S01111 of the laminated plate is calculated as (see The equality (5.1), be considered with respect to the function E(z) taking m possible values, is a CCP. Its solution is given by the formula (2.3).Introduce the set Lp={z: E(z)=Ep} – domain occupied by the pth material (p=1,…,m). The measure xp of Lp is the volume ratio of the pth material.Consider the design problem when only two materials are available. In this case the variable xi takes values x1 and x2; and the variable μi takes values μ1 and μ2. The condition that the plate has the in-plane stiffness S01111 and the bending stiffness S21111 can be written in the form (see where x1 is any solution of CCP corresponding to Here {Mr} mean the lengths of the intervals forming the set M1 (see ) and {Lr} means the lengths of the intervals Systems (5.2) and (5.3) are solvable only if S21111∈[Lmin,Lmax], where Lmax is determined in A partial solution of the problems (5.2) and (5.3) can be constructed in the following way. Let us introduce an interval [a,b] whose length M1 is equal to x1 (it is the interval occupied by the first material). We will obtain a partial solution of the problem if we find a and b such that the following equation is satisfiedThis equation with respect to the variable x can be solved numerically One can consider the more general case when the first material occupies K layers (the thicknesses and the positions of the layers are unknown). In this case we come to the following equationwhich is an algebraic equation for a function of 2K variables. It can be solved numerically Note 5.1: The number K of the layers is arbitrary. It is interesting to know the minimal number of layers sufficient to design the plate.Consider the following problem: Indicating the minimal number of layers that allow designing a plate with every possible value of stiffnesses. A problem of such kind (different from the problem considered here) was analyzed by In the case under consideration (remember that we consider plates made of two materials) solution is the following: the first material must be distributed among two (not more) layers.Really, solutions corresponding to Lmin and Lmax are not more than two layers solutions; see and (c) (here we say about the layers occupied by the first material). The problems (4.1) and (5.1) continuously depend on the function E(z). Then, continuously transforming the function E(z) from the first solution to the second solution (obviously, it is possible) one obtains solution of the problems (4.1) and (5.1) for every S21111∈[Lmin,Lmax].Reminding about the second material forming the plate, we conclude that the total number of layers is equal to five.Thus, solution of the problem (5.6) with K=2 provides a design for every possible values of in-plane and bending stiffnesses. The problem (5.6) with may be useful in design of plates of symmetric (with respect to the plane z=0) structure. For the non-symmetrical plates it is necessary to take into account the coupling stiffnesses.Let us consider a plate with balanced placement of laminae about Ox1x2 plane (called also plates of symmetrical structure). For such a plate all the out-off-plane stiffnesses S1ijkl=0 and, consequently, ) represent the general form of the problem.Consider the case when the stiffness S01111 is fixed. Using the designs presented in and (c) we can find that the bending stiffness S211111 can take any value between the minimal valueHere E1>E2 are Young’s modulus, ν is the Poisson’s ratio (it is assumed the same for both the materials), h is the thickness of the plate.We can obtain designs of the plate using the procedure described in . In order to obtain a symmetric design we must distribute the sets Mp in Oμ axis symmetrically with respect the line μ=1/2.In the following sections we consider the case when a finite number of materials (indexed by the numbers 1,…,n) is available to manufacture the plate. It means that the function E(z) takes values in a finite set Zn={E1,…,En}.Let us divide the segment [−1/2,1/2] (the plate thickness in undimensional variable z) into m intervals [−1/2+(i−1)/m,−1/2+i/m). It means that we divide the plate into m laminae of thickness 1/m. The function E(z) is constant over the interval [−1/2+(i−1)/m,−1/2+i/m).Note 7.1: If the function E(z) takes the same value in adjacent intervals it means that the material occupies a “thick” layer.Then the design problem (2.4) may be written in the form are unknowns. The unknowns Ei>0 in accordance with the nature of Young’s modulus.We consider the problem (7.2) in the general form. Let Zn⊂[0,1] be a finite set (consisting of n numbers); be the given vectors. Consider the following problem with respect to the numbers The problems (8.1)–(8.3) will be called a discrete CCP.In this section we construct the general solution of the problems (8.1)–(8.3) – the set Λ(v) of all the solutions of the problems (8.1)–(8.3).Omitting the condition of discreteness (8.3) in problems (8.1)–(8.3), we obtain a continuous CCP (3.1) and (3.2). The general solution Λ(v) of the continuous CCP (3.1) and (3.2) is given by the formulas (3.3) and (3.4).Then to solve the discrete problems (8.1)–(8.3) it is sufficient to select in Λ(v) the vectors whose coordinates satisfy the condition (8.3).Present an algorithm performing this selection. Problems (3.3) and (3.4) may be considered as CCP (with respect to unknowns λγ). We must find x1,…,xm for whose the CCP (3.3) and (3.4) is solvable and which belong to the set Zn. We use the following property of CCP (see ): If the first (i−1) equations in (3.3) with the conditions (3.4) are satisfied then the ith equation in we obtain the following necessary and sufficient condition solvability of the discrete CCP:Now we describe an iterative algorithm constructing all the vectors x satisfying (8.5).In the first step we take an arbitrary start point T(0)={x0} (the root of a tree T).In the (i−1)th step we have a set T(i−1) of the points {x(i−1)}={(x0,…,xi−1): x1,…,xi−1∈Zn} for which the first (i−1) equations in with the condition (3.4) are solvable. Let us calculate the intervals Z(i,x(i−1)) corresponding to all the vectors x(i−1)∈T(i−1). After that let us construct the set T(i) of all the vectors of the form x(i)=(x0,…,xi−1,xi) where If Zn∩Z(i,x(i−1))=∅ for every x(i−1)∈T(i−1) then stop (the discrete CCP is not solvable).If i=m then stop (the discrete CCP is solvable).The tree T(m) has the following property. If the mth level of the tree T(m) is not empty then the discrete CCP (8.1)–(8.3) is solvable (otherwise it has no solution) and any vector x(m)∈T(m) (a branch of the tree) is solution of the discrete CCP (8.1)–(8.3). On the other hand any solution x of the discrete CCPs (8.1)–(8.3) is a branch of the tree T(m). It means that the set of all the branches (x1,…,xi−1) (is not taken into account) of the tree T(m) is the general solution Δ(v) of the discrete CCP.Transition from CCPs (3.1) and (3.2) to CCPs (3.3) and (3.4) – calculation of the vectors may be calculated on the base of the convolution algorithm presented in the simplex method can be applied. Using this method, we consider at the (i−1)th step the first i−1 equations in (3.3) and the condition (3.4) as a restrictions and introduce the coast function L(λ) corresponding to the ith equation in After that we find mini (maxi) solving the problemAdvantage of the method based on the simplex method is that this method does not generate large data.The treeT(m): The tree can be realized on the base of any known data structure.The results of numerical calculations are presented in often there exist the designs, which do not satisfy the equations in exactly but satisfy these equations approximately. It is clear that these solutions may be suitable for the practice. We write the design problem giving these solutions.Let us consider the problem (7.2) with the condition that the quantities Sμ, μ=0,1,2 belong to intervals [Sμ−δSμ,Sμ+δSμ], n=0,1,2, where δSμ, n=0,1,2 are the allowed derivations of these quantities from the required values Sμ, n=0,1,2.Introducing the additional variables xm+1,…,xm+5, we can write and xi=Eiδ/(S0−δS0), v1=(S1+δS1)/(S1−δS1), v2=(S2+δS2)/(S2−δS2).The problem (9.2) can be transformed into CCP. Note that the problem (9.2) itself is not a CCP because the first equation in Consider the case when we want to give a required value not to the stiffnesses themselves but to some combination of the stiffnesses. The design criterion takes the form with respect to Sμijkl. Note, that Sμijkl are not the design variables. Then the design problem is reduced to the followingFor any l problem (10.2) can be solved as above and write the general solution Λ of the problem (10.1) in the form Λ=⋃l∈LΛ(l), where Λ(l) means solution of An example. The numerical values of the coupling and bending stiffnesses depend on choose of the coordinate system. Consider the stiffnesses Sμijkl and Sμijkl(h) and quantities Sμ and Sμ(h) (2.4) (μ=0,1,2) computed with respect to coordinate systems z and z+h (h is an arbitrary number), correspondingly. The quantities Sμ and Sμ(h) are related as follows (see , we can form the following two invariants (functions depending on Sμijkl, but not depending on h):The invariants (10.4) represent the physical in-plane and bending stiffness. In particular, D2(Sμijkl) is the bending stiffness computed in the coordinate system such that S1(h)=0.In the case under consideration the system (10.2) takes the formwhere l is an arbitrary number (a parameter). Analyzing the second integral in , where Emax and Emin mean the maximal and minimal values of E(z), correspondingly. is suitable to solve the problem (10.5) with l=0 and the method developed in is suitable to solve the problem (10.5) with arbitrary l.It was shown that the laminated plate design problem is related with the CCP. To write the CCP corresponding to the plate design problem we proposed to use Young’s modulus as coefficients of the convex combinations.We considered the continuous design problem (when one can use materials with any elastic characteristics to manufacture the plate) and the discrete design problem (when one can use a finite set of materials).Using the CCP technique, we analyzed the continuous design problem in details. In particular we described the general solution (the set of all solutions) of the continuous design problem.We presented a method solution the discrete CCP. This method can be used to solve the discrete design problem numerically.Kappa carrageenan fluid gel material properties. Part 2: TribologySemi-solid and liquid food thickeners typically take the form of either polymeric or particulate structures. These structures are known to control flow properties and mixing efficiency which can influence performance, texture and the perception of tastants and aromas. However, their structural influence on thin-film rheology (tribology), which is also relevant for texture perception, is not so well understood. In this investigation, the tribology in a boundary regime of lubrication is tested using kappa carrageenan lubricants formulated both in solution and as gelled particles in suspension (fluid gels) to provide new insights into the structural influence of thickener type on tribology. Polymeric lubricated systems were shown to be dominated by elastic deformation of the tribo surfaces and particulate suspensions were dominated by particles acting as contacting asperities of the mating surfaces. The tribology of gelled particles was shown to depend strongly on particle elasticity where less deformable (stiffer) particles reduce surface–surface contact and therefore reduce friction coefficients. The effect of particle volume fraction on friction coefficient is related to the number of particles entraining the contact and not particle–particle interactions or bulk rheological behaviour.► Fluid gels were prepared by sheared gelation of kappa carrageenan. ► Their volume fractions were determined from a novel centrifugation technique. ► Their tribology was assessed as a function of volume fraction and particle elasticity. ► Volume fraction determines the number of particles in the contact. ► Particle elasticity determines surface–surface contact and therefore lubrication.Polymeric and particulate thickeners represent two principle classes of thickener that are often used to impart thickness, texture and stability to a wide range of food products. When prepared at comparable viscosities, their structural dissimilarities have been shown to influence the perception of taste, where scores are higher with particulate thickeners than polymeric thickeners (). This was suggested to arise from differences in the efficiency with which they mix with saliva, where particulate thickeners allow for efficient mixing and, therefore, transfer of tastants to receptors on the tongue, whilst polymeric thickeners mix poorly with saliva due to the entanglements of polymer chains (Polymeric solutions above a critical concentration (C*) exist as an entangled network whilst below C*, the polymer chains act as single entities (Aqueous gelled particles have been used as fat replacements for phase separated semi-solid foods, e.g. mayonnaise or margarine (), where they mimic the physical behaviour of the dispersed phase. An example is microparticulated whey protein concentrates that are formed by shearing proteins during a heating step to form aggregates of a size determined by the applied shear forces (). Their sensory perception is dependent on protein aggregate size where watery/empty sensations are perceived below 0.1 μm, creaminess is perceived between 0.1 and 3 μm and powdery to gritty sensations are perceived on increasing size beyond 3 μm (). A similar effect of particle size on creaminess perception has been observed with calcium carbonate and alumina-type particles () thus highlighting the sensorial benefits of including particulates in food formulation, provided they are of appropriate dimensions. Creaminess has been shown to be strongly related to a function of the perceptions of thickness, smoothness and slipperiness (). Thickness can be related to viscosity (); smoothness relates to particle sizes within the dispersion () where in-mouth particle detection (inversely related to the perception of smoothness) depends on particle size, shape and hardness (); and slipperiness has been shown to relate to lubrication where friction is measured in a soft tribological contact (). The dependence of rheology on polymeric thickeners is relatively well reported in terms of molecular weight, concentration and chain conformation (); so too is its dependence on particulate hardness, swellability and volume fraction (). The impact of these factors on tribology, however, is not as well established in the literature. Previous work has shown that the conformation of polymeric hydrocolloid thickeners in solution (random coil versus rigid rod) has an influence on entrainment for lubrication () and so too does the properties of hydrocolloids as surface adsorbed boundary films (). The diameter of particles has shown to influence the mechanism of lubrication, where those smaller than the tribological surface roughness dimensions are entrained in all conditions () whilst larger particles require film thicknesses greater than the particle diameters for entrainment (). However, a detailed understanding of the differences between lubrication by particulate and polymeric thickeners is still lacking.In this work, aqueous gelled particles of kappa carrageenan (κC) were produced with diameter ∼1 μm that were not detected on oral consumption. With a view to understanding the texture perception of tribologically related attributes, the lubrication behaviour of suspensions was tested as a function of particle stiffness and phase volume. Using the same polymer, κC, in the form of a linear polymeric thickener, a direct comparison is also made between the tribology of polymeric and particulate thickeners.Kappa carrageenan (κC) (510,600 g mol−1) (GS 350 from Pierrefitte Auby, as in the preceding paper ()) was used for both polymeric and particulate thickener tribometry studies. It is a (1→4)-β--galactose-4-sulphate-(1→3)-3,6-anhydro-α-). In dilute solution it adopts an expanded chain conformation (), or ‘rigid-rod’, due to intramolecular electrostatic repulsions from the sulphated groups (). Aqueous gel formation is favoured on cooling κC solutions in the presence of appropriate cations, such as K+, via a coil-helix transition (The κC was ion-exchanged with tetramethylammonium salt by ion exchange on Amberlite IR 120 thus preventing gelation and allowing linear polymeric behaviour. The required mass of κC was dispersed in deionised water then heated to ∼85 °C for 1 h, whilst stirring, until fully solubilised. A range of concentrations was then prepared by dilution from a 2 wt.% batch. Log viscosity/log concentration plots reveal a coil overlap concentration (C*) of 0.23 wt.% using the method described by . Thus the κC chains will behave as single entities below 0.23 wt.% and as an entangled network at greater concentrations.Fluid gels were employed as particulate suspensions for κC to avoid the use of oil and surfactants which would influence tribological behaviour. The fluid gels used were identical to those described in the preceding paper (), where a sheared gelation route formed spherical microgel dispersions via κC gelation under the application of a shear force. For their production, κC solutions (∼85 °C) were prepared as described above (section ), but with 0.3 wt.% KCl (Sigma Aldrich) to allow for gelation on cooling. The heated solutions were transferred from a hot-plate to a non-sheared vessel maintained at ∼50 °C followed by a pin-stirrer (sheared vessel) cooled to 5 °C, rotating at ∼1438 rpm. The vessels were connected using silicone tubing and flow was induced from a peristaltic pump at 10 mL/min. The setup allows sheared cooling from 50 to 5 °C which was sufficient to produce fluid gels with small particle diameters (∼1 μm); for more information on the setup, the reader is referred to (Whilst maintaining a fixed KCl concentration (0.3 wt.%), the fluid gels were produced using a range of κC concentrations (0.5, 1 and 2 wt.%) to control particle elasticity's where stiffer particles are produced from greater κC concentrations. These fluid gels were then diluted with deionised water to provide a range of volume fractions, thereby allowing the influence of particle stiffness and phase volume on tribology to be investigated. Water was used for the dilution, rather than a KCl solution, because salts are known to drastically influence tribology () discussed a centrifugation method to determine the fluid gels' volume fractions (ΦFG) and explained, in detail, their rheological behaviour as a function of κC concentration and ΦFG. From that study, data to provide a rheological characterisation of the fluid gels used here, is represented in (a, b and c). The data characterises the fluid gels zero shear viscosity (η0), infinite shear viscosity (η∞, determined from fits to the Cross equation ()) and storage modulus (G'). This characterisation shows that η0 and G' are strongly dependent on ΦFG and span several orders of magnitude throughout the tested range. During low deformation rheological testing (η0 and G'), the behaviour is dominated by ΦFG due to interparticle connectivity. However, under shear where connectivity is lost, the rheological behaviour, specifically η∞, can also be seen to be strongly influenced by κC concentration due to its effect on particle stiffness.To approximate particle stiffness, compression tests were conducted on quiescently cooled bulk gels using a TA.XT. plus Texture Analyser (Stable Micro Systems Ltd., UK). To form the quiescent gels, aliquots of the κC/KCl heated solutions were reserved for quiescent cooling at room temperature where the resulting cylindrical gels (21.43 mm diameter) were formed and cut into 10 mm length pieces and were analysed on compression from a 40 mm diameter aluminium probe at a rate of 1 mm s−1. True stress and true strain values were calculated from the measured force/distance data using equations described by An MTM2 ball-on-disc tribometer (PCS Instruments, UK) was used for the friction measurements. In these experiments, a ball (19.05 mm diameter) is lowered to a disc (46 mm diameter, 4 mm thickness) where the two surfaces make contact. Both the ball and disc are driven independently to rotate, providing a contact where the entrainment speed (U) is given by Equation . Udisc and Uball are the disc and ball speeds, respectively, and SRR is the slide-to-roll ratio which is maintained at 0.5 to provide mixed sliding and rolling motions. The ball makes contact with the disc at a user defined normal load (W) and a tangential friction force (Ft) is measured from the instruments force transducers. Friction coefficient (μ), a dimensionless parameter given by Ft/W, is often used to represent the data. Stribeck curves (μ versus U) were obtained from measurements by ramping the speeds up (from U = 1 to 1000 mm s−1) and down until 6 runs were completed constituting 1 test. Tests were repeated 3 times (for each lubricant sample) and, since the up and down runs were comparable (for both polymeric and particulate lubricants), Stribeck curves were generated from the mean of the 18 runs for each lubricant with error bars representing one standard deviation of error. Tests were conducted at 10 °C throughout.Two tribopairs were used for this study: stainless steel ball/elastomer disc and PDMS ball/PDMS disc. The stainless steel balls (PCS Instruments, UK) and elastomer discs (cut from 4 mm White Silicone Sheet, Samco Silicone Products, UK) were purchased and used as supplied. The PDMS (polydimethyl siloxane) surfaces were home-made using Sylgard 184 (Dow Corning) which is supplied as a separate base and curing agent. These were mixed together with a siloxane surfactant, poly [dimethylsiloxane-co-methyl (3-hydroxypropyl) siloxane]-graft-poly (ethylene glycol) methyl ether (Sigma Aldrich), to render the surfaces hydrophilic () and were used in the ratio 100:10:1 for the base, curing agent and siloxane surfactant, respectively. Elastomer discs were cleaned by rubbing with washing-up liquid, sonicating in ethanol (5 min) and then sonicating in deionised water (5 min) and were not reused. The stainless steel balls were cleaned in the same way but were sonicated in acetone rather than ethanol and were reused ∼30 times. The same cleaning procedure was used for PDMS surfaces but they were only sonicated in deionised water. PDMS surfaces were reused 3 times, that is, new surfaces were used to test each lubricant (tested in triplicate). Normalised friction coefficients (μnorm) were obtained by normalisation against the greatest friction coefficient for each series. Values of margins of error were calculated from their values (one standard deviation of error) as a percentage of each friction coefficient, averaged over the data sets.The ball and disc surface profiles were analysed for their roughness characteristics using interferometry (MicroXAM interferometer, UK) and representative scans are shown in using Scanning Image Processor software (Image Metrology, Denmark). Scanned areas of 432.3 by 321.5 μm were taken using a 20× objective lens on 9 locations of 3 surfaces, that is, 27 areas scanned for each surface. The surface profile plots were used to understand the dimensions of fluid components allowed for entrainment.To assess an approximation of the elasticity of the fluid gel particles, compression tests were conducted on quiescently cooled bulk gels. It has been shown (), however, that κC fluid gels have fewer helical domains, and therefore slightly weaker structures, than their corresponding quiescently formed gels due to the coil-helix molecular ordering process being disrupted by the applied shear. Thus, the compression tests were conducted only to provide an indication of the particle elastic properties and a trend with polymer concentration, and were not expected to represent actual particle stiffness values.True stress/true strain curves for the quiescently formed gels during compression tests are shown in . The curves shown are representative of the data obtained and the Young's moduli (E) values quoted (gradients below 0.05 strain) are the mean of 5 repeated experiments. The Young's moduli increase with polymer concentration providing a range of elasticity's expected for the fluid gel particles. The data is summarised in together with fluid gel particle diameters and their phase volumes after production.To identify the most appropriate tribopairs for the tribological analysis of both polymeric and particulate fluids, Stribeck curves were obtained (in triplicate) for a range of polymer concentrations. The choice of tribopair to be used for subsequent testing on each thickener type was then based on identifying tribopairs that reproducibly discriminate lubricants by their κC concentrations. Tribopairs of animal tissue have been prepared () and shown to be useful for enhancing the resemblance of tribological testing to oral behaviour. However, due to issues with availability and reproducibility, animal tissues were not considered in this study. The two tribopairs that were analysed in this study were: elastomer-steel, since it is known to provide friction coefficients that correlate with sensory attributes, specifically, the perception of slipperiness during consumption of guar gum solutions (); and PDMS–PDMS, because it can be formed to user defined properties and has previously been studied as a tribopair to understand the effect of surface elasticity (). The PDMS–PDMS tribopair may be considered to be more relevant for resembling oral surfaces than elastomer-steel in terms of surface elasticity, wettability, and roughness. However, as discussed, the choice of tribopair was based on maximising reproducibility and discrimination between samples thereby providing a setup where the structural influence of lubricants on tribology could be assessed. shows Stribeck curves for elastomer-steel and PDMS–PDMS tribopairs lubricated with 0.5, 1 and 2 wt.% κC as both linear and particulate structures. The data can be seen to have two regimes of lubrication typical for Stribeck curves: boundary and mixed regimes. The boundary regime is observed at the lowest speeds where friction is independent of U and indicates behaviour where the load is supported by asperity contact and surface adsorbed matter. As U increases and fluid is entrained into the contact, the fluid pressure increases at the site of the converging geometry formed by the ball-on-disc (). This pressure build-up partially separates the surfaces causing the load to be supported by both asperity contact and the lubricant film. This is a mixed regime of lubrication where friction reduces with speed (). The upper limit of the mixed regime is where the surfaces are fully separated and friction reaches a minimum. Friction would then be expected to increase with greater speeds as the volume of fluid being sheared increases (this is known as hydrodynamic lubrication, and was not observed here).a and b), the greatest reproducibility (smallest margins of error) and discrimination between varying concentrations is provided by the elastomer-steel tribopair. For the particulate fluid gel systems (c and d), the margins of error are similar for both tribopairs but PDMS–PDMS shows greater discrimination between differing fluid gel concentrations. Consequently, the elastomer-steel tribopair was selected for further analysis on polymeric behaviour; and PDMS–PDMS for the particulate fluid gels.Normalised friction coefficients (μnorm) were used in to allow direct comparisons of the influence of tribopair on the reproducible discrimination of lubricants. Absolute friction coefficients (μ) were not compared between tribopairs because their values (for the same lubricant) were very different. The two-term model of friction () states that, during the sliding of solid surfaces, friction forces can be considered to arise from breaking the adhesive forces at the interface and deformation at the sub-surface level. Thus, on comparison of the two tribopairs tested here, greater absolute friction values, which were observed with PDMS–PDMS, are expected to arise from greater adhesive forces and deformation under load; this effect is despite the fact that the PDMS–PDMS tribopair has a greater surface roughness and therefore lower real area of contact than elastomer-steel.The reason for such poor discrimination between fluid gel polymer concentrations using the elastomer-steel tribopair may result from the low surface roughness's () preventing entrainment of particles (∼1 μm) to the contact, thereby eliminating the effect of the differing particle elasticity's with κC concentration.The boundary lubrication characteristics of κC as a linear polymeric thickener were assessed on the elastomer-steel tribopair by measuring friction, at 3 mm s−1, as a function of applied normal load (W) (shown in a shows that for both water and a 0.5 wt.% κC solution, the friction force (Ft) follows a dependence of W2/3. This W2/3 dependency has previously been observed in soft surface tribometry () where the highly compliant surfaces have a contact area influenced by the applied normal load; the derivation of this behaviour will now be explained. Hertz theory states that elastically deforming contacting asperities have a contact area that increases with load proportionally to W2/3 () to be directly proportional to the real area of contact; in that case, Ft is then dependent on W2/3. For non-compliant surfaces, this behaviour is only observed when there is a single asperity contact, such as that observed during friction measurements of an Atomic Force Microscope (AFM) (). For multiple asperity non-compliant (‘real’) contacts, the contact area increases linearly with W due to an increasing number of asperity-contacts with increasing load; as observed experimentally and theorised by . Transitions between linear and W2/3 behaviour have been reported in AFM studies as wear modifies multiple-asperity contacts to single-asperities () and for rough tips behaving as single-asperity contacts when contamination fills the voids between mating surfaces (), thus indicating how the contact type can be identified from the dependence of Ft on W. For the highly compliant elastomer surface used here, the observed W2/3 trends are provided by a fixed number of contacts deforming elastically under load.a also shows that κC provides lower friction forces than water at all loads. This behaviour is further probed in b by considering boundary friction coefficients (3 mm s−1 and a fixed load W = 2 N) as a function of κC concentration. The data shows that κC has an effect of reducing boundary friction, a behaviour which continues on increasing concentration. Significant boundary lubrication by κC was recently shown to be provided by hydrated viscoelastic surface adsorbed layers (). Further to this, the continued reduction in friction coefficient with increasing polymer concentration is consistent with the behaviour of hydrocolloids of an expanded chain conformation enabling entrainment to the ball and disc contact (Sheared gelation of κC with KCl allows for the formation of particles using similar ingredients to that used for the linear polymer tribological study. Comparisons can then be made between the behaviour of linear polymer and particulate fluid tribology. a shows friction force as a function of normal load for PDMS–PDMS surfaces lubricated with deionised water and fluid gels formed with three κC concentrations (0.5, 1 and 2 wt.