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cycles. Stress intensity range at the border of the IAA, ΔKIAA can be calculated using Eq. shows ΔKIAA versus cycles to failure. It may be noticed, that ΔKIAA is almost constant irrespective of cycles to failure. For the present material and loading conditions the stress intensity range is ΔKIAA
= 4.0 ± 0.2 MPa m1/2. Stress intensity range can also be calculated for a crack with area=areafish-eye. With the measured sizes of the fish-eyes, the stress intensity range at the border of the fish-eyes is ΔKfish-eye
= 7.4 ± 0.8 MPa m1/2.The depths of the crack-initiating inclusions below the specimen surface are shown in . Seven classes of 25 μm width are shown. No crack-initiating inclusion was found closer than 25 μm to the surface. In a distance between 25 μm and 50 μm to the surface, six crack-initiating inclusions are located. Between two and four crack initiating inclusions are found in the other five classes with distances between 50 μm and 175 μm below the surface.In the investigated nitrided 18Ni maraging steel sheets, fatigue cracks leading to failures in the regime from 107 to 109 cycles are initiated at internal inclusions. shows that crack initiating inclusions are situated more than 25 μm below the specimen surface. The much higher hardness of the nitrided surface layer compared with the core material and beneficial compression stresses effectively protect the surface from crack initiation. Surface crack initiation under cyclic tension–compression loading is reported for lifetimes below approximately 105
cycles and interior inclusion-induced failure above Fatigue cracks are initiated exclusively at TiN nonmetallic inclusions in the present 18Ni maraging steel. The fracture surface enclosing the inclusions appears granular and homogeneous without steps or secondary cracks and it does not indicate the crack propagation direction. This fracture surface area is named inclusion adjacent area (IAA). Granular appearing fracture surface areas around inclusions are frequently found after VHCF failure of high strength steels. These areas are named ODA (optically dark area), GBF (granular bright facet) or FGA (fine granular area) in the literature. A survey of several steels showed that the border of the FGA is at a stress intensity amplitude between ΔKFGA
= 4 MPa m1/2 and 6 MPa m1/2Progress of fatigue damage in the investigated steel may be captured assuming a slowly propagating crack. An adapted Paris law is suggested by Tanaka and Akiniwa is used to describe the dependence of stress intensity range ΔK and crack propagation rate Δ(area)/ΔN.Lifetimes are calculated by integrating growth rates with starting crack length area=areaINC to fracture. This leads to Eq. for the correlation of cycles to failure N and the stress intensity range ΔKINC assuming the crack initiating inclusion as an initial crack., the quotient of numbers of cycles to failure and square root of inclusion areas are presented versus ΔKINC. With stress intensity ranges in MPa m1/2 and areaINC in m, fit of data delivers n
= 8.04 and C
= 1.10 × 10-16.Scatter of data using the parameter ΔKINC may be quantified using the ratio TK of N/(area)1/2 with 90% fracture probability and N/(area)1/2 with 10% fracture probability. Data points are normalised using Eq. , and fracture probability is determined assuming a log-normal distribution. The ratio TK
= 2.9 is slightly smaller than Tσ
= 3.0 quantifying scatter of data in the S–N diagram.An alternative method to consider the influence of inclusion size on fatigue lifetime is based on Murakami’s area-model Numbers of cycles to failure are presented as a function of the product of stress amplitude and (area)1/6 in . With stress amplitudes in MPa and areaINC in μm the fit of data delivers n
= 10.7 and C
= 1.35 × 1038.Scatter of fatigue lifetimes using the parameter Δσ/2(areaINC)1/6 may be quantified using the ratio Tarea of fatigue lifetimes with 90% fracture probability, N90% and 10% fracture probability, N10%. Data points are normalised using Eq. , and a log-normal distribution of lifetimes is assumed. The ratio is Tarea
= 2.2 which is smaller than Tσ and TK. From the three methods to present fatigue lifetimes () the parameter Δσ/2(areaINC)1/6 shows the best correlation with the measured fatigue lifetimes.The stress amplitude leading to a fracture probability of 50% at 109
cycles in the investigated 18Ni maraging steel is Δσ/2 = 444 MPa, which is 22% of the tensile strength. This percentage may be compared with cyclic tension strengths of other high strength steels measured in the VHCF range. Comparison is possible, however, solely considering comparable loading of specimens. Due to volume effects, for example, rotating bending tests deliver significantly longer fatigue lifetimes and higher cyclic strength than cyclic tension–compression fatigue tests A mean lifetime of 109
cycles at a load ratio of R
= 0.1 was found for a turbine blade steel with tensile strength of 1000 MPa at 35% of its tensile strength This data survey of VHCF strength under cyclic tension conditions at load ratio R
= 0 or R
= 0.1 is summarised in . Cyclic strength of the presently investigated material corresponds well with the other high strength steels included in the survey. Under the investigated conditions, the 18Ni maraging steel tested in the present condition (i.e. tensile strength 2000 MPa, inclusion size areaINC