%). The water lubricated contact, for PDMS–PDMS (a), shows friction following a W2/3 dependence, as expected for the highly compliant surfaces. The three fluid gel particulate systems, however, follow a linear dependence on W (in contrast with the behaviour of κC as a linear polymer, a, which followed a W2/3 dependence). An explanation for the linear dependence with the particulate lubricants is that the system follows Archard's law () where a load dependent number of contact sites mechanism prevails. In this model, increasing the normal load would deform asperity contacts thereby allowing the particles between neighbouring asperities of the same surface (which would be allowed given the PDMS ball and disc surface roughness's, see ) to make contact with the opposite surface, thereby increasing the number of contacting sites. a also shows a reduction in friction on increasing κC concentration which is likely to result from the increased particle elasticity's. However, the fluid gel particle volume fraction also increases with κC concentration (); thus, understanding the effect of particle elasticity on tribology required the particle volume fractions to be controlled, the results of which will now be discussed.A range of particle volume fractions was prepared by diluting fluid gels with deionised water. As discussed in the Methods section, water was used, rather than a KCl solution, because salts are known to influence sliding friction (b shows the dependence of boundary friction (at 3 mm s−1 and W = 2 N) on the κC concentration used to form the fluid gels and their volume fraction (ΦFG). The data shows that boundary friction continually reduces with increasing number of particles until reaching a plateaued effect from ∼0.3 < ΦFG < ∼0.6; a further reduction in friction then occurs at ΦFG > ∼0.7. Increasing particle Young's modulus, through an increase in κC concentration, reduces boundary friction over the range of volume fractions tested.On comparison of the two thickener types, low concentrations of κC in the linear polymeric form showed a greater reduction in friction compared to water, than that for the particulate thickeners. Since this is due to polymeric κC adsorption to the tribopair surfaces it may not be relevant to in-mouth behaviour and requires sensory testing which was outside of the scope of this study.Particle entrainment to the ball and disc contact is suggested from b, even in boundary conditions, from the fact that increasing the number of particles, and their elasticity's, reduces friction coefficients below the value obtained for the solvent (water). Given that the fluid gel particle sizes () are able to fit within the surface asperities (), particle entrainment at all speeds seems reasonable.The plateau in boundary friction between ΦFG ∼ 0.3 and ∼0.6 occurs despite the significant change in viscosity and storage modulus throughout this range (). The dependence of boundary lubrication on volume fraction, therefore, seems related to the number of particles within the contact, rather than particle–particle interactions and bulk rheological properties. It would then follow that the number of particles within the contact increases throughout the range 0 < ΦFG < ∼0.3, remains unaffected between ∼0.3 < ΦFG < ∼0.6, and then at ΦFG >∼ 0.7 a multiple particle entrainment mechanism allows numerous ‘layers’ of closely packed particles to entrain. This proposed mechanism is depicted schematically in Throughout the volume fraction range ∼0.3 < ΦFG < ∼0.6, there is a clear effect of reduced boundary friction on increasing particle stiffness through κC concentration. This is expected to be because the resistance of the particles to a compressive force (i.e. their stiffness) determines the level of contact between the ball and disc, for a given normal load, and therefore the sliding friction coefficient. Thus, stiffer particles reduce surface-surface contact and therefore provide significant lubrication.The implications of reduced friction on increasing particle stiffness will now be discussed. Whilst an increase in particle elasticity reduces boundary friction, particle detection on oral mucosa will occur on consumption of very stiff particles (particle detection is known to increases with particle material properties e.g. hardness ()). Additionally, as the hardness of the particles exceeds that of the ball and disc, three-body-abrasion will occur resulting in surface wear (). Thus, the effect of reducing boundary friction with increasing particle stiffness is likely to occur only until the particle properties become similar to that of the rubbing bodies, which will depend on the use e.g. skin-creams, foods or mechanical parts etc.The tribological effect of fluid gel particle size was considered insignificant in this study as they were all of similar diameter () which was roughly equivalent to the surface roughness dimensions (). Previous studies on the tribology of dispersions with particles much larger than the tribopair roughness () have shown a particle exclusion effect in boundary conditions. Thus, the ratio of particle diameter to surface roughness clearly has a tribological importance. This effect may have an impact on the sensory perception of dispersions where particle diameters in relation to oral mucosa roughness dimensions could be a critical parameter and may explain the relation between microparticulated whey concentrate diameter and sensory response which, as discussed in the Introduction to this paper, has perceptions of watery to creamy to grainy as the average diameter is increased. By this argument, very small particles would produce a low reduction in friction compared to water (when at low enough phase volumes that boundary friction and single-particle layers occur) due to the particles being too small to provide surface seperation given the large surface irregularities.Although it was not in the scope of this fundamental tribological study, it would also be interesting to study the effect of the boundary friction plateau, ∼0.3 < ΦFG < ∼0.6, on sensory attributes. Considering the significant change in bulk rheology throughout this range, it is expected that any effects on sensory would only influence attributes generated during the late stages of oral processing where a thin-film is formed shortly before and after swallowing.Kappa carrageenan was used in aqueous systems in the absence of gelling salts to represent a linear polymeric thickener, and as a fluid gel to represent a particulate thickener. The dependence of tribological behaviour on thickener type and polymer concentration was then explored.Tribometry of the polymeric carrageenan thickener showed a large reduction in friction compared with water alone where entrainment to the contact occurs such that lubrication increases with polymer concentration. The boundary tangential friction force followed a dependence on normal load of W2/3 due to elastic deformation of a fixed number of contacting sites of the highly compliant surfaces.Tribometry of the particulate thickener also showed a reduction in friction, compared with water, that continued with increasing particle volume fraction and elasticity. The boundary friction force followed a linear dependence on normal load as the particles act as surface asperities increasing in number of contacting points with normal load. Contrary to the bulk rheological behaviour of fluid gels, which is dominated by particle–particle interactions and hence volume fraction, tribometry showed a comparatively weak dependence on volume fraction and a strong dependence on particle elasticity. This is due to particles being squeezed between the tribometry surfaces such that their strength against compression determines the ball-and-disc surface separation and, therefore, friction – where lubrication is increased with stiffer particles. This study therefore shows a clear example of bulk rheological properties failing to predict tribological trends, where a structural explanation is required to understand the behaviour of both. Further studies in this area are required to understand the effect of the observed tribological behaviour on sensorial attributes.Tool wear and its effect on microstructure and properties of friction stir processed Ti–6Al–4VTi–6Al–4V alloy was subjected to friction stir processing at rotation rates of 400, 800 and 1200 rpm using a polycrystalline cubic boron nitride (pcBN) tool and tool wear at different travel distances was investigated. At high rotation rates of 800 and 1200 rpm, the greatest tool wear, including mechanical and chemical wear, occurred at the initial tool plunge point. Detailed microstructural examinations on the tool plunge point at 1200 rpm by transmission electron microscopy indicated that the “onion ring” structure in the stir zone was caused by a variation in the distribution of TiB particles. Two similar but not identical spatial phase sequences around BN particles, BN–TiB2–TiB–α-Ti (N) and BN–TiB2–TiB–transformed β-Ti (N), as well as Ti2N phase were identified. The reaction mechanism between the tool and the Ti matrix was discussed. Moreover, when the tool wear reached a steady-state condition, the effect of tool wear on the microstructure and mechanical properties of the stir zone was evaluated. A fully transformed β with a Widmanstatten structure was observed at all rotation rates and the average size of prior β grains increased with the rotation rate. The tool wear led to an increment in hardness and tensile strength but a loss of ductility of the stir zone.Titanium and its alloys have been extensively applied in aerospace, chemical and biomedical fields because of their high specific strengths, excellent corrosion resistance and good compatibility Friction stir welding (FSW) has attracted great attention in the industrial world due to its many advantages since its invention in 1991 However, compared to low-melting-temperature alloys, the research on the FSW of titanium alloys is still limited mainly because of two issues. The first one is a limited FSW process window for obtaining defect-free joints due to low thermal conductivity and bad forming ability of titanium alloys. For example, Edwards and Ramulu W-series alloys such as W alloys and WC materials have been mainly used as the tool materials for FSW of titanium alloys Polycrystalline cubic boron nitride (pcBN), which is used as a cutting tool for steels In the past few years, several investigations on tool wear of pcBN in the FSW steel welds In order to evaluate the suitability of pcBN tools for FSW of titanium alloys, it is of practical importance to systematically examine tool wear under different parameters. It is also of great significance to clarify the nature of wear products of pcBN tools and to check whether B or/and N exist only in the form of BN or indeed react with the elements in titanium alloys to form other compounds. Furthermore, investigation of this subject can also provide some fundamental knowledge about the wear of pcBN tools for cutting titanium alloys Although the previous studies on the FSW of composites showed that tool wear significantly deteriorated properties of the welds In the current study, Ti–6Al–4V was friction stir processed (FSP) using a pcBN tool over a wide range of rotation rates from 400 to 1200 rpm, and tool wear and the microstructure and mechanical properties of the stir zones were examined. Based on the similar principle of FSW and FSP, the FSP sample essentially represents a bead-on-plate (no seam) weld, and tool wear and microstructure and properties in the stir zone for the FSP samples are the same as that for the FSW samples. Therefore, it is appropriate to use FSP to represent FSW to achieve the purpose of this study. The objective of this study is (a) to clarify the nature of wear products of pcBN tool and their effect on microstructure and properties and (b) to exploit a larger FSW window using a pcBN tool.Four-millimeter-thick commercial mill-annealed Ti–6Al–4V plate was used as the raw material. The plate was friction stir processed along the rolling direction at a constant travel speed of 100 mm min−1 with various rotation rates of 400, 800 and 1200 rpm. A pcBN tool with a shoulder 15 mm in diameter and a triangular prismatic pin 6 mm in diameter and 2.2 mm in length was used. Argon shielding was employed to prevent oxidation of the plate surface. shows macro- and microstructure observation locations away from the tool plunge point for investigating tool wear. Microstructural characterization and analysis were conducted using optical microscopy (OM), scanning electron microscopy (SEM, Supra 55) and transmission electron microscopy (TEM, FEI, Tecnai G2 20) with an energy-dispersive spectroscope (EDS, Oxford). The EDS experiments were operated on SEM and TEM with accelerating voltages of 20 kV and 200 kV, respectively. The OM and SEM specimens were etched in Kroll's reagent. The prior β grain size of the FSP samples was estimated by the linear inception method, and more than 400 grains were measured. Thin films for TEM were mechanically polished to ∼30 μm. In order to locate the region of the wear products precisely, thin films were etched in Kroll's reagent before being punched into 3 mm discs, dimpled to ∼10 μm, and finally thinned to perforation by the ion-milling technique.Mini-tensile specimens with a gauge length of 5.0 mm, a width of 1.4 mm and a thickness of 0.8 mm were cut from the base metal (BM) and the SZ of the FSP plate perpendicular to the processing direction. Tensile test was performed at room temperature at a strain rate of 10−3 s−1. Vickers hardness measurement was conducted using a Vickers indent with a load of 300 g and a dwell time of 15 s.In this work, the specimen cut from the location M mm away from the plunge point of the FSP plate at a rotation rate of N rpm will be simplified as N rpm–M mm specimen. For example, the specimen cut from the location 7 mm away from the plunge point of the FSP plate at 400 rpm is denoted by 400 rpm–7 mm specimen. shows the cross-section macrographs of 400 rpm FSP sample at different travel distances. All the SZs showed a parabolic profile. Near the top surface of the 400 rpm–0 mm specimen, black particles with sizes of about 1–100 μm were observed and as the travel distance increased, the number of these black particles increased at first (travel distance less than 7 mm) and then decreased until they almost disappeared at a travel distance of about 28 mm. At the bottom of the SZ, there were black bands with deeply etched lines and as the distance increased, the contrast of these bands became weaker and weaker until they disappeared.EDS analysis showed that the blocky black particles near the top surface mainly contained B and N elements ((a)) and the matrix in the SZ contained 5.8 wt.% Al, 3.7 wt.% V and 90.5 wt.% Ti, which suggested that these black particles were pcBN tool wear debris. In black bands at the bottom of the SZ, a number of fine rod-shaped white particles were observed in an equiaxed α + transformed β, i.e. bimodal matrix ((b)). These rod-shaped white particles should be related to tool wear products and will be studied in detail in the next part. In these bands, the microstructure was obviously different from that in other regions of the SZ where there was no tool wear and a Widmanstatten structure was observed ( shows the cross-section macrographs of 800 rpm FSP sample at different travel distances. Macrographs for all travel distances were similar which were characterized by band structures with deeply etched lines near the top surface and in the middle of the parabolic-shaped SZ. As the travel distance increased, the band contrast showed a trend of gradually becoming weak and then remaining unchanged. In these bands, BN particles and fine rod-shaped white particles, similar to those in 400 rpm–0 mm specimen, could also be found. Typical microstructures of the SZ in 800 rpm–0 mm specimen were shown in . Obviously, the microstructure in the dark bands also showed a difference from that in other regions where there was no tool wear. shows the cross-section macrographs of 1200 rpm FSP sample at different travel distances. In all the cross-section macrographs, there was also a band near the top surface, like that in 800 rpm FSP sample. In 1200 rpm–0 mm specimen, an “onion ring” structure that was commonly observed in FSW aluminum alloy welds was found. As the travel distance increased, the “onion ring” contrast became weaker and after a travel distance of about 14 mm, the contrast hardly changed and only obscure outlines were observed. Obviously, 1200 rpm–0 mm specimen showed an interesting “onion ring” structure which may be related to tool wear. In the previous investigations, no such “onion ring” structure was reported in FSW/FSP titanium alloys (c) show the “onion ring” structure more clearly. Detailed microstructural examinations of 1200 rpm–0 mm specimen showed that there were three types of microstructures in the SZ. The first type was a Widmanstatten structure, as shown in (d), which existed in bright regions of the SZ (D in (a)) and the bright bands of the “onion ring” structure.The second type of microstructure was in the dark bands of the “onion ring” region, where large quantities of rod-shaped white particles (50–300 nm in width and 0.2–2 μm in length) were observed in a Widmanstatten matrix ((e)). Besides, a core–shell structure, consisting of a large black particle core (several micrometers in size) with white particle layers around it, was also observed ((e)). EDS analyses indicated that the large black particle core contained 48.6 wt.% B and 51.4 wt.% N, and the matrix contained 5.9 wt.% Al, 3.8 wt.% V and 90.3 wt.% Ti. The compositions of the black particles were very close to those of the BN phase, suggesting that they were tool wear debris. The magnified image in (f) shows that such a core–shell structure contained three layers: the BN core, the second layer, consisting of large numbers of ∼20 nm spherical particles, and the third layer, consisting of rod-shaped particles (50–300 nm in width and 0.2–2 μm in length). These rod-shaped particles exhibited a clear trend of being swept into the matrix. Therefore, the rod-shaped particles in the matrix probably came from the third layer of the core–shell structure due to material flow.The third type of microstructure came from the dark band (rectangle E in (a)), which looked like the tail of the “onion ring” region. For the simplification, we called this band the “tail band”. In this band, large quantities of fine rod-shaped white particles were homogeneously distributed in the matrix ((a) and (b)). Besides, there were many disc-shaped “reliefs” with sizes from 1 to 10 μm, which tended to “bubble” from the matrix. These “reliefs” could be classified into three types on the basis of different cores, corresponding to three types of core–shell structures, and were marked with 1, 3 in The first type of core–shell structure (marked with 1 in (a)) contained four layers: three inner layers, similar to the BN core–shell structure in the “onion ring” region in (f), and a disc-shaped external layer, whose magnification is shown in (c). In other words, the BN core–shell structure in the “tail band” contained one more layer than that in the “onion ring” region. The second type (marked with 2 in (b)) contained an inner layer, consisting of fine rod-shaped white particles, whose magnification is shown in (d), and a disc-shaped external layer. The third type (marked with 3 in (a)) contained only a disc-shaped layer. Strictly speaking, the third type should not be called a core–shell structure, but here, it is just for convenience when explaining the reaction process between Ti and BN in the subsequent text.TEM examinations of the dark bands in the “onion ring” region and the “tail band” revealed the existence of several tens to hundreds of nanometers-sized particles with various shapes including rod, regular and irregular hexagonal morphologies. These different shaped particles were composed of the same elements and crystal structure, and could be identified as the same phase by selected-area diffraction (SAD). Typical TEM images of the rod-shaped particle, with inserted SAD with [100] and [10-1] zone axis patterns and an EDS image, and the hexagonal particle are shown in (a), a boron peak was clearly observed in the EDS and this particle was identified as TiB phase by the SAD patterns. TiB is orthorhombic, space group Pnma with the lattice parameters a = 6.123 Å, b = 3.060 Å and c = 4.560 Å. TiB particles usually exhibit three-dimensional hexagonal prism-shaped and observed TiB particles with different shapes are believed to be related to different cross sections of hexagonal prism TiB particles.Besides, in many TiB particles, stacking faults on the (100) crystallographic plane were observed ((c)). This feature was commonly reported in TiB particles in the previous study (d)). Ti2N is tetragonal, space group P42/mnm with the lattice parameters a = 4.945 Å and c = 3.034 Å.TEM examinations of different core–shell structures in the “tail band” confirmed that the rod-shaped particles in the third layer of the first type of core–shell structure and in the core of the second type of core–shell structure were the same phase as those in the matrix, that is, TiB phase. The most external disc-shaped layers of the three types of core–shell structures were identified as the same phase. Typical TEM images of the first type of core–shell structure are shown in . The core was identified as BN phase by SAD, which confirmed the previous inference from EDS, and the nanometer-sized particles in the second layer were identified as TiB2 by SAD ((a)). TiB2 is hexagonal, space group P6/mmm with the lattice parameters a = 3.036 Å and c = 3.238 Å. The rod-shaped particles in the third layer were TiB. The most external layer was identified as α-Ti by SAD ((b)). In the α-Ti layer, N element could be detected by EDS analysis (not shown), suggesting that N was dissolved into α-Ti to form an α-Ti (N) layer.Therefore, the first type of core–shell structure in the “tail band” consisted of a BN core and TiB2, TiB, and α-Ti (N) layers from the center to the outside. The second type consisted of TiB particles core and an α-Ti (N) layer. The third type had an α-Ti (N) layer. The BN core–shell structure in the “onion ring” region contained BN core, TiB2 layer, TiB layer and in the outside, there was a transformed β matrix.Based on the microstructural observations in Section , the tool wear at all rotation rates reached a steady-state condition at a travel distance of ∼28 mm, therefore, in this part, the specimens for investigating the microstructure and properties were cut from the locations over 50 mm from the plunging point, where the processing forces were also believed to reach normally steady-state conditions shows the cross-section macrographs in the locations about 75 mm from the plunging point at different rotation rates. The SZ in each FSP sample exhibited a parabolic shape and the SZ broadened as the rotation rate increased. In each cross-section, four distinct regions could be observed, which were named the SZ, TMAZ, HAZ and BM, as marked in . In the 400 rpm FSP sample, cavities were found at the bottom of the SZ. In the 800 rpm and 1200 rpm samples, no defects except for wear bands were found.Microstructures of the BM, HAZ and TMAZ of the 800 rpm FSP sample are shown in (a)) consisted of equiaxed primary α (αp ∼ 3 μm) with the transformed β (whose magnified image was shown in the insert) located at the “triple-points” of the α grains, which is usually called fully equiaxed microstructure. The microstructure in the HAZ ((b)) changed into an equiaxed primary α with a volume fraction of about 50% and transformed β (lamellar secondary α + residual β), that is, so-called bimodal microstructure. This change originated from that β phase increased its volume fraction due to the temperature rise and then was transformed into lamellar secondary α and residual β during the subsequent cooling. In the TMAZ, due to higher temperature and deformation, the volume fraction of primary α decreased rapidly to less than 5%. Therefore the TMAZ consisted of transformed β and a small number of primary α (SEM images showed that the SZs in all rotation rates consisted of fully transformed β with a Widmanstatten structure and prior β grains were decorated by fine grain boundary α marked with white lines ((a)–(c)). The average size of the prior β grains increased with the rotation rates and they were 22, 47 and 56 μm at rotation rates of 400, 800 and 1200 rpm, respectively.In the bands with wear particles of the SZs at 800 and 1200 rpm, the size of prior β grains was similar to that in regions where there was no tool wear. Typical microstructure in the wear band of the 1200 rpm FSP sample is shown in (d) and (e). In this region, fine rod-shaped TiB particles but no BN particles or core–shell structures were observed. Besides, the number of α variants increased and the length of α variants decreased largely compared with that in the SZ where there was no wear particle at 1200 rpm (Vickers hardness in different regions at different rotation rates is shown in . The HAZs or TMAZs in all the FSP samples were the lowest hardness region. The SZ at 400 rpm showed a slightly higher hardness than that at 800 and 1200 rpm. The hardness in the wear bands of the SZs showed a little increment compared with that in regions where there was no tool wear.Tensile properties of the SZs at different rotation rates are shown in . All the SZs showed a slightly lower tensile strength and ductility than the BM. The tensile specimens containing the wear bands at both 800 and 1200 rpm showed a higher strength but a lower ductility than those without wear bands. There were 20% and 32% losses of ductility in the tensile specimens containing wear bands at 800 and 1200 rpm, respectively.At all rotation rates, tool wear including mechanical wear and chemical wear occurred (). This phenomenon was also found in FSW stainless steel joints using pcBN tool At 400 rpm, however, the greatest tool wear was not observed at the plunge point. The blocky wear particles including several single cBN particles were detected at the plunge point at 400 rpm because of insufficient heat input. Blocky wear debris was peeled off from the tool, which probably deteriorated the wear-resistance of the tool and thereby greater tool wear occurred in the subsequent travel process. As the travel distance increased, the processing temperature increased, which decreased the trend that BN particles were peeled off from the tool. It was reported that a self-optimized geometrical shape of the tool could be obtained in the FSW joints of ceramic particle reinforced Al matrix composites as the travel distance increased An “onion ring” structure was evidently visible in the 1200 rpm–0 mm specimen ((a)). In the previous studies of FSW Al alloys, the “onion ring” structure was considered to be related to geometrical effect (c)), which were caused by the reaction between pcBN tool and Ti.It is known that different reaction products between BN and Ti could be obtained dependent on the reaction condition and the proportion of the reagents. In this study, core–shell structure in the “onion ring” region and the “tail band” () clearly indicated that different reaction layers were obtained. The different core–shell structures in the “tail band” should correspond to different intermediate reaction products between Ti and BN. Based on the different reaction products, the reaction mechanism of Ti and BN is proposed as follows ((a)), Ti was rapidly softened and stuck to BN particles at high temperature. The peak temperatures of the welding tool were reported to exceed 1300 °C when Ti–6Al–4V was friction-stir welded at a rotation rate of 800 rpm (b)), a TiB2 layer around the BN particle and an α-Ti (N) layer outside were formed. Due to the high affinity between Ti and both B and N, the reaction products between Ti and BN could be titanium boride or/and nitride. TiB2 is the most stable compound when the temperature is over ∼800 K because the Gibbs free energy of its formation is minimal compared with other compounds (c)), BN was further consumed and a TiB layer formed. At this reaction stage, Ti and TiB2 further reacted at the α-Ti/TiB2 interface to form a TiB layer due to the small negative Gibbs free energy of the reaction: Ti + TiB2 → 2TiB (a)). Such a spatial phase sequence was also reported in a diffusion experiment when BN was embedded into Ti matrix (d)), BN and TiB2 disappeared. For some BN particles, as the time increased, BN was totally consumed by reacting with Ti to form TiB2. Because of the diffusion of B atoms, TiB2 was also consumed by its further reaction with Ti. Therefore, finally TiB and α-Ti (N) were left (the second type of core–shell structure in (b)). Due to the “stirring” effect of the tool, TiB particles flowed into the matrix, and therefore only α-Ti (N) was left in some cases (the third type of core–shell structure in Obviously different microstructures with wear products were observed in the 0 mm specimens for various tool rotation rates (). These phenomena were related to the change of β transus temperature because different contents of the wear product [N] atoms dissolved into the matrix (). As mentioned above, the peak FSP temperature at 1200 rpm probably exceeded 1300 °C but was lower than the melting temperature of Ti–6Al–4V (∼1670 °C). In the “onion ring” region of the 1200 rpm–0 mm specimen, sufficient stirring effects made N be homogeneously dissolved into the matrix, leading to a low N concentration. EDS analysis showed that the contents of [N] in the “onion ring” were 0.7–2.7 at.%. When the temperature exceeded 1300 °C, material in the “onion ring” quickly entered to single phase β-Ti (N) field (marked with A in ) and, after cooling down, transformed β-Ti (N) consisting of lamellar α-Ti (N) + residual β-Ti (N) was left. Based on the discussion above, it can be concluded that the BN core–shell structure in the “onion ring” contained four layers, that is, BN core, TiB2 layer, TiB layer and transformed β-Ti(N) layer (the matrix).It was reported that the tool wear was more prominent on the advancing side (AS) . Therefore, the spatial phase sequences in the “tail band” and the “onion ring” region around BN particles in the 1200 rpm–0 mm specimen at high temperature during FSP were BN–TiB2–TiB–α-Ti (N) and BN–TiB2–TiB–β-Ti (N), respectively. Similarly, at the bottom region of the SZ in the 400 rpm–0 mm specimen, [N] dissolved into the matrix, making material enter in the α + β phase field during FSP, marked with C in , and then cooled down to form a bimodal microstructure (It should be pointed out that the [N] concentration in the 1200 rpm–0 mm specimen by EDS measurement was just for reference, which was inaccurate to express the [N] concentration during FSP because of two reasons. One is that the measurement in the content of light elements such as C, N, and O by EDS is inaccurate. Another is that the content of [N] would change significantly when cooling down because of its different solubility at different temperatures (). However, the locations of the materials in different regions with tool wear in the phase diagram (A, B and C in ) were rational because they were inferred based on the microstructure. Besides, in this study, Ti2N phase were found in the region with tool wear in the 1200 rpm–0 mm specimen (, however, Ti2N phase obviously could not exist above 1100 °C. Therefore, Ti2N probably precipitated during cooling because of significantly decreased solubility of N with decreasing the temperature.When the tool wear reached a steady-state condition, cavities were evidently visible at the bottom of the SZ at 400 rpm, while no such defects were observed at 800 and 1200 rpm (). These defects should be the result of insufficient heat input and material flow. For all the rotation rates, the SZs consisted of fully transformed β ((a)–(c)), suggesting that the peak processing temperature at all rotation rates exceeded the β transus point (∼1000 °C). Moreover, the mean size of prior β grains increased with the rotation rate. It is rational because higher rotation rate could produce higher peak temperature and longer exposure time at high temperature, and therefore β grains grew more rapidly without the retard of α phase after the tool passed away. Compared with the microstructure in the SZ where no tool wear was found, the bands with TiB particles consisted of more α variants and smaller size of α colonies ((d) and (e)). The microstructural change should be on the basis of the fact that TiB particles formed because of the reaction between the pcBN tool and Ti–6Al–4V workpiece at high temperature during FSP, which became the heterogeneous nucleation fields for α variants during cooling.At all rotation rates, the HAZs or TMAZs of FSP samples, consisting of bimodal microstructure, showed lower hardness than the SZs (). It was the result that alloy element partitioning effect played a more obvious role than the β grain size, even though for the bimodal microstructure in the HAZ or TMAZ, the β grain sizes were much smaller than that in the SZ. At both 800 and 1200 rpm, the regions with wear products showed a higher hardness and tensile strength but a lower ductility than those without tool wear (). This phenomenon should be attributed to the combination of brittle TiB particles and the dissolution of N element. Dispersed TiB particles increase strength through load transfer by shear lag mechanism; however they increase the strain incompatibility between brittle TiB particles and relatively ductile titanium alloy matrix, thereby reducing the ductility of the material The present study indicated the feasibility of FSP of Ti–6Al–4V alloy over a large range of rotation rates using a pcBN tool. Based on the similar principle of FSW and FSP, at high rotation rates (over 800 rpm) defects-free FSW Ti–6Al–4V joints are expected to be obtained using a pcBN tool. Unfortunately, under all conditions, tool wear occurred and it led to the loss of ductility of the SZ. Therefore, pcBN is probably not a good choice as a tool material for the FSW/FSP of titanium alloys, although it is proper for the FSW/FSP of steel. One of the main aspects for the FSW/FSP of titanium alloys in the future is still to seek for high wear-resistance tool materials, such as Co-based alloys At higher rotation rates of 800 and 1200 rpm, the greatest tool wear occurred at the tool plunge point. At a lower rotation rate of 400 rpm, the greatest tool wear occurred at the location 7 mm from the tool plunge point.At the tool plunge point at 1200 rpm, an “onion ring” structure formed because of the variations of the distribution of TiB particles. Spatial phase sequences around BN particles in the “tail band” and the “onion ring” region during FSP were BN–TiB2–TiB–α-Ti (N) and BN–TiB2–TiB–β-Ti (N), respectively, which were all the reaction products between BN and Ti.At the plunge point, the dissolution of N atoms resulting from reaction between BN and Ti, led to different microstructures at different rotation rates: a bimodal microstructure at 400 rpm, a Widmanstatten microstructure in the “onion ring” region and a disc-shaped microstructure in the “tail band” at 1200 rpm.At all the rotation rates, fully transformed β microstructures in the SZs were obtained. The mean grain size of the prior β grains increased with the rotation rate.Tool wear products – TiB particles and α-Ti (N) led to the increment in hardness and strength but the loss of ductility of the SZs.Modeling medium carbon steels by using artificial neural networksAn artificial neural network (ANN) model has been developed for the analysis and simulation of the correlation between the mechanical properties and composition and heat treatment parameters of low alloy steels. The input parameters of the model consist of alloy compositions (C, Si, Mn, S, P, Ni, Cr, Mo, Ti, and Ni) and heat treatment parameters (cooling rate and tempering temperature). The outputs of the ANN model include property parameters namely: ultimate tensile strength, yield strength, percentage elongation, reduction in area and impact energy. The model can be used to calculate the properties of low alloy steels as a function of alloy composition and heat treatment variables. The individual and the combined influence of inputs on properties of medium carbon steels is simulated using the model. The current study achieved a good performance of the ANN model, and the results are in agreement with experimental knowledge. Explanation of the calculated results from the metallurgical point of view is attempted. The developed model can be used as a guide for further alloy development.The properties of alloy steels mainly depend on the mechanical treatment, alloying elements and heat treatment variables. These three affect the microstructure, which in turn affects the properties. All alloys have defects such as intrusions, micro-blowholes and cracks. Apart from these defects, when alloys are made under industrial conditions, some amount of inhomogeneity and inconsistencies invariably creep in. These make the system-model chaotic. Besides this, the input variables that are considered are in reality fuzzy in nature. The first hurdle to overcome during modeling of steels is to acquire a reliable database. The industries that manufacture these alloys (or steels) tend to classify their process variables for obvious reasons. It is therefore very difficult to get a data set or information that would consist all of the above details. As the relationships between these outputs and inputs are nonlinear and complex in nature, it is impossible to develop them in the form of mathematical equations. Techniques such as linear regression are not well suited for accurate modeling of data which exhibits considerable ‘noise’, which is usually the case. Regression analysis to model non-linear data necessitates the use of an equation to attempt to transform the data into a linear form A BPNN model consists of an input layer and an output layer with as many units as their respective number of variables. In-between the input and output layers are the hidden layers, each having a certain number of nodes (or units). The actual number of nodes depends heavily on the system and the acceptable error level of the model. The error-correction step takes place after a pattern is presented at the input layer and the forward propagation is completed. Each processing unit in the output layer produces a single real number as its output, which is compared with the targeted output specified in the training set. Based on this difference, an error value is calculated for each unit in the output layer. The weight of each of these units is adjusted for all of the interconnections that are established with the output layer. After this, the second sets of weights are adjusted for all the interconnections coming into the hidden layer that is just beneath the output layer. The process is continued until the weights of the first hidden layer are adjusted. As, the correction mechanism starts with the output units and propagates backward through each internal hidden layer to the input layer, the algorithm is called as back-error propagation or back propagation (BP). A BP network is trained using supervised learning mechanism. The network is presented with patterns, (inputs and targeted outputs), in the training phase. Upon each presentation, the weights are adjusted to decrease the error between the networks’ output and the targeted output Typical applications of low alloy steels are general engineering components, high tensile bolts and studs, crankshafts, gears, boring bars, lead screws, shafting, milling and boring cutter bodies, collects. In the softened condition, the machinability of these steels is approximately 60% of that of mild steel, while in the hardened and tempered condition; the machinability is 45–55% of that of mild steel. The data on this low alloy steel has been collected from the handbook on Standard EN Steels The various heat treatment processes applied to low alloy steels are softening (sub-critical annealing) at 650–690 °C followed by air cooling or oil quench, hardening at 830–860 °C followed by oil quench and tempering at 550–660 °C followed by air cooling or oil quenching. The data consists of different section sizes and their heat treatment temperatures and type of quenching. So, the cooling rate varies for different section sizes, which is not uniform; furthermore, the variations of cooling rates are not linear. Based on ASM Metal handbook ), the cooling rate equations were developed for different section sizes (). The equations obtained based on the best fits are shown below.Y=5.77−0.01X−0.002X2+2.19E−5X3−1.11E−7X4+1.41E−10X5Y=6.16−0.15X+0.003X2−2.72E−5X3+9.33E−8X4+7.31E−11X5where, X and Y are diameter of the specimen and cooling rate, respectively.Based on the above equations, the cooling rate has been calculated for different section sizes and used as one of input parameters for NN training. After coding, the total sets available for modeling are 140 and shown in . Among the 140 data sets available, 112 data sets have been used for NN training. When training a model, the choice of input variables is of great importance. Also, when a combination of these variables is believed to be of particular importance, the model can be improved by adding the combination as an explicit variable. The model was trained on the ratio of Mn and S, where the concentrations are in wt%. This is because sulphur reacts with manganese and forms MnS. To avoid biasing of the model, the individual variables making up the Mn/S ratio are also included, so that the direct influence of any of them can also be detected. The statistics of the steels data used for neural network modeling is presented in Results obtained from modeling studies are presented and discussed in detail in this section. In this study, the optimal parameters of the network are determined based on the minimum mean sum square (MSE) error where Etr(x) = average error in prediction of training data set for output parameter x. N

= number of data sets, Ti(x) = targeted output, Oi(x) = output calculated.In applying the BPNN for the proposed estimation work, the following key design issues, i.e. number of hidden layers and hidden neurons, neural network parameters (learning rate and momentum rate) and number of iterations are discussed.The influence of the number of hidden layers and the number of neurons in each hidden layer on the convergence criterion is studied extensively In the first case, the BPNN structure of one hidden layer with a learning rate of 0.25 and a momentum rate of 0.9 was trained with different hidden neurons starting from 8 to 30. Eight hidden neurons in single layer yield a value of MSE of 0.02045 after 200,000 iterations. shows the variation of MSE and Etr for different properties with the number of neurons in the hidden layer. With an increase in the number of neurons, the MSE value increases up to 10 hidden neurons and then gradually decreases with further increase of hidden neurons. In order to examine the effect of number of layers, the NN structure is also designed with two hidden layers, each containing 8–30 neurons in each layer, and the results are shown in . The effect of different combination of hidden neurons on two hidden layers is also shown in . Excellent convergence was observed with 22 hidden neurons in each layer, and a value of MSE of 0.00427 was obtained after 200,000 iterations with η

= 0.25 and α

= 0.9., it is clear that the convergence is better for the two hidden layers than the single hidden layer with different number of hidden neurons in the layer. Hence, 22 hidden neurons with two hidden layers have been selected for further training to optimise other parameters. Even though the MSE is 0.00359 with 30 hidden neurons, which is far less than that of 22 hidden neurons, the average error in output predictions is greater in all the mechanical properties. Hence, 22 hidden neurons in two layers were selected for analysis. One more advantage with the 22 hidden neurons selection is its less complexity in comparison to if 30 hidden neurons were to be selected.For back-propagation learning algorithm with fixed values of learning rate, η, and momentum rate, α, the optimum values are obtained by simulation with different values of η and α. Two values, η