⩽ 5.3 μm) shows a correlation of cyclic and tensile strength that is comparable to other high strength steels.Fatigue properties of nitrided 18Ni maraging steel thin sheets have been investigated in the regime of mean lifetimes between 107 and 109 cycles with a further developed ultrasonic fatigue testing method.Mounting sheet specimens on a carrier specimen, generation of static mean stresses by bending, calibration and monitoring of static and cyclic loading with strain gauges is an appropriate method to test thin sheets with ultrasonic fatigue testing equipment.The investigated 18Ni nitrided maraging steel shows solely interior crack initiation at TiN inclusions with areaINC between 2.5 μm and 5.3 μm. The hard nitriding layer effectively protects the surface from crack initiation. No endurance limit is found below 109
cycles.Considering crack initiating inclusions as cracks, their stress intensity ranges are between 1.3 MPa m1/2 and 2.4 MPa m1/2. A granular and homogeneous appearing fracture surface without steps or secondary cracks is formed next to the inclusion with the border at the stress intensity range 4.0 ± 0.2 MPa m1/2. Fish-eyes visible on the fracture surfaces have a serrated border at a stress intensity range of 7.4 ± 0.8 MPa m1/2.The size of crack initiating inclusions influences the fatigue lifetime. This can be considered presenting the ratio of cycles to failure and areaINC versus the stress intensity ranges of crack initiating inclusions. Lifetimes can be also presented versus stress amplitudes multiplied by (areaINC)16, which reduces data scatter compared with a presentation in a S–N diagram.Cyclic stress amplitude leading to a mean lifetime of 109
cycles at load ratio R
= 0.1 is 22% of the tensile strength. This ratio of cyclic to tensile strength for the presently investigated 18Ni maraging steel in the VHCF regime is comparable with other high strength steels tested under similar loading conditions.A multi-scale simulation of tungsten film delamination from silicon substrateTo bridge the different spatial scales involved in the process of tungsten (W) film delaminating from silicon (Si) substrate, a multi-scale simulation procedure is proposed via a sequential approach. In the proposed procedure, a bifurcation-based decohesion model, which represents the link between molecular and continuum scales, is first formulated within the framework of continuum mechanics. Molecular dynamics (MD) simulation of a single crystal W block under tension is conducted to investigate the effect of specimen size and loading rate on the material properties. The proposed decohesion model is then calibrated by using MD simulation of a single crystal W block under tension and using available experimental data, with a power scaling law to account for the size effect. A multi-scale model-based simulation of W film delamination from Si substrate is performed by using the proposed procedure within the framework of the material point method. The simulated results provide new insights into the mechanisms of the film delamination process.Thin films usually develop high residual stresses during the deposition process. The films subjected to large residual stresses may fail by delaminating and buckling away from the substrates in the working environment. The delamination of compressed films has been studied by many researchers in both academia and industry, as shown by representative papers (). Existing approaches are mainly based on conventional elastic stability theory and interfacial fracture mechanics, with a focus on the stability of blisters (). Recently, much research has been conducted to model and simulate pattern formation during the delamination process, based on the buckling-driven mechanism (; among others). However, a systematic study of the complete process from the formation of films to their eventual delamination from substrates is not yet available from the open literature, due to the complexity of multi-physics and multi-scales involved.Based on the experimental observation of the transition from tensile to compressive stress as a function of the argon gas pressure in magnetron sputter-deposited tungsten (W) film onto silicon (Si) substrate ( proposed that the delamination of compressed films is essentially due to the interaction between geometrical and material instabilities which results in the formation and evolution of localization, depending on different stress states in the domain of influence. By formulating a bifurcation-based decohesion model within the framework of the material point method (MPM), which is one of the “meshfree” methods (), a numerical effort was made to investigate the transition from continuous to discontinuous failure modes involved in the W film delaminating from the Si substrate. Within the framework of continuum mechanics, the numerical study of the effects of aspect ratio and failure mode on the evolution of failure patterns under different boundary conditions provides a better understanding on the physics behind the film delamination process (However, the bifurcation-based simulation of the transition from localization to decohesion in the film delamination process is based on a phenomenological framework which could only provide a qualitative analysis of film delamination process. The bifurcation-based decohesion model, as proposed by is formulated via thermodynamics constraints with the result that the dissipation inequality is automatically satisfied. However, the constitutive relation of decohesion–traction, τ(u¯), as a key part of the decohesion model, cannot be calibrated via existing experimental techniques. Since the decohesion–traction constitutive relation is directly related to the interatomic binding energy and film microstructure developed during