= 0.25 and α

= 0.9, are initially chosen and varied to get the optimum value for each parameter. shows the variation of MSE and Etr for mechanical properties of the training data for different values of η and α with two hidden layers consisting of 22 hidden neurons in each layer. From , it is clearly evident that larger value of learning rate results in higher MSE and Etr, which is an expected behavior ). For the above combination, the MSE of 0.001015 is obtained after 200,000 iterations.The number of iterations executed to obtain optimum values is an important parameter in the case of BPNN training. The MSE achieved from different iterations is shown in . It is evident that the value of MSE gradually decreases during the progress of training, as expected. An error of 0.07067 after 1000 iterations reduces to 0.00237 after 100,000 iterations and falls to 0.00104 after 180,000 iterations, and no change has been found with further increase in the number of iterations. It has been observed that the MSE does not change significantly beyond 200,000 iterations and hence further processing has been stopped after the above-mentioned iterations. Finally, the 11 units in input layer, 22 hidden neurons in two hidden layers and 5 units in output layer (11-22-22-5) architecture with a learning rate of 0.55 and a momentum rate of 0.65 are used for prediction and analysis of the EN100 steels.The sigmoid function is used as the activation function in the present network. From , it is very much clear that the distribution of weights of the trained network, with 11-22-22-5 architecture, takes sigmoid shape. The initial values for the weights are randomly generated between −0.5 and 0.5, but as the training progresses the weights varied between a minimum value of −56.87 to a maximum value of 57.61. The magnitude of the variation of the weights indicates the complexity of the present system. A total of 885 weights will be available ((11 + 1) × 22 + 23 × 22 + 23 × 5). On completion of the training phase, the mechanical properties for the test data are estimated simply by passing the input data in forward path of the network and using updated weights of the network obtained.Total data sets available for BPNN Model training is 140. The randomly selected 112 data sets have been used for training, and the remaining 28 data sets are used for testing. The predictions of 114, 115, 116, 118, 119, 123, 125, 127, 128, 131, 133, 136, 137, 138 and 140 data sets (a total of 15 sets) shown in (a), (c), and (e). The comparison between the actual and predicted values and the respective percentage error for 15 testing data sets is also shown in (b), (d), and (f). It has been observed that most (nearly 95%) of the outputs predicted by the model are within 4% of the error band (indicated in (b), (d) and (f)). For the testing data that has never been seen by the model, the NN gives a reasonably accurate prediction. In the case of sample 11 (data set of 133 in ), it can be seen that there is a less variation between actual and predicted values as shown in (e), but the percentage error is higher because the actual values are very small.The developed model can be used in practice to manipulate the mechanical properties of EN100 steels, in general, by altering chemical composition and heat treatment variables. The effects of all of these can be estimated quantitatively by using the BPNN model to observe whether they make any metallurgical sense. The combined effect of a single variable or any two variables on the properties has also been studied. Here we present some hypothetical alloys by varying the composition and heat treatment variables and their effect on mechanical properties namely: (a) yield strength (YS), (b) ultimate tensile strength (UTS), (c) % elongation (EL), (d) % reduction in area (RA) and (e) impact strength (IS) for sample number 91 of . The effect of combined variation of two elements on properties is presented in . The composition of sample 91 is given in Carbon is an essential non-metallic element in iron to make steel. None of the other elements so dramatically alters the strength and the hardness as do small changes in the carbon content does. Carbon is the principal hardening element, influencing the level of hardness or the strength attainable by quenching. The model predictions as indicated in show that the YS and UTS increase while the EL and RA decrease with increase in C content. As carbon increases from 0.32% to 0.44%, (), there will be approximately a 15% increase in the formation of pearlite accompanied by a reduction of ferrite by the same amount, which results in an increase in strength and a decrease in ductility. The increase in strength and the decrease in ductility with the increase in carbon content are also due to the increase in the formation of various carbides with the other alloying elements as the carbon percentage is increased from 0.3 to 0.44. The impact strength would also decrease, as the area under the stress–strain curve would decrease owing to the reduction in ductility. Thus, the predictions of are clearly is in agreement with the expected experimental trend.Silicon is one of the principal deoxidizers used in steel making and therefore the amount of silicon present is related to the type of steel. Usually only small amounts (0.20%) are present in rolled steel when it is used as a deoxidizer. Silicon dissolves in iron and tends to strengthen it. In the low alloy steels, Si is present in the range of 0.2–0.4%. shows the variation of mechanical properties with silicon content in the range of 0.2–0.4%. The variation in mechanical properties as observed in cannot be explained based on the effect of Si alone. It is possible that a number of other elements present might be responsible for the behavior represented in shows that a significant change occurs in mechanical properties at around 0.3% Si, which needs to be explained based on metallurgical principles involving the complex combined effects of a number of elements. However, it is important to note that a significant increase in the UTS at around 0.3% Si brings a significant reduction in EL and RA exactly at the same composition. This suggests that the model is able to establish strong correlations between the individual output parameters, though such information is not fed to the model a prior.Manganese is a deoxidizer and degasifier, which reacts favorably with sulphur to improve forging ability and surface quality as it converts sulphur to manganese sulphide. Manganese increases tensile strength, hardness, hardenability, and resistance to wear and increases the rate of carbon penetration during carburizing. There is a tendency nowadays to increase the manganese content and reduce the carbon content in order to achieve steels with an equal tensile strength but improved ductility. shows the effect of Mn/S variation on mechanical properties. As Mn/S ratio increases strength increases with a corresponding reduction in ductility, which is clearly brought out by the model in Nickel is used to stabilise alloy steels. Nickel and manganese exhibit very similar behavior and both lowers the eutectoid temperature. It strengthens ferrite by solid solution but is a powerful graphitiser. Nickel increases the impact strength of engineering steels considerably. It increases the strength and hardness without sacrificing ductility and toughness. Steels with 0.5% nickel is similar to carbon steel but is stronger because of the formation of finer pearlite and the presence of nickel in solution in the ferrite. Among all of the common alloying elements, chromium ranks near the top in promoting hardenability. It makes the steel apt for oil or air hardening as it reduces the critical cooling rate required for the formation of martensite. (a)–(c) shows combined effect of Cr and Ni on the YS, UTS and EL, respectively. The figure clearly points out that the YS and UTS decrease with an increase in Cr content at lower concentrations for a given Ni concentration, which can be attributed to the ferrite stabilisation. However, at higher Cr content, the strength starts to increase again due to the formation of carbides. The percentage elongation shows exactly the opposite trend, as expected. Thus, the model is able to predict the combined effect of Ni and Cr quite successfully.The effect of cooling rate on properties is non-linear and complex, and it is difficult to explain. (a)–(c) shows the combined effect of cooling rate and tempering temperature on the YS, UTS and EL, respectively. Increase in tempering temperature brings in an initial increase in the strength in the temperature range of 450–550 °C, which could be attributed to the secondary hardening. Further increase in the tempering temperature leads to a decrease in the strength, as expected. The EL shows a reverse trend as expected. It is also important to note that the variation in the mechanical properties is larger with different heat treatment parameters (cooling rate and tempering temperature), in comparison to that with Cr and Ni variation. This clearly suggests that the mechanical properties are more sensitive to heat treatment parameters than the concentration of alloying elements such as Cr and Ni, which is clearly predicted by the model. shows actual and model predicted mechanical properties for different hypothetical alloys for sample 91. Though it is difficult to explain each and every behavior of hypothetical predictions, the model predicted a sudden increase in ductility, whenever there is a sudden decrease in the strength and vice versa, which has to be noted. It is very much clear that the error in the model predictions is less than 4% in all cases. This shows the efficiency of the model in understanding the relationships between input parameters and output parameters. This will greatly help the designing of alloy to achieve certain target properties.A comparison of the modeled and experimental results indicated that NN can very well be employed for the estimation and analysis of mechanical properties as a function of chemical composition and/or heat treatment for low alloy steels.Two hidden layers converged better than the single hidden layer. At higher learning rate, the MSE and Etr significantly increased as expected.Present model was able to map the relation between the output parameters, even though such a relation was not explicitly fed to the model. For example, the relationship between ductility and strengths was clearly brought out by the model (for example, Results from the current study demonstrated that the neural network model can be used to examine the effects of individual input variables on the output parameters, which is incredibly difficult to do experimentally. (Development of hypothetical alloys.)A fatigue life model for 5% chrome work roll steel under multiaxial loadingThe fatigue behavior of 5% chrome steel heat-treated for wear resistance has been investigated under axial–torsional loading. This material exhibits brittle fracture under monotonic and cyclic loading. The preferred site for crack initiation appears to be carbide clusters on or near the surface. Crack propagation initially progressed in a transgranular mode followed by a mixed transgranular–intergranular mode at a later stage. A parameter given in terms of the maximum normal stress range and the hydrostatic stress range is found to correlate fatigue lives reasonably well. This parameter correctly predicts the experimental trend that in-phase loading is more damaging than out-of-phase loading under a given ratio of axial/shear stress amplitudes. Models for tensile and compressive mean stress effects have also been proposed based on the uniaxial test results.Heat-treated 5% chrome steel is widely used for work rolls in cold rolling operations. Work rolls are subjected to surface damage of various types. Among these are normal wear, bruising and spalling.Micro-cracks are commonly observed in ultrasonic and eddy current testing during periodic dressing of the roll surface. Cracks may be initiated by thermal shocks Another type of surface damage of a work roll is fatigue damage due to repeated contact loads. The material in the contact zone is subjected to complex, multiaxial, compressive stresses, which can initiate fatigue cracks and cause surface damage. Contact fatigue models have been reviewed by Tallian The purpose of this paper is to investigate the fatigue behavior of heat-treated, 5% chrome steel under uniaxial, torsional and combined axial–torsional loading conditions that lead to tensile fatigue fracture. A fatigue model will be proposed suitable for the material under the loading conditions employed. Some uniaxial tests will also be conducted in the presence of mean stress, and a model will be proposed for the mean stress effect. The results obtained in this work will be useful for studying the multiaxial fatigue behavior of other similar hard steels such as tool steels and high-speed steels.The chemical composition of 5% chrome steel under consideration is given in . Specimens used in this study are solid specimens with a round cross-section. The gage section had a diameter of 6 mm and a length of 20 mm. The specimens were machined from forged material that has undergone electrical remelting and spheroidizing. Prior to heat treatment initial machining was done such that the diameters at the gage section and at the grip area were 0.5 mm larger than the final dimension. The specimen was then austenized at 980 °C for 20 min and oil quenched at 60 °C. Then, the specimen was tempered for 3 h at 130 °C and cooled in air. The gage section of the heat-treated specimen was ground at a very slow rate to the final size to ensure that heat generated in the grinding process would not affect hardness. Finally, the gage section was polished with alumina powder. After this step, the specimen had hardness in the range of Rc 64–65. The microstructure of the material is primarily tempered martensite matrix with carbides (Fe,Cr)7C3. Most of the grains were observed in the size range of 10–15 μm. The average carbide diameter was 0.52 μm, with some having diameters as large as 2 μm.The monotonic stress–strain curve of this material is asymmetric in tension and compression. The compression test was conducted in a nonstandard way using a fatigue specimen, and terminated before failure occurred for safety reasons. It was found that this material is much stronger in compression than in tension (see ). The mechanical properties obtained from these tests are: Young’s modulus 197 GPa; 0.2% tensile yield strength 900 MPa; tensile strength 1400 MPa; elongation 1.3%; 0.2% compressive yield strength 2000 MPa; compressive strength >2500 MPa.Fatigue tests were carried out with an axial–torsional servo-hydraulic Instron machine at room temperature. The waveform utilized was triangular, and frequency varied from 0.5 to 5 Hz, with higher frequencies applied to lower amplitude tests. Failure was defined as a complete separation of the specimen. All tests were carried out under load control. It was unnecessary to measure strain because the load–displacement response was approximately linear for all test conditions. Loading conditions for uniaxial tests and torsional tests are given in . The combined axial–torsional tests are summarized in are fully reversed tests. Three phase angles between the axial and shear stresses were investigated under a given ratio of stress amplitudes. It is noted that the phase angles were found somewhat shifted from the intended values of 0°, 45° and 90° (see ), where suffices 1, 2, and 3 in the specimen numbers are in the order of increasing phase angles. The phase angle, nevertheless, stayed steady during each test.The fatigue parameter to be used in this study is given in terms of the maximum normal stress range and the hydrostatic stress range. This parameter has been constructed based on the fact that fracture of a brittle material is dictated by the maximum tensile stress, and on the fact that the parameter must be able to describe the relative experimental trends for different loading conditions. The fatigue criterion is given by:where Pn is the normal parameter, Δσn is the maximum normal stress range, Δσh is the hydrostatic stress range, Nf is the number of cycles to failure, k1, b and σ′f are material constants to be determined from uniaxial and torsional fatigue test data.The plasticity effect has not been included in this fatigue criterion since the cyclic stress–strain response of the material was elastic for all test conditions. The hydrostatic stress term in the parameter was introduced to model the differences in fatigue lives between uniaxial and torsional loading with identical maximum normal stress ranges. The hydrostatic stress was entered in various fatigue criteria in different ways. Haigh The computation of fatigue life was carried out using a computer program written for this study. It was assumed that the crack initiates and propagates on the critical plane where the maximum normal stress range occurs. The critical plane was determined using an increment of 1° in the angle of orientation of the plane that varied from 0° to 180° from the specimen axis. The fatigue parameter and life were then evaluated on the critical plane.It is worth noting that a shear fatigue criterion given by Δτ+sΔσn=τ′f(2Nf)b, where Δτ is the maximum shear stress range, Δσn the normal stress range on the Δτ plane, τ′f, s, b are fatigue properties, was also investigated for the possibility of shear fracture in the very early phase, which is difficult to verify because of the extremely small crack sizes involved. A similar attempt can also be found in an early study by Sines The orientation of fracture planes in uniaxial and torsional tests resembled that of a typical brittle material; 90° for uniaxial loading and 45° for torsional loading as shown in . A low magnification SEM micrograph of the fracture surface () was taken on a specimen subjected to uniaxial loading of Δσ =350 MPa, Rσ = 0.125. The crack appears to have initiated in the area marked by A and propagated approximately 0.4 mm deep in thumbnail shape before the onset of unstable fracture occurred. SEM micrographs of higher magnification revealed that crack initiation might have taken place at a cluster of subsurface carbide particles (). A similar observation can be found in Mueling et al. ) which was followed by mixed transgranular and intergranular fracture at a later phase (). The development of intergranular fracture is attributable to the carbide particles on the grain boundary, which reduce the grain boundary strength.The stress–strain hysteretic response obtained in all of the tests in was essentially elastic, even if the stress amplitude was considerably larger than the monotonic tensile yield stress. No significant changes of the hysteresis loop were observed during the test. An example is given for the axial–torsional test on specimen A1 in . The linear behavior during unloading and reloading is expected to span over the range of tensile yield stress plus compressive yield stress in view of the Baushinger effect in elastic–plastic materials. It is expected for this material that this range will be extended due to the substantially larger linear response on the compression side.The fatigue parameter versus life curve was determined from the results of uniaxial and torsional fatigue tests shown in (solid symbols), and fatigue properties are found to be: σ′f=4100 MPa, b =−0.079, k1 =0.77.The fatigue criterion in the presence of mean stress was not possible to be described with a single equation. The following two equations are proposed for tensile and compressive mean stress effects, respectively:where σnm is the mean normal stress on the plane of maximum normal stress range, k2 and k3 are material constants.For tensile mean stresses, the parameter versus life relation had the same slope as the no mean stress case. It is noted that is in the same form as Morrow’s mean stress model . The proposed model provides the general trend of mean stress effects. The constants k2 and k3 were found to be 3.49 and 2.49, respectively. It is apparent in that compressive mean stress is more beneficial at high cycles than at low cycles, while tensile mean stress results in the same degree of detrimental effects at both low and high cycles. The considerable scatter found in life data would be related to the statistical nature of carbide size and distribution. More scatter is found with compressive mean stress data, for which the slope of the fatigue curve is small.The results of life prediction are summarized in along with the experimental lives. It is found that the angles of fracture surface, measured from the plane normal to the specimen axis, agree reasonably well between predictions and measurements. The scatter in the data considerably obscures the phase-angle dependence of life. However, it seems certain that life is shorter for test conditions closer to in-phase loading (suffix 1) than for tests under more out-of-phase loading (suffices 2 and 3). The proposed fatigue parameter models this trend correctly. Under strain control tests on ductile metals, it is usually found in the low cycle fatigue regime that out-of-phase loading is more damaging than in-phase loading. This may be attributed to higher stress amplitudes due to additional hardening under nonproportional loading. The stress control employed in this study does not differ from strain control since the material response is linear and there is no cycle-dependent change. Thus, the life trend between in-phase and out-of-phase loading is reversed for the present material from that of ductile materials under strain control in the low cycle regime.An interesting comparison of the present results with available data can be seen in high-cycle in-phase and out-of-phase fatigue, where deformation is basically elastic as in the current study. Such data can be found in Refs. The predicted lives were compared with experimental lives in . It is observed that the parameter correlates the data but with some conservatism. The dotted line represents a band of life factor 3. Most of the data points fall within or very close to this band. It is also noted that there is more scatter in life data than usually observed in ductile metals. This is believed to be an inherent character of materials whose life is controlled by defects A series of axial–torsional fatigue tests were conducted on 5% chrome steel heat-treated for wear resistance. This material is widely used for work rolls in strip milling operations. The following conclusions can be drawn:The test material fails in a brittle manner with insignificant plasticity being developed under fatigue loading. Fracture occurs on the maximum tensile stress plane.The crack tends to initiate at a cluster of carbide particles on or near the surface. The crack propagates in a transgranular mode initially followed by a mixed transgranular–intergranular mode at a later stage.A multiaxial fatigue parameter has been developed in terms of the maximum normal stress range and hydrostatic stress range. This parameter correlates experimental lives with most data points in a band of factor 3.Under axial–torsional fatigue loading with a given ratio of stress amplitudes, in-phase loading produces greater damage than out-of-phase loading for the test material.Compressive mean stresses are more beneficial at high cycles than at low cycles, while tensile mean stresses are detrimental to the same extent at low and high cycles. Separate models have been proposed for tensile and compressive mean stress effects.Interaction between super-quadric particles and triangular elements andits application to hopper dischargeThe discrete element method (DEM), proposed by Cundall and Strack, has been shown to be a practical approach to studying various granular materials []. In this approach, two-dimensional disks or three-dimensional spheres were initially employed because they enable simple calculation and efficient operation []. However, the granular systems commonly encountered in industry or nature comprise non-spherical grains. Although the particle shape strongly affects the dynamics of granular systems, such as packing [], experimental measurements and numerical simulations have focused mainly on spherical particles. Meanwhile, the applicability of the conclusions drawn from spherical particle systems to non-spherical particle systems is doubtful []. To model particles of various shapes reasonably, different methods, including a composite approach based on regular elements [], dilated polyhedra based on Minkowski sum theory [], arbitrary convex shapes based on orientation discretization [], and super-quadricelements based on continuous function representation (CFR) [], have been developed. The super-quadric equation, which allows the aspect ratio of particles and the smoothness of the surface to be changed efficiently, is a more common approach to describe particle shapes. Meanwhile, 80% of solid shapes can be represented by super-quadrics [], and other solid shapes can be derived from higher-dimensionalhyper-quadrics [Contact detection between two super-quadric elements has benefitted from the development of approaches such as the common-normal concept [], and the geometric potential approach []. Compared to the common-normal concept [], the geometric potential approach has higher computational efficiency []. However, a disadvantage is that it may not meet better the definition of contact mechanics, i.e.,the normal force is perpendicular to the surface of two overlapping particles. For the interaction with boundaries, Podlozhnyuk etal. [] simulated industrial granular flows by constructing a triangular finite-element mesh; however, thus far, little effort has been devoted to the comprehensive description of the algorithms, including particle–particle and particle–boundary contact detection.Moreover, in discoid (2D) or spherical (3D) DEM, corresponding contact models such as the linear spring Hertzian model and the non-linear Hertz and Mindlin–Deresiewicz theories [] have been developed and widely applied; however, these approaches cannot be applied directly to non-spherical particles. Recently, the non-linear force model of spheres has been well extended to non-spherical particles [] and arbitrary convex shape based on orientation discretization [], leading to the accurate predictions of effects. Meanwhile, Podlozhnyuk etal. [] introduced the equivalent radius of particles in the linear contact model, which has been well verified. To date, the contact forces between super-quadricelements have mostly employed the linear spring Hertzian model, which may affect the calculation accuracy. Therefore, based on the standard spherical contact model, a corresponding non-linear force model considering the radius of curvature at the local contact point is applied for super-quadric particles.In recent years, the dynamics of granular discharge has been widely studied [], and the focus of investigation has shifted from spherical to non-spherical particles modeled using different construction methods [] used the composite spheres method to model rice particles and analyzed the characteristics of particle pulsation during discharge by relating the total force and velocity fluctuation. Liu etal. [] studied the shape non-uniformity and the polydisperse nature of granular materials for both spherical and polyhedral particle systems. The hopper configurations and the angularity of polyhedral particles had a significant effect on the mass flow rate. Fraige etal. [] showed that the discharge rate of cubes is lower than that of spheres and a large number of cubic particles remain in the hopper when discharge ceases. Mack etal. [] reported the flow characteristics of polyhedral granular particles. Excellent agreement between experimental and numerical results was observed for the discharge rates, arch structures, and flow patterns in the hopper. Höhner etal. [] performed DEM simulations of the discharge of non-spherical particles modeled using the composite spheres, polyhedron, and super-quadric methods. However, the different modeling approaches have been reported to affect the discharge characteristics strongly. Soltanbeigi etal. [] used the open-source code LIGGGHTS to represent super-quadric particles and studied the influence of the surface bumpiness of cubical particles on the flow characteristics. Cleary etal. [] investigated the effects of ellipsoids and cubes with different aspect ratios and blockiness on the discharge rate using a simplified super-quadric equation. However, the influences of ellipsoids (spheres), cylinders, and cubes with different aspect ratios and blockiness on the flow characteristics have rarely been compared. In addition, the superposed effects of different base angles on the discharge rate of differently shaped particles are infrequently described in detail.The super-quadric method was developed by expanding the quadric surface, which has been used extensively to describe particles with convex and concave shapes. The super-quadric equation is given as [where a, b, and c are the half-lengths of the particles along the principal axes, and n1 and n2 control the blockiness of the cross-section of the particles. When n1=n2, the above equation can be simplified to [This simplified equation may not describe cylinder-shaped particles accurately. Therefore, we used Eq. as the standard equation for the super-quadric particles in the present work. An ellipsoid is obtained for n1 = n2 = 2, a cylinder-shaped element is obtained if n1 ≫ 2 and n2 = 2, and a cubic shape is obtained if n1 = n2 ≫ 2. For n1, n2 → ∝, it is theoretically possible to describe real particles with sharp corners, but this model is usually limited by the search algorithm. Currently, the construction of non-spherical particles by the super-quadric equation is usually given a reasonable range of n1 and n2, thereby ensuring the stability and high efficiency of the algorithm [ shows the different particle shapes obtained by varying five parameters of the super-quadric equation. However, in the future, it will be necessary to compare further and analyze the effects of these approximate models and real particles with sharp corners on the macroscopic and microscopic characteristics of the granular systems.A given particle in a granular system can have two types of motion, translational and rotational, which are governed by Newton's second law of motion:Here, mi, Ii, vi, and ωi are the mass, moment of inertia, and translational and angular velocities of particle i, respectively. Fn,ij and Ft,ij are the normal force and tangential force acting on particle i by particle j or triangular element j, which both include the elastic force (Fije) and the viscous damping force (Fijd). Mn,ij and Mt,ij are the torques determined by the normal force and tangential force if the normal force does not pass through the centroid of the non-spherical particles, and Mr,ij is the rolling friction torque.In a DEM simulation of irregular particles, the local coordinate is applied to model the rotation of the particles conveniently. In general, to describe the transition relation between the local body-fixed reference frame and the globally fixed coordinates, three Euler angles and quaternions are the primary methods for determining the rotational motion of the particles. Compared with Euler angles, quaternions avoid the appearance of a singularity. Here, rotation matrix A can be determined with quaternion Q(q0,

q1,

q2,

q3):A=q02+q12−q22−q322q1q2+q0q32q1q3−q0q22q1q2−q0q3q02−q12+q22−q322q2q3+q0q12q1q3+q0q22q2q3−q0q1q02−q12−q22+q32The quaternions are related to the Euler angles byq0=cos∅2cosφ+ψ2,q1=sin∅2cosφ−ψ2q2=sin∅2sinφ−ψ2,q3=cos∅2sinφ+ψ2where ∅, φ, and ψ are the Euler angles. The orientation of a super-quadric particle specifies the relationship between fixed space system es and body system eb. These components are related by rotation matrix A:Here, the rotation matrix has the property A−1 = AT. For a more detailed description of the calculation of quaternions, refer to the work of Fritzer [Compared with the simple and efficient contact detection between spherical particles, the ratio of the time of contact detection between irregular particles to the entire simulation time will increase significantly, and the computational efficiency is mainly affected by the particle shape, boundary conditions, and search algorithm []. Because of the complexity of contact detection between non-spherical particles and the orientation under different contact patterns, the bounding spheres and oriented bounding boxes (OBBs) have been well developed, as shown in . The bounding sphere is used as the first point of approximate contact detection between two super-quadric particles. If the distance between two particle centers is larger than the sum of their corresponding radii, they are not in contact. Otherwise, they are in contact. Moreover, OBB is the second rough contact detection. If the distance of two centers of particles projected onto the separation axis is larger than the sum of the projections of each box onto it, the boxes do not intersect each other. More details can be found in reference [Finally, the Newton–Raphson approach is used to calculate the overlap between the particles i and j, which is based on finding a “midway” point X0. The corresponding non-linear equations are as follows [where Fi and Fj are the super-quadric equations of particle i and particle j in globally fixed coordinates, respectively, and λ2 is the non-negative multiplier. Newton's iterative algorithm for this problem can be expressed as∇2FiX+λ2∇2FjX2λ∇FjX∇FiX−∇FjX0dXdλ=−∇FiX+λ2∇FjXFiX−FjXwhere X = X + dX and λ = λ + dλ. If Fi(X0) < 0 and Fj(X0) < 0 can be satisfied for point X0, the two particles are in contact, and the corresponding normal direction can be described as n = ∇Fi(X0)/‖∇Fi(X0)‖, as shown in . Then, given Xi = X0 + α0n and Xj = X0 + β0n, we can easily determine the unknown parameters α0 and β0 by Newton's method []: α0k+1 = α0k − Fi(Xik)/(∇Fi(Xik) ∙ n) and β0k+1 = β0k −Fj(Xjk)/(∇Fj(Xjk) ∙ n), and the normal overlap is δn = Xi − Xj.In industry, non-spherical particles are frequently used; thus, a numerical calculation method (i.e.,the DEM) has been used to resolve the interaction between particles and complicated geometric boundaries. Based on the advantages of the finite element method, the arbitrarily geometric boundary models can be discretized and meshed by a series of triangular elements with controllable accuracy. Therefore, the aforementioned interaction can be simplified to the interaction with a triangular element. Meanwhile, the contact detection between spheres and triangular elements has been well established [] and can provide a reference to the same contact patterns as super-quadric particles, as shown in The vertices of a triangular element are denoted A, B, and C, where xA, xB, and xC are three position vectors. Therefore, the three edge vectors are easily obtained and denoted a, b, and c, respectively. Meanwhile, the normal direction, nw(nx,

ny,

nz), is given by nw = a × b/|a × b| and is directed outwards with respect to the particle. In addition, the centroid of particle and the projection point of the centroid onto the plane where the triangular element is located are denoted P and Q,respectively, and vector d directs from vertex A to point P. To determine if a particle is in contact with a triangular element, the contact between the particle and the plane where the triangle element is located must be detected first. The bounding sphere can be reintroduced as the first rough contact detection between a particle and a plane. The distance |PQ| is expressed as |PQ| = |d ∙ nw|. Therefore, the bounding sphere is in contact with the plane if |PQ| is less than or equal to the radius R0 of the sphere.Secondly, the contact point x on the surface of the particle and the projection, x∗, of the contact point onto the plane () can be determined by the analytical solution of particle–plane contact, which has been described well previously []. The final calculation results are as follows:α1=bny/anx1/n2−1γ1=1+α1n2n1/n2−1β1=γ1nzc/nxa1/n1−1x=a/1+α1n2n1/n2+β1n11/n1signnxy=α1bx/asignnyz=β1cx/asignnzifnx≠0ω=bny/n1n1/n1−1+cnz/n1n1/n1−11/n1−1x=0y=bbnyω/n11/n1−1signnyz=ccnzω/n11/n1−1signnzifnx=0where a, b, c, n1, and n2 are the function parameters of a particle. Therefore, the particle is in contact with the plane when the value of ((xA − x) ∙ nw) is less than or equal to zero.Thirdly, to obtain three different contact modes, such as face, edge, and vertex contacts, it is necessary to determine whether projection point x∗ is located in the triangular element. Point x∗ in the triangular element can be expressed by α and β with respect to vertex A. is then multiplied by vectors a and b, respectively.Here, the values of α and β can be calculated by Eqs. and the value of F(x∗) is less than or equal to zero, the particle is in face contact with the triangular element and the corresponding overlap δn can be given by δn = x∗ − x. Otherwise, edge contacts and vertex contacts will be detected.Taking edge b(bx,

by,

bz) as an example (), the projection of centroid P on edge b is point Q. Points E and F are obtained by extending the distance of ∓R0 from point Q in the direction of vector b. In the same way, points A′ and B′ can also be obtained by extending the distance of ∓R0 from vertices A and B in the direction of vector b. This means that the particle may be in contact with the edge when the projection point Q is within the range of segments AA′ and BB′. Then, the distance |PQ| can be expressed byA rough but necessary condition to prove edge contact is that the point Q satisfies Eq.Next, point xe1 with the minimum potential energy can be determined on segment EF. Here, segment EF can be expressed as a function of parameter t,where xE(xEx,

xEy,

xEz) and xF(xFx,

xFy,

xFz) are the position coordinates of points E and F. The corresponding super-quadric equation can be expressed as a function of parameter t, and the derivative of this equation with respect to t can be easily obtained:∂f∂t=n1{xEx'an2+xEy'bn2n1n2−1·[xExaxEx'an2−1·signxEx'+xEybxEx'an2−1·signxEx']+xEzcxEz'cn1−1·signxEz'}Therefore, point xe1 is easily given by the dichotomy of the super-quadric gradient function. If f(xe1) < 0, the particle and the triangular element are in edge contact. Another contact point, xe2, on the particle surface is expressed as xe2 =xe1 + αe∇f(xe1), and the unknown parameter αe can be solved by Newton's method, i.e., αek+1 = αek − f(xe2k)/(∇f(xe2k) ∙ ∇f(xe1)). The corresponding overlap is δn =xe2 −xe1. If the particle is not in contact with all three edges, vertex contacts will be detected.Taking vertex A(xAx,

xAy,

xAz) as an example, the particle and the triangular element are in contact if f(xA) < 0. In the same way as the method for calculating edge contacts, another contact point xA2 on the particle surface is expressed as xA2 =xA + αv∇f(xA), and the unknown parameter αv can be obtained using Newton's method. The normal overlap is δn =xA2 − xA.Finally, the contact determination rules are crucial for excluding invalid contacts when a particle is in contact with a series of triangular elements at the same time. It is worth noting that the contact of a super-quadric particle with a single triangular element is significantly different from that of a spherical particle; however, the algorithm for determining effective contacts is the same. Therefore, this method can be extended to super-quadrics. For more detailed calculations refer to Hu etal. [], and the corresponding verification tests are described in In the DEM simulation of spherical elements, the non-linear contact force model has been well established []; the ellipsoidal contact model, which considers surface curvature, can also provide a good reference. Therefore, a corresponding non-linear force model considering the equivalent radius of curvature is applied for super-quadric elements, as shown in In this model, the normal force mainly includes the elastic force and the viscous force:where Cn and vn,ij are the normal damping coefficient and the normal relative speed, respectively, and Kn and A are the normal equivalent stiffness and the viscous parameter, respectively, which are given bywhere E∗=E21−ν2, m∗=mi∙mjmi+mj, and R∗=Ri·RjRi+Rj, and E and ν are the Young's modulus and Poisson's ratio, respectively. R is the equivalent radius of curvature at a contact point with a maximum value of ten times the radius of the volume equivalent sphere, and this maximum is the same as the value used in the previous study []. The parameter R is obtained using R = 1/Kmean, where Kmean is the local mean curvature, given by [Kmean=∇FT·∇2F·∇F−∇F2∂2F∂x2+∂2F∂y2+∂2F∂z22∇F3The tangential contact force also includes the elastic force (Fte) andthe viscous force (Ftd) that considers the Mohr-Coulomb law. Here, Fte is given bywhere μs is the sliding friction coefficient, and δt is the total tangential displacement, which is added to the tangential relative displacement in each DEM step, given by δt =δt +vt,ij ∙ dt. Here, vt,ij is the tangential relative speed, and δt,max = μs(2 − ν)/2(1 − ν) ∙ δn.The tangential viscous force Ftd is given byFtd=Ct6μsm∗Knδn3/21−minδtδt,max/δt,max1/2/δt,max1/2·vt,ijwhere Ct is the tangential damping coefficient.When the particles rotate relative to each other, the moment (Mr,ij) caused by rolling friction can be expressed aswhere μr is the rolling friction coefficient, and ω^ijn is the normal relative rotating speed, given by ω^ijn=ωijn/ωijn.To validate particle-boundary contact detection, the DEM simulations and theoretical results [. Although super-quadric elements can construct cylinder-like particles, there is a difference between this shape approximation and a real cylinder. shows that six particles with different blockiness were modeled by changing the parameter n1/n2(n2 = 2). Meanwhile, gravity and friction are not considered during the impact process. The post-impact angular speed (ωy+) and translational speed (Vz+) for different impact angles are given by [where m is the mass of the cylinder, Vz− is the pre-impact translational speed of the cylinder, ε is the rebound coefficient at the contact point, ϕ0 is the angle between the surface of the cylinder and the line connecting the contact point and the center of the cylinder, r is the distance between the contact point and the center of the particle, θ0 is the angle between the cylinder surface and the wall, and Iyy is the mass moment of inertia about the y-axis. For each impact angle (θ0), the initial pre-impact translational velocity (Vz−) and the rebound coefficient (ε) are constant at 1 m/s and 0.85, respectively. The DEM simulation parameters are listed in For the various impact angles, the dimensionless rebound translational speed (Vz+/Vz−) and angular speed (rωy+/Vz−) were calculated by DEM and compared with the analytical results [(b,c). As the blockiness parameter increases, the numerical results become closer to the theoretical results []. When parameter n1 is greater than eight, the numerical results do not change significantly with increasing blockiness. In addition, the point contact does not occur at the impact angles of 0o and 90o for the true cylinder. Therefore, for the theoretical solution, the translational rebound speed is only related to rebound coefficient ε, and the angular speed is zero. For the DEM simulations, the dimensionless translational rebound speed is 0.85, and the angular speed is zero. The results of the super-quadricsimulation agree well with the theoretical results. It is also shown that the blockiness has a significant influence on the macroscopic mechanical response of non-spherical particles.In DEM simulations, the geometric boundaries are discretized into a series of standard triangular elements, and these elements are connected to each other by sharing edges or sharing vertices. To demonstrate the continuity of the contact force when a particle slides from one triangular element to another, four differently shaped particles were slid along the plane at a constant speed of 1 m/s (). Meanwhile, this plane is composed of twelve triangular elements, including thirteen shared edges and two shared vertices at the center of the plane, as shown in (b). The particles have parameters of D = 2b = 2c = 0.2 m and the aspect ratio (α) is given by 2a/D. Acube-like particle is obtained for n1 = n2 = 8, and a cylinder is obtained for n1 = 8,