the film formation process, atomistic simulation might provide required information for establishing the decohesion model. Furthermore, the size of the film–substrate structure usually ranges from nano/micro to macroscale, and which is beyond the capability of the conventional continuum mechanics. Hence, a multi-scale decohesion–traction model is required to accommodate the suitable constitutive laws for the film structures at different size scales. In other words, a thorough understanding of the physics behind the film delamination process necessitates a multi-scale investigation ranging from atomistic simulation to continuum mechanics.For the purpose of simplicity, a multi-scale sequential approach is proposed in this study, as illustrated in , to simulate the film delamination process. When bifurcation occurs in the MPM discretization of macroscopic responses, the proposed procedure would zoom in to the desired scale level in order to obtain the τ(u¯) constitutive relation curve. By coupling the multi-scale τ(u¯) constitutive law with the discontinuous bifurcation analysis within the framework of the MPM, the multi-degree discontinuous failure modes involved in the film delamination process could then be simulated.With the rapid development of micro-electromechanical systems (MEMS) and nano-technology, atomistic simulation of mechanical behavior of metals has drawn considerable attention in recent years (; among others). The deformation of atomic system at finite temperatures in general is an intrinsically dynamic process. Size and strain rate effects arise out of several factors and play important roles in determining the response of nano-structures. The behavior and properties of micro/nano-structure are size-dependent due to the discreteness of atomic system, crystal arrangement and boundary condition. The dynamic inertia effect and the finite speeds at which lattice waves propagate also introduce the size effect to the problem and contribute to the size-dependence of atomic behavior. The inertia effect and finite wave speeds, along with phonon effects, also cause the response of nano-structures to be deformation-rate dependent. A part of this study thus focuses on the size and rate effects on the constitutive law of single crystal W block under tension in order to develop a multi-scale decohesion–traction model for W.To determine material properties for elasto-plasticity and decohesion at different size scales, a power scaling law is proposed to account for the effect of structure size. Thus, MD simulation of single crystal W block under tension could be combined with available experimental data to develop a multi-scale τ(u¯) model for W based on the proposed scaling law. The multi-scale decohesion–traction model is then employed to simulate the film delamination process.The remaining sections of the paper are arranged as follows. To be self-contained, a brief introduction of the bifurcation-based decohesion model within the framework of continuum mechanics is presented in Section . The MD simulation of single crystal W block under tensile loading is conducted in Section , which is followed by the formulation of the multi-scale decohesion–traction relation for W in Section . The multi-scale simulation of W film delamination from Si substrate is presented in Section To catch the essential feature of the film delamination process, a discrete constitutive model was formulated by by using the bifurcation analysis to predict decohesion or separation of continuum. As can be seen from , discontinuous bifurcation can occur before, at or after the peak state, depending on the continuum tangent stiffness tensor and stress state. It is therefore not rigorous to distribute arbitrarily cohesive surfaces in a computational mesh and initiate decohesion at the peak state in order to achieve computational efficiency, as discussed by the representative papers (), in fact, the discontinuous bifurcation analysis could be performed without too much computational cost if an associated von Mises elastoplasticity model is used with a linear hardening and softening law. Hence, the proposed discrete model is coupled with the bifurcation analysis based on the von Mises model (). As a result, rigorous and mesh-objective results could be obtained since the location and orientation of the cohesive surfaces are determined via the discontinuous bifurcation analysis (By taking the bifurcation point as the initiation of decohesion, the transition from continuous to discontinuous failure modes could be simulated. As shown in for a plane strain problem, n and t represent the unit normal and tangent vectors to the cohesive surface whose orientation is obtained through bifurcation analysis. To determine the constitutive relation between traction τ and decohesion (displacement jump) ud, the following equations must be solved for a given total strain increment:Fd=τe-U0[1-(Δλd)q]=0Consistencyconditionwhere E is linear elasticity tensor, λd is a dimensionless monotonically increasing variable characterizing the evolution of decohesion, namely, effective decohesion, Le is the effective length representing the ratio of the volume to the area of the decohesion within a material element. It is assumed that no additional plastic strain would occur as long as decohesion evolves in the material element. For the purpose of simplicity, an associated evolution equation is employed, namelyso that the effective traction takes the form ofwith the reference surface energy U0 being the product of the reference decohesion scalar u¯0 and the corresponding traction τ¯0. The components of the positive definite tensor of material parameters, Ad, with respect to the n