n2 = 2. The particle density, the Young's modulus, and the friction coefficient are 2500 kg/m3, 1.0 GPa, and 0.1, respectively. The DEM simulation results of the force acting on the particles during the sliding process are compared with the analytical results, as shown in (c). The simulation results are consistent with the theoretical results, indicating that the smooth contact force can be ensured during the sliding process.] represented by several triangular elements was used to verify the contact detection between the super-quadric particles and the triangular elements. This model is divided into three parts: the hopper at the top, the mixing device in the middle, and the base at the bottom. The mixing device is composed of 56 triangular elements and includes 52 shared edges and 12 shared vertices, which is favorable for the occurrence of three contact modes (i.e.,face, edge, and vertex contacts) between the particles and the triangular elements. Only the contacts between the particles and the mixing device are recorded. The spheres, cylinders, cubes, and ellipsoids (α = 1.5) were constructed of super-quadric elements, and their volume is equal to the volume of the sphere. The normal and tangential damping coefficients between particles are both 0.15, and the normal and tangential damping coefficients between the particles and the boundary are both 0.3. The remaining calculation parameters were chosen based on reference [A total of 2500 red and blue particles were dropped into the hopper to form a bed under gravity and remain motionless until the orifice is opened. Thus, the particles flow into the device and produce the desired stirring and mixing behavior. shows snapshots obtained from the simulation of the cylinder-like particles in the device at different moments. The counts of the three contact patterns for differently shaped particles are listed in . The face contacts account for the majority of the three contact patterns, whereas the vertex contacts usually account for a tiny proportion. For spherical particles, the ratio of the count of face contacts to edge contacts is close to 20:1, which is consistent with previously obtained numerical results []. In addition, the cylinders, cubes, and ellipsoids have a higher ratio of face contacts to edge contacts. This is reasonable because both the blockiness and the aspect ratio can increase the count of collisions between particles and triangular elements, resulting in a more significant number of face contacts.The observed discharge dynamics are typical of granular flow, and simulation using super-quadric elements was carried out for validation. The first test is the presence of arch structure of cube-like particles under the same conditions [], i.e.,particle side length 2a = 2b = 2c = 12.7 mm; blockiness parameter n1 = n2 = 8; particle density ρp = 1200 kg/m3; Young's Modulus Ep = 1 GPa; Poisson ratio νp = 0.3; friction coefficient μ = 0.4; and normal and tangential damping coefficients cn = cs = 0.3. The arch structures observed experimentally and in the DEM simulation are shown in , where the orifice length was 80 mm. A comparison of the flow rate between the experimental and simulation results is shown in (c). Although the initial packing structures of the cubes are not the same and the shapes of the arch are slightly different, the present algorithms are applicable for modeling hopper discharge and arching of non-spherical particles.The second test is the discharging of ellipsoids from a hopper. Real Smarties® chocolate candies from a previous study [] can be modeled by super-quadric elements that have parameters of 2a = 13.56 mm, 2b = 2c = 7.19 mm, n1 = 2, and n2 = 2. The main calculation parameters are listed in . In the DEM simulation, the hopper was approximately 290mm in length and 55mm in width, and two orifice diameters were used: D0 = 54 and 63 mm. A total of 10,500 particles with random initial positions and orientations were dropped into this container, and the orifice was not opened until all the particles had become motionless in the hopper.] and simulation snapshots of hopper discharge at different moments. When the orifice was opened, a V-shaped flow pattern gradually appeared because of the difference in the flow rate of the particles on both sides and at the middle of the hopper. Finally, this pattern almost disappeared, and the remaining particles followed the shape of the slope. shows a comparison of the percentage of particles remaining in the hopper between the experimental [] and simulation results. For the orifice having D0 = 54 mm, good agreement was observed. For the orifice having D0 = 63 mm, the percentage obtained from simulation is lower than that of experiment. The reason for this discrepancy may be that the friction coefficient and the damping coefficient have a more significant effect on the granular flow when the orifice becomes larger and the flow rate becomes faster. However, these parameters should better reflect the mechanical properties of the experimental material.Knowledge of the effect of particle shape on the discharge rate is crucial for the reliable design and application of hoppers in industrial processes. Therefore, the aforementioned method was further tested for the simulation of hopper discharge. In these simulations, the hopper container consisted of an upper base and a lower hopper and measured 11D in length and 4D in width. Periodic boundary conditions were applied in width. The orifice was always 3.6D in length and 4D in width, and the base angles of θ = 15o, 30o, 45o, 60o, and 75o were used for differently shaped particles to demonstrate the superposed effect of the hopper configuration. Meanwhile, the total mass of the particles remained unchanged, approximately 0.1 kg. The super-quadric elements have parameters of D = 2b = 2c = 4mm and the aspect ratio given by α = 2a/D. The shapes considered are ellipsoids, cylinders, and cubes with aspect ratios varying from 0.5 to 1.5, as shown in . Furthermore, the particle angularity increases with increasing blockiness parameter from 2 to 8. Given the geometric characteristics of the super-quadric center symmetry, a quarter of the outline of the super-quadric elements is shown in . The shape of the particles can then be changed progressively between the spheres, cylinders, and cubes using a fixed aspect ratio of 1.0, as shown in (b). The particle density, the coefficient of friction, and the DEM time step are 2500 kg/m3, 0.1, and 1 × 10−6 s, respectively; other parameters are the same as those in . The particles with random initial positions and orientations were dropped into the hopper to form a bed under gravity, and the orifice was not opened until all the particles had become motionless. In addition, it is necessary to phenomenologically observe the discharge process. shows a comparison of the discharging of spheres within a bed having θ = 30o, ellipsoids within a bed having θ = 45o, cylinders within a bed having θ = 60o, and cubes within a bed having θ = 75o at 0, 0.5, and 1.0 s. shows a comparison of the flow characteristics of the spheres (a), ellipsoids (b), cylinders (c), and cubes (d)within beds having θ = 15o, 30o, 45o, 60o, and 75o. The percentage of discharged mass increased with time almost linearly for the different particle shapes and base angles, and the flow rate of the particles depended on both the particle shape and the base angle. shows the relationship between the average mass flow rate and the base angle for differently shaped particles. When the base angle was less than 45o, the discharge rate increased slightly with increasing base angle, and the particle shape appeared to be the primary influencing factor. However, we found that the particle shape and the base angle had a superposed effect when the base angle was greater than 45o. In addition, the “flowability” of the cubes was the lowest, whereas the spheres had the fastest discharge rate for different base angles; the ellipsoids had a faster discharge rate than the cylinders. Meanwhile, the effect of the particle shape on the discharge rate increased with increasing base angle. This is mainly because when the base angle becomes large and the orifice is constant, the height of the hopper increases and the residence time of the particles in the hopper increases; thus, the influence of the particle shape on the flow rate becomes more pronounced. shows the percentage of discharged mass of the ellipsoids (a), cylinders (b), and cubes (c)in beds having θ = 30o and 60o. The percentage of discharged mass increased almost linearly with time for different aspect ratios of the particles, and the discharge rate of the particles decreased with increasing the aspect ratio from 0.5 to 1.5. shows the average mass flow rate for particles with different aspect ratios. In addition, as shown, the ellipsoids were discharged fastest, whereas the discharge rate of the cubes was the lowest. For the same aspect ratio, the effect of the base angle and blockiness on the discharge rate is significant and cumulative. However, for the same base angle or blockiness, the influence of the aspect ratio on the discharge rate is of secondary importance. shows a comparison of flow characteristics in the processes ofchanging from spheres to cylinders (a, b), cylinders to cubes (c, d), and spheres to cubes (e, f)within beds having θ = 30o (a, c, e)and 60o (b, d, f). The percentage of discharged mass increased almost linearly with time for different blockiness, and the discharge rate always decreased with increasing blockiness. Meanwhile, the flow of cube-like particles exhibited greater volatility than the flow of spheres and cylinders. As the blockiness increases, the contact pattern between the particles becomes the face–face contact, which results in a more stable particle system and more non-continuous particle flow. shows the average mass flow rate of particles with different blockiness within beds having θ = 30o (a)and 60o (b). The influence of the blockiness on the discharge rate was greater when a base angle of 60° was used. However, this effect became insignificant when the blockiness parameter was greater than six.The simulation of the flow of a binary mixture of differently shaped particles was performed for a total mass of about 0.1 kg. Initially, each particle has a 50% chance of being produced as a sphere, a cylinder, or a cube. shows the average mass flow rate for different binary mixtures (i.e.,sphere–cylinder, sphere–cube, and cylinder–cube) within beds having θ = 30o (a)and 60o (b). Anon-linear relationship between the average mass flow rate and the percentage of each particle type can be observed. Meanwhile, the flow rate was reduced as the proportion of particles with sharp vertices or planes in the granular system increased. Furthermore, the influence of the mixing ratio on the discharge rate became significant when a base angle of 60o was used.The friction effect was analyzed by varying the particle-particle friction coefficient over the range of 0–0.5. Spheres, ellipsoids (α = 1.5), cylinders, and cubes were considered, and the influence of the friction coefficient on the average mass flow rate in the bed having θ = 60o was investigated, as shown in . Anon-linear relationship between the friction coefficient and the average mass flow rate for various particle shapes was observed. Meanwhile, a lower flow rate was obtained on increasing the friction coefficient. The particle friction induces an increase of the local heterogeneity of particle contact force, which may be partially related to the local arch of rough particles during the discharging process []. In addition, for cubic and cylindrical particles, the friction coefficient had a more pronounced effect on the flow rate than for spherical particles, mainly because of the larger contact area between the particles.The packing fraction of granular materials is a commonly used parameter describing the packing characteristics []. For super-quadric particles with an aspect ratio (α) of 1, the variation in packing fraction with blockiness during the three changing processes is shown in . The packing fraction increases with increasing blockiness parameter when the blockiness parameter is less than four and is independent of the blockiness parameter when the blockiness parameter is greater than four. Meanwhile, the cube-like particles have the highest packing fraction, and the packing fraction of the cylinder-like particles is higher than the packing fraction of the spheres. Therefore, the particles are more likely to form dense face-face contacts and ordered structures with high packing fraction. These denser packings have a higher orientation and a lower flow rate.Furthermore, the contact force between the particles plays a substantial role in structural stability and force transmission and is relevant to the macroscopic properties of the granular material []. Therefore, the probability density functions (PDFs) of the normal contact force between the particles at the initial moment are shown in on a log-log scale. As shown, as the blockiness increases, the probability of weak force gradually decreases, whereas the probability of strong force gradually increases. Meanwhile, the particles are more likely to formface–face contacts with increasing blockiness, and most face-face contacts contribute to the strong force. However, the contact forcesmainly depend on the equivalent radius of curvature because oftheminor deformation of the particles and strongly affect the flow rate.Based on the aforementioned method, the effects of the aspect ratio and the blockiness on the discharge rate within beds having different base angles were studied. The results showed that the percentage of discharged mass increases almost linearly with time for different particle shapes and base angles. The flow rate always decreases as the base angle decreases or as the blockiness, particle friction, or aspect ratio (0.5–1.5) increases. Meanwhile, the spheres have the fastest discharge rate, whereas the discharge rate of the cubes is the lowest. With increasing the blockiness, the particles are more likely to form dense face–face contacts and ordered packing structures, which results in an increasingly non-continuous granular flow and a lower flow rate. In addition, the influences of the base angle, blockiness, and friction coefficient on the discharge rate are significant and cumulative; in contrast, the aspect ratio in the range of 0.5 to 1.5 is of secondary importance.In future work, the approximate inclination of the corresponding parabolic surfaces needs to be further considered for the non-linear contact force model. Meanwhile, the GPU-based parallel computing will be employed to accelerate the computational efficiency. Furthermore, the method of contact detection between the super-quadric particles and the triangular elements described in this paper will provide research ideas with large-scale engineering applications and DEM–finite element method (FEM) coupling calculations.Freestanding abradable coating manufacture and tensile test developmentAbradable coatings are used extensively within gas turbines. Abradable material is applied to the inside surface of the compressor and turbine shroud sections using thermal spray methods, coating the periphery of the blade rotation path. The function of an abradable seal is to wear preferentially when rotating blades come into contact with it, while minimising the over-tip clearance, and improving the overall efficiency of the engine. There is a distinct lack of established materials property data for all abradable materials, due to the difficulty of testing this very unique class of materials. Abradables understanding is historically limited, with the field often described as a ‘black art’, and component/material improvements habitually the result of ‘firefighting’ actions. This work is part of a wider programme in partnership with Rolls-Royce plc to gain a greater understanding of abradable materials, how they perform, and ultimately how to improve their performance in-service. The paper describes a novel method, devised in tandem with Rolls-Royce plc, of producing free-standing abradable tensile test specimens via thermal spray. The specimen mould is composed of a dissolvable polymer composite which maintains its integrity during spraying and cooling, and is then ‘washed’ away in an ultrasonic water bath. This results in near-net shape specimens, which are machined to a specific geometry. The paper details the iterative testing development that contributed to a final working design and testing methodology for a previously untested class of materials.The aim of abradable materials is to reduce the gap between rotating and stationary parts in gas turbine engines. The function of an abradable seal is to wear preferentially when rotating blades come into contact, while minimising the over-tip clearance, and improving the overall efficiency of the engine by reducing the specific fuel consumption (SFC) This work focuses primarily on compressor abradable materials, but the technology and methodologies developed within this research can be applied to turbine abradable materials and other coating applications. In the production of gas turbines, thermal spraying is used to manufacture abradable seals around the inside surface of the compressor shroud sections. There are many different powder materials used as compressor abradables. Coatings produced by thermal spray processes have unique structures; the abradable powder is rapidly heated and is then accelerated at high velocity onto the surface of the substrate. The powder particles are deposited in a molten or semi-molten state A coating produced by thermal spray processes is highly anisotropic An example of an abradable material currently used in the compressor section of a gas turbine is the air plasma applied AlSi-hBN coating. The microstructure is essentially a composite material consisting of an AlSi metal matrix, containing a solid lubricant phase of hBN (hexagonal boron nitride) bound to the matrix using an organic adhesive . This 3-phase system is typical of most abradable coatings. The role of the matrix material is to provide the coating strength and resistance to its environment, while not resulting in excessive blade wear. The second phase, known as the dislocator phase can be either a material phase, regions of porosity within the matrix, or a combination of both. The dislocator phase functions as an initiation and propagation route for cracks, providing the coating with inherent weaknesses whilst ensuring abradable ‘break-off’ debris is sufficiently small not to block cooling holes or instigate erosion downstream. The third phase sometimes included is the binder phase, ensuring there is minimal segregation of material during spraying.Assessing the mechanical properties of coating materials, and in particular inherently weak abradable coating materials without the interaction of the substrate and bond coat materials has historically proved difficult. The majority of mechanical testing on coatings provides results specific to the coating/substrate system, such as pull-off, shear, peel, indentation, and scratch testing There is a clear requirement for a repeatable method of assessing the mechanical properties of thermally sprayed coatings without substrate interactions, perpendicular to the spraying direction. The novel method of testpiece manufacture described in this paper has been accepted as a patent A novel method of testpiece manufacture was developed in partnership with Rolls Royce plc, Derby. The aim was to produce a self-supporting freestanding abradable coating specimen for subsequent tensile testing. The first stage was the production of a near-net shape sprayed specimen, with minimal subsequent machining to produce the final testpiece geometry. This was achieved by spraying the material into a dissolvable mould.The mould material is made from a dissolvable polymer composite which is able to withstand temperatures of up to 200 °C during the spraying operation, and breaks down into a non-toxic powder The moulds are arranged on a rotating stage, and molten/semi-molten abradable coating material is sprayed onto the surface of the mould, filling the cavity. This configuration replicates the thermal spray process at Rolls Royce plc. where the compressor rotor path shroud is rotated around the thermal spray stream, building up an abradable coating in a number of passes. Once cooled the moulds are dissolved in water, leaving a near-net shape specimen.The machining and finishing operations were developed at the Materials Research Centre, Swansea University. Firstly, each of the side faces of the tab-end region (not the gauge length area or blend radius) were end-milled to specification. The second machining operation is face-milling of the top and bottom faces of the specimen. Equal amounts of material should be removed from each face of the specimen. After these machining operations all overspray was removed. Grinding was employed to produce a high quality specimen surface finish and ensure uniform thickness across the specimen gauge length and blend radius, although grinding was only used for AlSi-hBN coating materials. Finer face-milling operations were employed for other, more porous abradable materials to prevent densification of the microstructure during grinding. The final operation is CNC machining of the blend radius and gauge length areas to produce the critical dimensions of the testpieces. The blend radius and gauge length of the development specimens was varied, and the results studied, in order to develop a reproducible tensile testing procedure.As previously highlighted, there are very few comparable mechanical properties of freestanding coating materials, and none for the abradables class of materials. The importance of gaining a greater understanding of how abradable materials behave in order to increase their lives in-service and to improve the efficiency of the aero-engine has grown in recent years. As an area once considered a ‘black art’, it is now pivotal to current and future studies that a method exists for measuring accurate materials properties of abradable materials, particularly for modelling purposes These were tested under tension with varying specimen dimensions, shown in Prior to testing, specimen curvature was measured using a Dial Test Indicator Gauge (DTI). The DTI was placed exactly 40 mm to the left of centre of the gauge length at the centre of the specimen’s width and then subsequently zeroed, ensuring that minimal load was applied to the specimen through the ball-bearing foot. Displacement readings were made at − 30, − 20, − 10, − 5, 0, + 5, + 10, + 20, + 30 and + 40 mm from the central position. A final measurement was taken again at − 40 mm to determine if there had been any offset in the initial zero value.Specimens that used strain gauges were prepared and applied using standard methods . Pressure was held for 1 min and then immediately removed. Strain gauge readings were taken at least every 0.5 s during loading and for the first 30 s of unloading and then every 5 s for a further 4 min afterwards. In total, three repeat experiments were performed.A tensile test with a strain rate of 1 mm/min was performed on a Hounsfield H25KS S-Series Benchtop Test Machine with a 25 kN load cell using the specimens highlighted in . A second 10 kN load cell with a voltage output signal was attached in series to the first load cell. The second load cell was required to provide a common reading for each strain gauge measurement as the standard Hounsfield load cell had no external output signal facility. The top half of the universal joint was attached to the second load cell and the bottom half to the upper grips. The lower grips were attached to the base of the load frame, ensuring that both grips were fully opened to allow ease of specimen insertion. Guide rails and additional alignment markers ensured vertical alignment of the specimen in both grips. The lower grip was tightened, ensuring horizontal alignment. It was necessary to temporarily raise the crosshead prior to tightening the lower grips to avoid applying torsion strain to the test specimen. The second load cell output signal and all strain gauges were wired to the monitoring equipment (System 2100 signal conditioner with separate PC logging software). The upper grip was closed tightly, whilst avoiding over tightening. Under no circumstances did the grip encroach onto the blend radius section at either end. The offset strain readings of each strain gauge were trimmed to zero as required.For certain tests, a 25 mm clip gauge was applied to the gauge length of the convex face of the specimen, using guide rails and markers to ensure vertical and horizontal alignment. Both load cell outputs and all strain gauges were trimmed to zero as required.The following section highlights testing improvements made during the investigation as well as new measurement techniques introduced.Three specimens were tested with original as-received dimensions of 40 mm gauge length, 2 mm gauge width and a relatively steep blend radius of 5 mm. Specimen extension was measured from machine cross-head displacement. Specimen failure occurred at the point where the blend radius met the gauge length resulting in a relatively low tensile strength value.Accurate measurement of specimen extension was required to calculate specimen modulus for each test. Therefore, specimen extension of remaining tests was measured using a clip gauge in addition to cross-head displacement. The blend radius of one specimen was increased to 30 mm (gauge length reduced to 30 mm) to limit its influence on failure. Gauge width was also reduced by end-milling thereby producing a much better surface finish than the as-received condition. Tensile strength was greatly increased and failure location moved closer to the centre of the test specimen (due to a shorter gauge length) but failure still occurred at the point where the blend radius met the gauge length.There was a varying extent of specimen curvature observed in tested and remaining specimens so curvature of all remaining specimens was measured using a Dial Test Indicator Gauge (DTI) prior to testing. The blend radius of one specimen was increased to 40 mm (gauge length reduced to 20 mm). Tensile strength remained the same, failure location moved even closer to the centre of the test specimen (due to even shorter gauge length) but failure still occurred at the point where the blend radius met the gauge length.To prevent total loss of strain data remaining test specimens had strain gauges applied in addition to the clip gauge and cross-head displacement measurements. Specimen bending strain or “strain to straightness” was measured prior to testing on remaining specimens. The blend radius was increased to 55 mm (gauge length reduced to 10 mm) on one specimen. Tensile strength again remained the same, failure location moved even closer to the centre of the test specimen (due to even shorter gauge length) but failure still occurred at the point where the blend radius met the gauge length.Results appeared to indicate that any increase in blend radius above 30 mm did not result in an increase in tensile strength. For ease of strain gauge application and accuracy of clip gauge measurement, remaining test specimens were machined with dimensions based on a design with a blend radius of 30 mm and a gauge length of 30 mm.Four specimens were produced for repeat tests using the testpiece geometry stated in stage 5. Failure of the specimen was observed within the measured gauge length. The results of the repeat tests are presented in allowed for descriptive and predictive statistical analyses. The assumption is made that the data are normally distributed. A critical step in assessing the measured response of this specimen geometry was to calculate confidence intervals of the material properties Modulus (E), Ultimate Tensile Stress (UTS), and the failure strain (εf %) for the 5 sets of data. In engineering, stated materials properties are generally mean values generated from repeated tests; therefore the confidence in the value of the mean is a valid method of assessing these tests.The confidence intervals of the three materials properties were calculated using Eq. Where:t(α/2,n

− 1) is the upper critical value of the t-distribution with n

− 1 degrees of freedomis the desired significance level (a level of 0.05 was used)is an estimate of the standard deviation of the populationThe results of the statistical analyses are presented in . It can be assumed that with 95% confidence, the true mean of E lies in the range (population mean ± 17.09%), the true mean of the UTS lies in the range (population mean ±11.09%), and the true mean of εf lies in the range (population mean ± 7.94%).The variation in measured E, UTS, and εf for AlSi-hBN can be attributed to several potential sources. Firstly, the sample population is relatively small. Five samples with inherent variability lead to larger confidence limits. With a greater number of repeat tests the limits would be expected to decrease. Secondly, the nature of thermally-sprayed abradable materials is such that the microstructure contains randomly distributed weaknesses in the form of the extremely low strength lubricator phase hBN, porosity, and splat boundaries. The size, distribution, and orientation of these weaknesses can vary during a thermal-spray operation, resulting in inherent variability in their measured mechanical properties.The shape of the stress–strain curves in highlights progressive plastic deformation in the abradable material, with no pure elastic response or identifiable yield point. Failure of this abradable material could be due to decohesion of adjacent splats along splat boundaries and at interfaces between the matrix and dislocator materials. A measured pseudo-elastic modulus was used as a result of the progressive failure, and the associated shape of the stress–strain curves.To formulate a novel testpiece manufacturing method for freestanding tensile abradable specimens by spraying into a dissolvable mould.To devise specific machining operations.To design a specimen geometry and testing methodology.The abradable material studied was an AlSi-hBN coating produced by air plasma spraying. The following conclusions can be drawn:The method of producing freestanding tensile specimens described in this work proved to be successful.The machining procedure for producing final specimen geometries from near-net-shape sprayed samples proved to be a repeatable method of manufacturing specimens.A freestanding specimen with a blend radius of 30 mm and gauge length of 30 mm enables controlled tensile testing and failure within the gauge length.The repeat tests using the above specimen geometry show that this method can produce tensile materials properties for abradable materials, without the complication of substrate interactions. The testing and subsequent statistical analysis demonstrate that with 95% confidence the mean of E for the AlSi-hBN coating lies within ± 17.09% of the population mean, the mean of the UTS lies within ± 11.09% of the population mean, and the mean of the εf lies within ± 7.94% of the population mean.Hyperbaric chamber test of subsea pipelinesAn experimental study of buckle propagation in subsea pipelines is presented in this paper. The experimental protocol consists of two types of experiments; hyperbaric chamber and ring squash tests. Intact and dented steel and aluminium pipes with different diameter-to-thickness ratio are used in these tests. The experimental results are presented and compared with available analytical and empirical solutions. The sensitivity of buckle initiation to initial geometric imperfection is evaluated. The evolution of hoop and longitudinal strain during buckle propagation is presented to show the extent of plastic deformations.Oil and natural gas combined represent more than 50% of the world's energy needs. The diminishing onshore hydrocarbon reserves resulted in an unprecedented increase in subsea operations. It is expected that 25% of offshore petroleum production will be in deep water by 2015. Hydrocarbon production in deep water requires long pipelines (several hundred kilometres) and the design of such pipelines poses many engineering challenges and potential risk. The recent blowout incidents of Deepwater Horizon at the Gulf of Mexico and Montara at the Timor sea are reminders of the disastrous consequences of failure in subsea operation In deep water, the catastrophic propagation buckling can quickly transform the pipe cross-section into a dumb-bell shape that travels along the pipeline, as long as the external pressure is high enough to sustain propagation. Buckle propagation is a snap-through phenomenon that can be triggered by a local buckle, ovalization, dent or corrosion in the pipe wall. shows a typical buckle propagation response obtained from testing an aluminium pipe in a hyperbaric chamber is depicted in terms of the applied hydrostatic pressure against the pipe's volume change (ΔV/V) and is characterised by; the pressure at which the snap-through takes place (the initiation pressure PI) and the pressure that maintains propagation (the propagation pressure Pp) which is a small fraction of PI.In the above equations, D and t are the pipe diameter and wall thickness, E, ν and σy are the material elasticity modulus, Poisson's ratio and yield stress respectively. were proposed in order to account for strain hardening and extensional deformation. An extensive experimental study was conducted by Mesloh et al. with α and β are taken to be 33.941 and 2.5 respectively. Eq. . Based on experimental study conducted on stainless steel pipes, Gong et al. In this paper experimental investigation is conducted using aluminium and steel pipes with four different D/t ratios as shown in . The nominal and measured (average) diameter and thickness of each of these pipes are listed in together with the elasticity and tangent (E and E′) moduli obtained from longitudinal coupon tests. The experimental protocol consists of two types of test; the ring squash test (RST) and hyperbaric chamber test (HCT). For each D/t ratio, two RST tests and six HCT tests were conducted. The test results are consistent and the average values are presented in the following sections.. From the RST, and using equilibrium considerations and energy balance approach, the effective yield stress of the material,σy () and an estimate of propagation pressure PRST () are calculated as described by Albermani et al. A 4 m long stiff hyperbaric chamber with 173 mm internal diameter is used in this test as shown in . The chamber is rated for 20 MPa internal pressure (about 2 km water depth). A high pressure pump is used to pressurise the chamber and to obtain buckle propagation response under quasi-static steady-state conditions. The pipe sample being tested is sealed by welding a stiff cap at each end. Two valves are installed at one of the pipe's ends through the stiff cap. One valve is used for bleeding the pipe while filling it with water before testing commence. The second valve is used to vent the pipe sample to the atmosphere through the chamber wall and to collect water flow from the pipe sample during buckle propagation. The pipe sample is inserted in the chamber, filled with water and vented through the chamber wall. The chamber is sealed, filled with water then gradually pressurised. As the chamber is pressurised and due to the elastic deformation of the pipe sample inside the chamber, tiny amount of water flow out from the pipe sample, however, once buckle propagation commence, steady flow of water from the pipe sample is observed. The water flow from the pipe sample is collected in a container attached to a load cell for measuring the amount of water and hence the volume change of the pipe sample as the buckle propagates. In some tests, four strain gauges attached to the outer surface of the pipe sample at various locations are used to monitor hoop and longitudinal strain evolution during propagation. The data from pressure transducers, four channels of strain gauges and the load cell are acquired at 20 Hz rate and used to monitor the test.A typical propagation response obtained from HCT of a 3 m long aluminium pipe with D/t=25 (. The chamber is gradually pressurised until the initiation pressure PI is reached when a section along the pipe sample collapses leading to a significant drop in chamber pressure and steady flow of water from within the vented pipe sample. By maintaining a low rate of pressurising, the chamber pressure is stabilized at the propagation pressure, PP, with the buckle longitudinally propagating along the pipe accompanied by steady water flow from the vented pipe sample. In comparison to RST, the HCT is more demanding and time consuming test to conduct.In order to investigate the effect of the length of pipe sample used in the HCT, aluminium pipe samples () with length of 1.5 m (25–30D) and 3 m (50–60D) were prepared and tested. A comparison of PI and Pp obtained from the HCT for these pipe samples is shown in . It is clear that as long as the pipe sample is long enough to exclude any end effects, the results are not sensitive to the length of the pipe used in the test. In all the tests reported in the following sections, 3 m long pipe samples are used.For each D/t ratio, six intact pipe samples (each 3 m long) were tested in the hyperbaric chamber. Prior to testing the steel and aluminium pipes, the initial ovalization, Ω, of the intact pipe samples was measured at 10 stations (300 mm interval) along each pipe, where Ω is obtained fromIn which Dmax and Dmin are the maximum and minimum measured outer diameter of the pipe sample. The average ovalization of the intact samples was in the range of 0.46–0.67%.In this section the experimental results obtained from RST and HCT are first compared to the analytical/empirical results from Eqs. . This is followed by further analysis of the experimental results to investigate the length of the transition zone and the effects of D/t ratio and initial geometric imperfection on propagation response.The initiation and propagation pressures obtained from HCT and RST are listed in . It is clear that Pp is a small fraction of PI ranging from 19 to 28%. Since the design of deep subsea pipelines is governed by Pp, this implies a substantial increase in material and installation cost. As expected the elastic collapse pressure Pc (Eq. ) overestimates PI. On the other hand, Pp from HCT is 1.38–1.52 times PRST derived from the ring squash test. This agrees with the factor of 1.4 suggested by Kamalarasa and Calladine shows a comparison of Pp obtained from HCT with the analytical/empirical results from Eqs. ) consistently underestimates Pp for aluminium and steel pipes, Eqs. (PM, PAPI, PDNV and PG) underestimates (11–24%) Pp for aluminium and overestimates (4–12%) for steel pipes.The effect of D/t on PI and Pp obtained from HCT is shown in . In this figure, PI and Pp are normalised by the elasticity modulus E and the yield stress σy, respectively. Also shown in this figure are the results according to Eqs. which give an upper and a lower bound, respectively, on the HCT results.The deformed shape of one of the pipe samples (D/t=25) following HCT is shown in shows a comparison of the measured λ from HCT to that obtained from Eq. and the 10D stipulated by Chater and Hutchinson while 10D overestimates λ. Since the length, L, of the pipe samples used in HCT is 3 m, this gives L/λ in the range of 4.7–10 in our tests. shows a number of sections cut at uniform intervals along the buckle following HCT of one of the D/t=32.7 samples. The profile of nine sections was traced to show the extent of deformation along the transition zone and the symmetry of the buckles., the propagation response is dominated by a snap-through. Hence PI is expected to be very sensitive to imperfections (such as a dent, ovalization or corrosion in the pipe wall) while the response is stabilised at Pp regardless of imperfections. The HCT results reported so far are for intact pipes with average measured ovalization of 0.46–0.67%.The HCT was also conducted on a series of dented 3 m long pipes to investigate imperfection sensitivity. For each pipe sample a local dent is imposed at a location along the pipe using a rigid indenter similar to that used in the RST (). The local dent provides the initiation site for the propagating buckle. For each pipe sample, a rigid indenter of the same diameter as the pipe and with a length of one diameter is used as shown in . A thick rubber mat is used to support the opposite side of the pipe while the rigid indenter is pushed against the pipe using a vice. Taking δ as the dent's depth and l is the dent's length (with δ being more critical than l ), the dent magnitude is defined according to the maximum ovalization ratio Ω (Eq. ) obtained along l. Three normalised dent profiles for three pipe samples with D/t=20 are shown in corresponding to Ω equal to 16, 23 and 31%. shows a comparison of the normalised propagation response obtained from HCT using intact and dented steel pipes with Ω=10%. As can be seen from this figure, the dent makes a drastic reduction in PI, while Pp is unaffected. This highlights the vulnerability of deep subsea pipelines to propagation buckling. shows the percentage reduction in PI due to imperfection for eight dented pipes used in the HCT. According to this figure, a reduction of 40–70% is expected for 10–30% ovalization. Pipes with lower D/t, which are more compatible with deep subsea applications, are more sensitive to imperfection as can be seen from Four HCT were conducted for each D/t ratio with the pipe sample (3 m long) instrumented with four strain gauges to monitor the strain evolution in the hoop and longitudinal directions during buckle propagation. Only four strain gauges are used due to the limitation of the high pressure bulkhead connector fitted to the hyperbaric chamber. Since it is not possible to predict the exact location along the intact pipe where propagation commences during the HCT, two configurations for the strain gauges are used. The first configuration, seen in a, with three gauges in the longitudinal direction (one at the middle and two at 500 mm on either side) and one gauge in the hoop direction at the middle of the pipe sample. In the second configuration, three gauges are used at the middle of the pipe (two gauges in the hoop direction, at 90°, and one longitudinal) and the fourth gauge is in the longitudinal direction at 500 mm away from the middle toward one of the ends. b shows some of the instrumented samples after the completion of HCT. shows longitudinal and hoop strain evolution during HCT of a dented D/t=25 pipe sample. The strain, normalised by nominal yield strain (εy=0.2%), shown against the pipe's volume change (ΔV/V) as the buckle propagates. The buckle initiates at the dent site and the buckle front propagates towards the far end. The longitudinal strain gauge close to the dent site peaks first, with around 5εy tensile longitudinal strain that switches to compressive strain as the buckle front by-pass the gauge location. As the buckle front approach mid-length, the two hoop gauges peak with the top gauge reading close to 18εy compression and the side gauge close to 5εy tension. This is consistent with the expected dog-bone deformed shape shown in . The strain (longitudinal and hoop) are well above the nominal yield strain indicating the extent of plastic deformation during buckle propagation. The strain values are comparable to that reported by Nogueira and Tassoulas Experimental protocol for buckle propagation in subsea pipelines is presented. Two types of experiments are used; a simple and expedient ring squash test RST and the more demanding hyperbaric chamber test HCT. Intact and dented steel and aluminium pipes with different D/t ratios are tested. The obtained propagation pressure, Pp, is 19–28% of the initiation pressure PI which highlights the vulnerability of subsea pipelines to propagation buckling. HCT gives Pp that is 1.38–1.52 times that obtained from RST (PRST). The elastic collapse pressure and Palmer and Martin . The high sensitivity of buckle initiation to initial geometric imperfection is seen from HCT results of dented pipes, a drastic reduction (40–70%) in buckle initiation is obtained for initial ovalization of 10–30%. The results show that pipes with lower D/t ratio, which are more compatible with subsea applications, are more sensitive to imperfections. On the other hand, buckle propagation is unaffected by initial imperfections. The evolution of longitudinal and hoop strain during HCT show the extent of longitudinal plastic stretching and circumferential plastic bending during propagation.Fatigue failure analysis of rotor compressor blades concerning the effect of rotating stall and surgeDetailed investigation was performed on the effect of the rotating stall and surge on the fatigue failure mechanisms of the axial compressor first stage rotor blades. The static stress distribution of the blades was analysed using three dimensional (3D) finite element method (FEM). The critical fracture stress was calculated using the linear elastic fracture mechanics. Fractographic observation revealed different fatigue fracture modes corresponding to the different fatigue loads. Results demonstrated that during operation two kinds of fatigue loads can occur which are tension-torsion fatigue and bending fatigue. The tension-torsion fatigue stems from the periodic tension-torsion stress induced by the surge, while the bending fatigue load is caused by the rotating stall.Blade is one of the most important components of the axial compressor used to transfer the kinetic energy of the gas to pressure. The failure of the compressor occurred mostly in the blade due to the complex working environment, not only the constant centrifugal force, but also the air exciting vibration force. In general, compressor blade failures can be grouped into two categories: (a) creep rupture; (b) fatigue failure, including both the high-cycle fatigue (HCF) and low-cycle fatigue (LCF) The analysis of the fatigue fracture of the compressor blades has received much attention from researchers In the present work, the characteristics of the failure of the axial compressor blades were studied by combining the FEM calculation of the stresses and the fractographic analysis.The 2Cr13 martensitic stainless steel, having a chemical composition of 0.17–0.22 wt.% C and 12–14 wt.% Cr, is commonly used in petroleum industries, as a structural material for blades of air compressor operated under fatigue loading and relatively low corrosion environment Mechanical test results and the analysis of the chemical composition using Energy Dispersive Spectrometer (EDS) showed that the mechanical properties and the chemical composition of the blade material are in accordance with the 2Cr13 steel standard.The typical failure of the axial compressor rotor blades is shown in . It can be seen that the failed blades were mostly first stage blades, and the crack was located at or close to the root of the compressor blades. The sketch of the compressor blade is shown in Based on the fracture morphology, failed blades can be divided into two types, as shown in . Type-1 was oblique fracture with multiple fracture platforms. Type-2 was plane fracture with ribbon shell pattern structure. shows the Type-1 fracture morphology and illustrates the failure position with the arrow indicating the crack initiation site. It can be seen that the crack was initiated at the tip of outlet edge, which is 20 mm from the blade root, and then propagated to the inlet edge and formed the fracture region I (). During operation, the fatigue crack continued with an uphill propagation to form the II, III, IV and V regions on the fracture surface, in which the region III was damaged by foreign object. The boundaries between different regions may result from the interruptions of operation, for maintenance for example. The final rupture started from region VI. The different appearances of regions VI, VII, VIII and IX may be due to the complex loading states such as tensile and torsional loads.b that the Type-2 crack initiated at the blade back, and propagated to the blade basin. The distance from the crack position to inlet edge and blade root is 25 mm and 10 mm. The shell pattern structure is present on the propagation surface (b) which is the typical characteristic of fatigue fracture. The ribbon structure on the fracture surface may be formed by stop-start operation or working load change. The morphology of the Type-2 failure surface in b suggests that the fatigue crack propagation was driven mainly by bending load.Fractographic analysis was carried out using scanning electron microscope (SEM) to reveal the failure mechanisms of the blades. Higher magnification of the initiation site in showed that the corrosion pits were responsible for the nucleation of the fatigue crack (). The EDS analysis of the corrosion pit () found that the main corrosion elements were oxygen, potassium, sulfur and chlorine. shows that the direction of the fatigue crack propagation is zigzag as the arrows indicate, which confirmed that the fatigue crack propagation was driven by tensile and torsional stresses. However, the fatigue propagation of the Type-2 failed blade is different from Type-1. b reveals that the Type-2 failure possesses the typical fatigue fracture morphology under opening fatigue load mode resulting from both tensile and bending stresses. The image of dark ribbon shell pattern structure is present on the propagation surface (c). The reason for the formation of ribbon structure is the variation of the bending fatigue stress, probably due to working load change. d demonstrates that this dark region was formed with severe deformation and tearing which implies that the fatigue stress driving the fatigue crack to propagate over this dark region is much higher than that for the neighbouring regions.The axial compressors failed due to fracture of the first stage rotor blades during normal operation. The detailed working parameters of the failed axial compressors are listed in The tangential force (Fu) at failure position under working condition and axial force (Fa) of the blade at failure position which is required for the FEM stress analysis can be calculated based on the following formula where P′ =