−
t basis are given byAt the initiation of decohesion (λd
= 0), it follows from Eqs. where the normal and tangential tractions, τnb and τtb are obtained from the discontinuous bifurcation analysis. By letting Cm
=
τtf/τnf in Eq. , different failure modes can be simulated by utilizing different values of Cm. For example, mode I failure dominates if Cm
= 10, while mode II failure dominates if Cm
= 0.1. Mixed failure mode could be simulated by using Cm
= 1. Well-designed experiments are required to calibrate the value of Cm. The reference traction values, τnf and τtf, can be found from Eq. evaluated at the initiation of bifurcation for given Cm. As can be seen from the above formulations, the discrete model parameters to be determined from the experiments are U0, q and Cm if the choice of τ¯0=τnf is made. Thus, the decohesion model could be calibrated via mode I experiments. The relation between the traction and decohesion can be adjusted by changing the value of q, as illustrated in In order to calibrate the parameters in the bifurcation-based decohesion model and develop a multi-scale decohesion–traction relation for W at different size scales, MD simulation of single crystal W block under tension is conducted in this section. To be specific, the deformation fields and stress–strain curves of single crystal W blocks with different sizes are investigated under different tensile loading rates via MD.The computational set-up for MD simulation of single crystal W block under uniaxial tension is shown in . The simulation super-cell is a three-dimensional box where x, y and z are the global coordinates. The simulation cell consists of two parts. One part is referred to as the active zone in which the atoms move according to the interactions among the neighboring atoms; the other part, wrapped by the boxes as shown in , is referred to as the boundary zone, where the atoms are assigned a constant velocity with a same magnitude but an opposite direction for each end, to simulate a displacement-controlled tensile loading in the z-direction. The dimension of the active zone is indicated by H, D and W, while the thickness of each boundary zone in the z-direction is 2ao with ao being the lattice parameter of W. A periodic boundary condition (PBC) is imposed along the x-direction. Either a PBC or a free surface (FS) will be applied in the y-direction.) have identified the 〈1 0 0〉 axes as the weak directions in tension and the {1 0 0} planes as the cleavage planes for bcc tungsten. The crystal orientation of (x[1 0 0],
y[0 1 0],
z[0 0 1]) will therefore be investigated in this study since the decohesion process of single crystal W is of the interest in the current research. By simulating the separation of {1 0 0} planes along the 〈1 0 0〉 direction via MD, a multi-scale decohesion model could be formulated as discussed later.In the MD simulation, initially all atoms are placed at their equilibrium positions at room temperature of 298 K. Those atoms in the boundary zone are then fixed. After the system has equilibrated for a certain period, constant velocities with the same magnitude and opposite direction are assigned to the atoms in the top and bottom boundary zones, respectively, to simulate a displacement-controlled uniaxial tensile loading in the z-direction. A velocity scaling technique () is employed through the simulation to maintain a constant temperature of 298 K. The Embedded Atom Method (EAM) developed by is used to model the interatomic potential among W atoms. The method applied to integrate the equations of motion is the 6-value Gear predictor–corrector algorithm with corrector coefficients for a second-order equation. The integration time step size is determined based on the compromise between simulation accuracy and efficiency. The largest time step size that can keep the total system energy remaining a constant in the adiabatic simulations for W atoms with the EAM potential is used for the numerical study. To make the time integration stable, a time step size of 0.5 fs is chosen after several adiabatic simulations for W at different initial temperatures up to 2000 K. is a powerful tool to model the interatomic potential for metals and alloys. The basic equations of the EAM are given bywhere E is the total potential energy of the system, ρi is the electron density at atom i due to all other atoms, f(rij) is the electron density at atom i due to atom j as a function of the distance between them, rij is the separation distance between atoms i and j, F(ρi) is the energy to embed atom i in an electron density ρi, and ϕ(rij) is a two-body potential between atoms i and j. The detailed discussion on functions ϕ(rij), f(rij) and F(ρi) and the corresponding parameters for W can be found in the paper by Stress calculation in MD simulations has been a focus of study for many years (). For the stress at a given atom, one could set up a volume element surrounding the atom, and calculate the force across each face of the element. This is a so-called mechanical definition which is conceptually straightforward but computationally quite tedious. The virial stress, derived from the virial theorem of as a thermodynamics approach to the formulation of atomic-level stress, is widely used to calculate the system pressure ( showed that the virial stress is equivalent to the mechanical definition of stress for a homogeneous system, and that the equivalence can be demonstrated using the concept of volume average if inhomogeneities occur. However, the virial