P/Ns, ω

= 2πn

/ 60, Dm

= (Dh

+

Dt) / 2. P is the total power, NS is the stage number, n is the rotary speed, Dh is the mean diameter of hub, Dt is the tip diameter of blade, Nb is the blade number of first stage impeller, β is the air flow angle, ω is flow rate.According to the detailed compressor parameters at failure position in , the tangential forces and axial forces for Type-1 and Type-2 can be calculated, the results are listed in In this study, the twenty nodes element 3D mode was established in order to improve the calculation accuracy. The FE model of the blade presented in consists of 16,383 nodes and 4266 elements.In the static stress analysis, the boundary condition used in the analysis consists of the displacement constraint at the circumferential surface of the blade root and all freedom constraint at the gear bearing surface of the blade root. The loads applied to this model are listed in . An axial force is applied to the blade tip, the tangential force is uniformly distributed along blade height. shows the static stress contour map of the Type-2. It can be seen that the maximum Von-Mises stress occurred at the blade back close to the blade root where the fatigue crack was initiated for the Type-2 failed blade. The maximum Von-Mises stress is 299.5 MPa. The Von-Mises stress of the blade outlet edge is in the range of 20 MPa to 57 MPa. The load distribution of the Type-1 failed blade is approximately the same, only the maximum stress is smaller than that of Type-2.According to the equipment operation record, it was found that the working conditions are different between the failed compressors. Taking one typical broken compressor of each fracture type for discussion: the air flow value of one axial compressor with a Type-1 failed blade was below the minimum design value, and this situation lasted for 5 days (120 h). Then abnormal sound was heard and the value of compressor vibration increased from 15/16 μ to 61/56 μ. The fracture of a Type-2 failure compressor was accompanied by great vibration without surge warning, and the abnormal working condition lasted for 44 h. It is obvious that strong vibration happened before the fracture of the blades which may result from the rotating stall or surge.), the fatigue life values (Nf) of the Type-1 and Type-2 failed compressors corresponding to the abnormal working conditions are 3.9 × 107 (120 h) and 1.5 × 107 (44 h), respectively. Fatigue tests have been carried out for the 2Cr13 martensitic stainless steel concerned in the present study Considering the failure analysis of Type-1, the loading spectrum for the Type-1 fracture can be taken as the superimposition of the fatigue stress amplitude (427.8 MPa) on the Von-Mises stress (20 MPa) at the blade outlet edge. Surge is an axisymmetric oscillation with such a large variation of mass flow along the axial length of the compressor. When surge occurs, the rotor blades always operate in reversed flow during part of the cycle. Consequently, the rotor blades are stressed by the periodic oscillating flow along the axial direction. With the effect of setting angle of the blade, the periodic axial oscillating flow may translate into torsional cyclic load concentrating on the outlet edge of the blade which may result in the initiation of the fatigue crack. This is in good agreement with the fractographic observation as shown in and explains the reason for the fatigue crack propagation surface as shown in . The Type-1 fatigue fracture can therefore be considered as the tension-torsion fatigue fracture resulting from the surge during operation. The tension-torsion surge fatigue fracture mode is illustrated in Rotating stall results from a severe non-axisymmetric distribution of axial flow velocity around the annulus of the compressor b that Type-2 bending fatigue crack was initiated at the blade back, which is coincided with the position having the maximum bending fatigue stress induced by the rotating stall. Type-2 fatigue fracture can therefore be considered as the bending fatigue fracture caused by the possible rotating stall during service operation. The mode is illustrated in It is assumed that the fatigue crack of the failed blades is opening mode crack. The critical fracture stress values can then be calculated based on the linear elastic fracture mechanics method Type-1 fracture crack can be seen as the single edge notched plate crack, the critical fracture stress (σ) is calculated based on the following formula where C is calibration factor taken as 1.12, a is the fatigue crack length measured as 60 mm from the fracture surface of the corresponding Type-1 failed blade. Based on the fracture toughness (KIC) value (230.1 Mn/m3/2) listed in , the value of critical fracture stress can be calculated as 472.4 MPa.Type-2 fracture crack can be seen as the half elliptical crack, σ is calculated based on the following formula where C and ϕ is calibration factor taken as 1.325 and 1.235 respectively. The crack length (a) of the elliptical crack is 26 mm. The σ value can then be obtained as 750.5 MPa.It can be seen that the critical fracture stresses of Type-1 (472.4 MPa) and Type-2 (750.5 MPa) fracture estimated from the fracture surface analysis are in good agreement with the maximum fatigue stresses of the Type-1 (447.8 MPa) and Type-2 (762.6 MPa) fatigue fracture calculated based on FEM analysis and the fatigue test results. It clearly demonstrates that the fatigue loads resulting from surge and rotating stall are the main reasons of the first stage rotor blades failure.(1) Two kinds of fatigue fracture modes for the first stage rotor blades in the axial compressor were identified as tension-torsion fatigue fracture mode (Type-1 fracture) resulting from surge and tensile-bending fatigue fracture mode (Type-2 fracture) resulting from rotating stall.(2) Normally, the bending fatigue crack was initiated at the blade back due to stress concentration and corrosion pits, and propagated to the blade basin under bending cyclic stress caused by periodic variation of pressure at blade basin, and led to the final failure.(3) The tension-torsion fatigue crack was nucleated at the tip of outlet edge, and propagated under the tensile and torsional cyclic stress induced by the periodic axial oscillating flow.An equivalent ellipse method to analyse the fatigue behaviour following ‘multi-surface initiations’This paper discusses the mechanisms of fatigue when cracks synergetically initiate in multiple sites at the surfaces of specimen. Metal–matrix composites such as aluminium matrix composites reinforced by silicon carbide particles are good candidates to accelerate fatigue failures following multi-surface initiations (MSIs). Closure effects of MSIs on the variation of fatigue behaviour were explored for various applied stress in two states of composite used: pre-treated state and non-pre-treated state. Using an equivalent ellipse method (EEM), it is found that the quality of surface finish of the specimen is of great role in crack initiation and growth. It is revealed that total lifetime of specimen is sensitive to heat treatment. Considering no transition from small to long crack, predictive formula used leads to identification of the Paris law exponent. It is found that this exponent is sensitive to both the applied load and the value of crack growth rate below threshold.Recently, the importance of metal–matrix composite (MMC) in the development of engineering components in automotive and aerospace sectors has been pointed out by many researches throughout the world. In early publication, Lim and Dunne The material studied is an extruded composite. It is a 2009 aluminium matrix reinforced with discontinuous silicon carbide particles (Al/SiCp-MMC). The average dimension of the SiCp particles is about 5–8 μm (typical microstructure is shown in ). The reinforcement is arbitrarily distributed into the longitudinal cross-section of the material. Contrary to long- fibre reinforced materials, where orientation is easily detected, the considered reinforcement does not exhibit any preferred orientation.The parameters used are cutting speeds of 90 m min−1 and feed rates of 0.15 mm rev−1 and 0.3 mm rev−1. Pre-treated specimens were manufactured after heat treatment; the surface of specimens was not polished. The depth of cut is kept constant at 1.25 mm. For ensuring good comparisons between the results of fatigue, the finishing operation uses a new tool for each specimen. As recommended in literature Fatigue tests were performed using a SIMPLEX bending machine equipped with four-point fixtures devices. The rotation speed of the machine was fixed at 3500 rev min−1. All experimental tests were carried out at the same load ratio, R=−1, and at room temperature. Two states of material were used: non-pre-treated state and pre-treated state. The material was heated up to 498 °C in a furnace and held at that temperature for 240 min before quenching in water to room temperature. This heat treatment has the advantage of enhancing mechanical homogeneity within the matrix material by relaxing residual stresses introduced at the particle–matrix interface from prior elaboration process of the composites. Thermal properties of ceramics are known to be significantly different from there of metal phases of composite matrices, which might result in the appearance of residual stresses and dislocations within composites on cooling from the fabrication temperature. summarises the mechanical properties, chemical composition of the material and specifications of heat treatment used.the total surface of n initiation sites is approximated by an ellipse with perfect shape, in the manner:a0eq and b0eq are the half-minor and half-major axes of the equivalent ellipse, respectively;the equivalent ellipse has to be included in the cross-section of the specimen: the major axis of the ellipse cannot be over the specimen radius r.The second condition verifies the transformation of multi-initiations to unique initiation due to physical growth of cracks that cannot propagate out of the cross-section of the specimen. This results in the following equation, which uses the relation cos 2γ+sin 2γ=1 (In the same way, the equation of propagation contribution can be established for the equivalent ellipse: determine the dimensions of the equivalent ellipse for multiple initiation sites and their associated propagations. From experimental observations, it is proven that (a0i/r<0.5) whereas (ai/r<0.5) is not always verified, especially for a large number of cycles. Thus, the following relations should be used for computing the equivalent surface of the propagation portion:The crack growth from a0 to a is considered depending on the material state and surface finish state of each specimen. It was assumed that cracks grow according to a constant propagation rate. This was formulated as follows:{a0eqaeq=ra=a01a1=⋯=a0iai=⋯=a0nanb0eqbeq=rb=b01b1=⋯=b0ibi=⋯=b0nbnra and rb are constant ratios that physically represent the lateral and radial rates of fatigue crack growth, respectively. They are material- and loading-conditions-dependent constants. The number of cycles (NSI-totali) associated with crack growth of a site i is the portion of the total experimental lifetime (NSI-totaleq). Referring to the surface ratio, the crack growth lifetime of the site i is estimated using the following formula:NSI-totali=Siπ∑i=1naibiNSI-totaleq=a0ib0irarb1aeqbeqNSI-totaleq shows the principle of EEM for characterising the crack growth when cracks occur at single site or multiple initiation sites. The subscript ‘SI’ denotes surface initiation., αeq (≈α for single-initiation case of metals) denotes the exponent of fatigue crack growth rate below the threshold corner The reliability of this relationship for predicting the crack growth rate and the corner has been proved in literature. Therefore, this observation has been basically considered for developing predictive formula available for estimating very-large-cycle fatigue failures. Unfortunately, no study has been conducted to explain the mechanisms of fatigue crack propagation following multi-surface initiations. This paper explores closure effects on this issue. Integrations of fatigue crack growth rates will be separated for equivalent crack growth below threshold NSI-inteq, small cracks NSI-a0eq→aieqeq and long cracks NSI-aieq→aeqeq. The addition of the three contributions gives the total estimated lifetime.NSI-totaleq=NSI-inteq+NSI-a0eq→aieqeq+NSI-aieq→aeqeqWhen there is no transition from small to long crack (aeq≤ai eq), Eq. NSI-inteq=(a0eq)αeq/2bg∫ainteqa0eq1aαeq/2da=a0eqbg1((αeq/2)-1)[(a0eqainteq)(αeq/2)-1-1]Y=(1.84/π)[tan(πa/4r)/(πa/4r)]0.5cos(πa/4r)[0.752+2.02(a2r)+0.37{1-sin(πa4r)}3]NSI-inteq=1πE2Yeq2(Δσ)21((αeq/2)-1)[(a0eqainteq)(αeq/2)-1-1]NSI-a0eq→aeqeq=(a0eq)3/2bg∫a0eqaeq1a3/2da=2a0eqbg[1-(a0eqaeq)1/2], the above relation may be rewritten as follows:NSI-a0eq→aeqeq=2πE2Yeq2(Δσ)2[1-(a0eqaeq)1/2] leads to an estimation of the total crack growth lifetime needed for a system of multi-surface initiations with an equivalent semi-elliptical surface failure. Thus, it can be written asNSI-totaleq=2πE2Yeq2(Δσ)2[12((αeq/2)-1)(a0eqainteq)(αeq/2)-1+αeq-3αeq-2-(a0eqaeq)1/2]For this, it was considered that aint eq=0.9a0eqNf-expπ2Yeq2(Δσ)2E2=[12((αeq/2)-1)(10.9)(αeq/2)-1+αeq-3αeq-2-(a0eqaeq)1/2]Nf−exp denotes the fatigue lifetime measured in experimental tests. Analysis of Eq. leads to the identification of the Paris law exponent αeq required for estimating the crack growth life portion below threshold. The last expression is more general than the one developed for single initiation in The turning operations were carried out on a numerically control turning machine. Lubrication is considered for all operations in order to delay damaging effects of SiCp particles on cutting tools. The fatigue behaviour of metal–matrix composites depends on several factors, including particle type, size and volume fraction, matrix microstructure, particles–matrix interfaces characteristics and ultimately conditions of cutting, i.e. feed rate. As known in machining, the finished surface is better as feed rate decreases. Moreover, it is extremely probable that friction at tool–work surface interface varies with the variation of the feed rate.Locally, at the material–tool interfaces, the friction effects not only depend on lubrication conditions but also on the cutting time of the tool. It is obvious that thermal and mechanical properties at tool–surface interface change with cutting parameters, especially, with feed rate. As a consequence, the layers, i.e. subsurface, close to the turned surface will be inevitably affected. Thus, mechanisms of crack initiations activated at finished surfaces under alternate mechanical loadings, i.e. fatigue load, evolve with microstructure and mechanical properties at the subsurface. For revealing the surface property effects on fatigue lifetime, two specimens with different surface finish were considered for fatigue tests (). For the used Al/SiCp-MMC, where the matrix was made from an aluminium alloy, micrographic examinations proved that the microstructure does not present interfacial defects between matrix and reinforcements.Generally, processing conditions that are used for producing Al/SiCp-MMC enhance the bonding at particles–matrix interfaces. For these reasons, it has been assumed that failure under fatigue load essentially occurs as a consequence of global fatigue mechanisms of the composite., it can be noted that failure occurring under fatigue load is localised at the median zone of one streak generated beforehand by the tool. Microscopic inspections have shown that failure was always caused at this zone and never at the board of streaks. When the tool operates in the material, temperature increases and reaches its maximum value at the nose of the tool, where lubricant circulation is technically hard to ensure, contrary to the lateral zones, where streak boards are generated. Thus, thermal effects, rapidly attenuated by the action of lubricant behind the tool once the tool advances, result in a kind of local treatment that strengthens microstructure at the median zone of streak and causes its cracking earlier than the streak boards.Microscopic observations did not explicitly show effects of surface finish quality on fatigue behaviour. Therefore, the S–N curves were plotted for 0.15 and 0.30 mm rev−1 feed rates. a and b clearly illustrate a drop induced in the material lifetime when the feed rate increases. This result has been confirmed for both pre-treated state and non-pre-treated states of the material. A long cutting time should affect the surface more than a relatively short time as recorded for large feed rates.The mechanical properties of the subsurface should be enhanced as a consequence of local thermal-induced effects caused by the operating tool. As known, thermal effects, i.e. heat treatments, are highly time-dependent phenomena. Hence, use of small feed rates (long cutting time) presents a good opportunity to ensure the effectiveness of these effects at least at subsurface layers. This phenomenon plays a large role in increasing the material resistance, recorded over remarkably large fatigue lifetimes.The physical limits of initiation and propagation zones have been studied through microscopic inspections (a and b). Investigations of failure surfaces show the difference between initiation site states and propagation site states of cracks. Initiation sites of cracks which are known as zones that consume the greatest contribution of cycle number, result in smooth failure aspect as seen in c. There zones occasionally exhibit a preferred orientation whereby cracks grow as can be observed in the micrographs of The failure at the end of the lifetime generates a rapid separation of materials with rough aspect as can be observed in the large delimited area of the micrographs of e and f. The final failure occurs as a consequence of the growth of micro-cracks initiating around particles. From the failure area of f, micro-cracks having a parallel direction seem to be weaker than those observed in e. This is essentially due to heat treatment, which probably seeks to homogenise properties at the interface between the matrix and particles in a manner so as to enhance the progress of separation mechanisms, and to ensure more regular shape and scatter of micro-cracks. This explains the fact that only pre-treated material states lead to large-cycle fatigue.The composite material discussed here is chosen in a manner so as to favour multi-initiation mechanisms. From experimental results, it has been noticed that only pre-treated material state can lead to large-cycle fatigue. Consequently, fatigue tests of only pre-treated specimens will be explored in this section. summarises the measured dimensions of each crack initiation and propagation area and the fatigue lifetime recorded for each applied load.A numerical study of constitutive equations leads to the identification of the fatigue law exponent αeq (). Smaller exponent values are obtained for lower number of cycles. This exponent is found to be sensitive to the testing load; the exponent seems to increase as fatigue lifetime increases and the ratio ra increases. From measurements, the mechanisms of initiation seem arbitrary. For the same applied testing load, fatigue crack may initiate from single surface site or multi-surface sites, which proves that the mechanisms of initiation depend only on the material state and constituents of microstructure. It is of great interest to note that when cracks initiate at surface from more than one sites, the number of cycles needed for initiation probably decreases with respect to other fatigue conditions and applied load. The fall noted in the number of cycles for initiation mechanisms is especially true for large fatigue loads, for which Nf−exp∼104 cycles, i.e. for Δσ=300 MPa. It was seen here in tests in the large-cycle regime, i.e. Nf−exp>105 cycles, that initiations are the most time-consuming part of the total experimental life as compared with crack growth (For estimating the crack growth life portion below threshold corner, Marines et al. show the evolution of the estimated exponent with testing load. A first observation proves the sensitivity of the exponent to fatigue load for both 0.15 and 0.3 mm rev−1 feed rates. From Eq. , the increase of the exponent αeq with the number of cycles, which sensitively varies with load, seems to be obvious. The highest specimen lifetime is recorded for the lowest load, which mathematically requires the largest values of the exponent as can be implicitly deduced from the predictive formula of the total crack growth lifetime. The difference between the numbers of cycles consumed at each feed results in marked deviations in the values of αeq. Even if the slopes of the curves are close, the Paris exponents identified for 0.15 mm rev−1 are about 37% higher than those found at 0.30 mm rev−1. Thus, it is of great interest to note that the exponent of Paris law is not constant and not the only material-dependent parameter either.The fatigue mechanisms did not evolve from the beginning of initiation to the end of initiation (beginning of propagation) in the same way. Generally, crack initiation consumes the largest portion of total life. From the starting point to the threshold point, the crack rate mechanisms should have enough time to change. This can be implicitly observed through the variation of the exponent α. Any change in the mechanisms of fatigue, results in changes of crack life. So, from multi-scaling analysis, it can be assumed that the coefficient α, which mostly depends on material properties, implicitly varies with crack life, which is related to the applied load. Scatter in the computed slope for a given condition (fixed load and material state) may be observed as a consequence of the deviation in number of cycles for the same condition (e.g. for Δσ=300 MPa and f=0.15 mm rev−1⇒αeq=44 for Nf=90,200 cycles and, αeq=34 for Nf=61,900 cycles). The drastic change in the exponent may be explained by the evolution of failure rate mechanisms with increasing crack lifetime.The variation of exponent αeq with crack growth rate below the threshold corner is given in The curves show the same trend and slightly increase with crack growth rate. When the feed rate increases, the estimated values decrease. When the crack growth rate below threshold passes from 0.9 to 0.96 for f=0.15 mm rev−1, the exponent increases about 3 times for the lowest load, whereas it reaches 4.2 times for the highest load. For f=0.30 mm rev−1, these ratios are 3.1 and 5.2, respectively. This observation agrees with the choice of Paris exponent value, which was taken as large as the crack growth rate increases The estimation of crack initiation and growth lives consumed by multi-surface initiation (MSI) mechanisms at large-cycle regime has been discussed herein for aluminium matrix composites. This is why a new approach based on equivalent ellipse method has been proposed for characterising initiation and growth area when cracks initiate at surface from more than one sites. The estimation of fatigue life portion below and beyond threshold corner has been performed without considering the transition from small to long cracks, using Paris law. The use of EEM does not depend on the nature of the material and shows its effectiveness especially for the composite considered where cracks might initiate from several sites. Thus, the following remarks can be drawn.The quality of surface finish plays a great role in the fatigue life of specimen. This observation is true for pre-treated as well as for non-pre-treated states of the considered material. Specifically, good surface state implies higher fatigue lifetime of the specimen.Application of the EEM for the predictive formula makes identification of the fatigue law for each portion of crack life possible. MSI mechanisms influence the initiation portion only at the largest testing load. These mechanisms act in a manner so as to reduce the number of cycles consumed at initiation when Nf−exp∼104 cycles. The initiation portion remains the most time-consuming contribution of the total experimental life as compared with crack growth period if tests are in the large-cycle regime (Nf−exp>104 cycles).The Paris law exponent varies with experimental considerations, which proves that it is not just a material-dependent parameter. The identification of αeq by applying Paris law for total fatigue life of the cracks proves that the exponent is sensitive to the applied testing load and the crack growth rate below threshold corner. For surfaces finished at both 0.15 and 0.30 mm rev−1, the exponent linearly decreases when the applied load increases and when the crack growth rate below threshold decreases.Molecular simulation on the material/interfacial strength of the low-dielectric materialsIn this paper, the material stiffness of amorphous/porous low-k material and interfacial strength between amorphous silica and low-k have been simulated by the molecular dynamics (MD) methods. Due to the low stiffness of the low-k material, the interfaces which include this material are critical for the most delamination and reliability issues around the IC back-end structure. MD simulation technique is applied to elucidate the crack/delamination mechanism at these critical interfaces. However, due to the amorphous nature of the low-k material (e.g., SiOC:H), the atomic modeling technique of the amorphous/porous silica is first established. Through the experimental validation, the accuracy of this amorphous modeling technique is obtained, and the results show that this algorithm can represent the trend of the mechanical stiffness change due to different chemical composition of low-k material. A novel interfacial modeling technique, which model the status of chemical bonds at interface during the delamination loading, is developed. Afterward, the simulation of the mechanical strength of the amorphous silica/SiOC:H interface, is implemented. The simulation depicts that the existence of the strong Si–O covalent bond will significantly enhance the adhesive strength of the interface. Instead of the covalent bond at interface, the simulation results also reveal the multiple atomic scaled crack path within the material during the interfacial delamination. Hence, improving the material stiffness of the soft low-k material and preventing the pore at interface can increase the adhesive strength of the silica/low-k interfacial system.As feature sizes for the advanced IC continue to shrink, the semiconductor industry is focusing the development on minimizing the intrinsic time delay for signal propagation, quantified by the resistance–capacitance (RC) delay ) are preferred by the industry because the fabricating processes of this materials exhibits high IC compatibility and high yielding rate. The k-value can be reduced in two ways: either chemically by replacing oxygen by the methyl groups, H or OH or physically by generating porosity within the material However, the delamination and reliability issues around the advanced IC back-end structure remain, due to the low mechanical stiffness of the low-k material Fracture/delamination is a phenomenon which spans many different geometrical scales. The macroscopic dimensions of the crack and the specimen determine the intensity of the stress at the crack tip and are equally important as the microstructure of the material, which provides preferred fracture paths. Ultimately, mechanism of fracture can be reduced to the breaking of atomic bonds, which in the case of brittle fracture occurs at an atomically sharp crack tip Nevertheless, traditional theory of brittle fracture processes does not focus on individual atomic bonds but resorts to the treatment of Griffith In order to implement the molecular simulation, the atomic structure and interaction between atoms should be well defined beforehand. For the low-k material, due to the uncertainty of an amorphous material, it is quite difficult to precisely describe the exact chemical structure. There are several methods to predict the chemical structure. One can simulate the whole fabrication process of the amorphous material, but is time-consuming if the fabrication process was not interested. Another trick is to generate the reasonable structure based on the known chemical characterization information. Without explicitly considering the real fabrication process of glass silica, Bell and Dean Two tasks are focused in this paper: mechanical modeling of the amorphous/porous low-k (SiOC:H) material and the interfacial strength between low-k and silica. A fast molecular generating algorithm is established to formulate the atomic structure of low-k material based on the inputs from its chemical composition (by experiment). The accuracy of this generating algorithm will be validated by the mechanical stiffness of low-k which is obtained by nano-indenter experiment. Moreover, an engineering approach is developed to model the chemical configuration at interface between the amorphous silica and low-k. Two remarkable simulation results are discussed: one shows the importance of the covalent bond and the other demonstrates the crack propagation path at the interface. A recommendation of improving the interfacial strength is proposed based on the simulation result.The molecular dynamics (MD) method, which is widely used in material science of IC technology, provides a theoretical and numerical framework for many particle problems. Based on the Newton’s second law of motion, the movements of the particle are described by the coordinate variables:for each particle i in a system constituted by N particles. In Eq. , mi is the mass of particle i, ai is its acceleration, and Fi is the force acting on the particle. Therefore, MD is a deterministic technique: given an initial set of positions and velocities, the subsequent time evolution can be determined. The interaction force between particles, which is required in Eq. , can be defined by the potential functions or force fields:where U is the potential function and rk(k

= 1 ⋯

N) is the atomic coordinate.Considering a system with an interface and a set of external loading applied onto that system. Assume that interfacial failure is observed by experiments. Therefore, according to the conservation of the total energy of the system, the work which is done by the external loading will equal the summation of material deformation energy, heat and the surface energy (intrinsic adhesion) of the interface Chemical interactions: The chemical interactions between the interfaces often refer to the covalent bond, ionic bond or the metallic bond. These bonds are relatively strong and termed primary bonds. In the electronic or packaging laminated structure, the most common chemical interaction at the interface is the covalent bonds besides the alloy system. The interaction scale of the chemical interaction is approximately 0.2–1.0 nm. For example, the interface of the silicon oxide and the SiOC:H film (low-k material). From the fabrication point of view, the amorphous SiO2 is deposited onto the SiOC:H film by PECVD at O2 atmosphere and 200–400 °C with the precursor of TEOS (tetra-ethyl-ortho-silicate, R–Si–R, R = –O–CH2–CH3) Physical interactions: The physical interaction often refers to the weak bonds between interface, like the Coulomb force or van der Waals force. Although the magnitude of the physical interaction is weaker than the one of the chemical bond, the physical can be formed at most interfaces and chemical interaction requires certain chemical condition to form. The interaction scale of the physical interaction is approximately 5.0–10.0 nm. Moreover, considering a polymer interface system, two chained polymers can entangle together when the polymer chains have enough energy to move though the interface and this phenomenon also contribute to the interfacial strength of polymer and polymer system.Mechanical interlocking: Both the physical and chemical adhesion mechanisms are on the microscopic scale. At the macroscopic scale, mechanical interlocking can be applied, as in the surface treatments applied to metal to increase the surface roughness and to obtain better adhesion strength. For a specific process and materials, the pattern and distribution of the surface roughness can be controlled. The interaction scale of the physical interaction is approximately larger than 10.0 nm. However, strictly speaking, mechanical interlocking is not one of the intrinsic material adhesion mechanisms.In this research, the physical and chemical interactions at the interface will be modeled. However, due to limit of the MD simulation, the mechanical interlocking is not considered.), Q, T, D and M, represent Si atoms having 4, 3, 2, and 1 capabilities to connect other basic blocks, respectively. Instead of building the amorphous structure manually Chemical nature of building blocks: When the pore, Q, T, or D is randomly distributed onto the node, the total link of that node is fixed to 0, 4, 3, and 2, respectively. In the other words, for each node, the exceed links is removed by random choosing from the former linkage status.Average distribution: The local high concentration of specific type of building blocks will be prevented. Hence, a reliable random number generator is used to obtain the homogeneous distribution.Minimal numbers of dangling bonds: Because the dangling bonds are not physically favored, reducing them will easily lead to minimal potential energy state.In the process of random distribution of building blocks and the selection of the removed bonds, the random number generator is used. Therefore, this algorithm does not guarantee that the Q, T, D, M and void elements can be allocated to the nodes exactly according to their chosen concentrations. Therefore, a series of iterations of procedures, with different random number (for the random distribution of pore Q, T, D and M) is often necessary.The appreciated molecular model can be achieved after applying a structural optimization (minimization of total potential energy) process to the obtained connection catalogue, as illustrated in . Note that the aforementioned optimization includes the iteration of local (by atomic perturbation) and global (by the systematic perturbation) Before the interfacial strength simulation, the situation of the chemical bond at the interface should be well defined. There is few theory or experimental method which is capable of predicting/measuring the chemical configuration at the interface. Therefore, to simulation the mechanical delamination at molecular level, an engineering approach is proposed. This approach use the artificial charge to attract two molecules and the covalent bond is established when the distance between two atoms is satisfied pre-defined criterion. For this low-k to silica interface (a) which the chemical bond can be formed (judged by chemical reaction energy), an engineering approach is applied as following:The silicon atoms at silica interface and oxygen atoms at low-k interface are artificially removed.The remained oxygen and silicon atoms at interface are artificial charged. A positive charge is applied to the silicon atom and negative is at the oxygen (A molecular dynamics simulation is performed and two separated molecules are attracted each other by the electrostatic force (When the distance of the atoms at interface smaller than the criterion, the chemical bond is formed. Afterward, the artificial charges are removed, and the partial charges of the atoms are re-calculated (This algorithm can provide a scheme of covalent bond distribution at interface. The forming criterion at step 4 can be a tuning parameter with respect to the covalent bond density along the interface.In order to understand the accuracy of the amorphous structure which generated by the proposed method, two molecules, the SiOC:H before and after UV treatment, are used as the qualitative validation. In reference Herein the Young’s modulus and density are considered. The simulated density is defined as the ratio of atomic mass and molecule volume, and the molecule volume is defined as the volume which is occupied by the molecular surface with the Connolly radius of 0.1 nm. The Young’s modulus is obtained by the equation: E=L02V0ΔFΔd, which follows the same simulation step. The result shows that the Young’s modulus and density of AU is slightly higher than BU, and the similar trend is also found in the experiment. This simple case study demonstrates that the MD simulation has the capability to describe the variation of Young’s modulus and density as function of chemical composition.Afterward, the parametric analysis is conducted to obtain the impact of the building block concentration to the Young’s modulus and density. The simulation results with different chemical concentrations (Q:rQ, T:rT and D:rD) are analyzed using a simple equation for Young’s modulus and density: E(rQ, rT, rD) =

EQ

·

rQ

+

ET

·

rT

+

ED