stress includes two parts, namely, the first part involves the mass and velocity of atoms, and the second part accounts for the interatomic forces. argued that the widely used virial stress in discrete particle systems is not a measure for mechanical force between particles but rather a stress-like measure for momentum change in space. He proved that interpretation of the virial stress as a measure for mechanical force violates balance of momentum and demonstrated that the interatomic force part alone is a valid stress measure and can be identified with the Cauchy stress. In this study, the formulations employed to calculate atomic-level stress are motivated by the above discussions, as described next.At each atom, the local stress tensor, β, is given bywhere i refers to the atom considered and j refers to the neighboring atom, rij is the position vector between atoms i and j, Nn is the number of neighboring atoms surrounding atom i, Ωi is the volume of atom i, and fij is the force vector on atom i due to atom j. The global continuum stress tensor is defined as a volume average, namely,in which N* represents the total number of atoms in a representative volume of continuum.To deal with large deformations, true strain, a nonlinear strain measure that is dependent upon the current length of the specimen, is used in this study and is given bywith Lo and L being the original and deformed lengths of the specimen, respectively.To study the effect of boundary condition, specimen size and strain rate on the dynamic responses of single crystal W block under tensile loading, nine MD simulation cases are designed. The details of the simulation design are listed in . In all the simulations, a periodic boundary condition is applied in the x-direction. The boundary condition in the y-direction for each case is given in . The crystal orientation is (x[1 0 0],
y[0 1 0],
z[0 0 1]).Simulations 1–3 are conducted to study the effect of boundary conditions on the tensile deformation of single crystal W block. shows the corresponding stress–strain curves. Although the stress reaches its peak value at about the strain of 0.34 in both Simulations 1 and 2, the peak stress with PBC in the y-direction is much larger than that with FS by using the same specimen size. In Simulation 2 the stress drops rapidly after its peak value and goes to zero at the strain of 0.348, however, the stress fluctuates for a very long strain range after the peak stress and does not reach zero even at the strain of 0.47 in Simulation 1. By doubling the specimen size in the y-direction in Simulation 3, the peak stress occurs at strain of 0.27, although its magnitude keeps almost the same as that of Simulation 1. The stress also fluctuates after its peak value and does not go to zero at the strain of 0.47. By comparing simulations 1 and 3, it appears that the strain corresponding to the peak stress is size-dependent with the FS boundary condition. presents the evolution of corresponding tensile deformation field in the y–z plane for Simulation 1. As can be seen from the figure, due to the use of FS and the lack of constraint in the y-direction the shrinking of the x–y cross sectional area in the active zone of Simulation 1 occurs when the stress reaches its peak value at the strain of 0.344. After the peak state, the stress fluctuates and the rearrangement of the crystal structure evolves as the strain increases. At the strain of 0.47, a severe necking occurs, but the corresponding stress is still not zero. shows the evolution of the corresponding tensile deformation field in the y–z plane for Simulation 2. The decohesion in Simulation 2, with the PBC in the y-direction, starts at the strain of 0.339 where the stress reaches its peak value, as shown in (a). The decohesion of W block evolves at the strain of 0.342, as shown in (b), and the complete separation of W block occurs at the strain of 0.345, as presented in (c). As a result, the cleavage of {1 0 0} planes is found at the end of decohesion in Simulation 2.It seems that neither decohesion nor cleavage of planes will occur with the use of FS in the y-direction since the cleavage of {1 0 0} planes is avoided by the rearrangement of the crystal structure. Hence, in the following MD simulations a PBC is always applied in the both x- and y-directions in order to investigate the evolution of decohesion in single crystal W block under tensile loading, and to obtain the constitutive law of W at the nano-scale.To study the effect of specimen size on the tensile deformation of single crystal W, Simulations 2, 4–7 are performed with the PBC applied along both the x-and y-directions. shows the corresponding stress–strain curves of different W blocks under tensile loading. As can be seen from the figure, the initial elastic modulus of single crystal W block is almost independent on the specimen size. However, the peak stress increases as the specimen size decreases, which is mainly due to the fact that larger specimens offer more opportunities for dislocation to occur. In addition to the constraints due to the boundary zones and the PBC used in the simulations, the single crystal W specimen is a discrete system with atoms distributed only in certain positions. The bonds among atoms are the relatively weak parts while the individual atoms are the strong parts of the system. The increase of specimen size increases the number of relatively weak bonds, which in turn offers more opportunities for bond breaking and dislocation to occur, and thus decreases the strength of the specimen. However, the size effect is diminished as the specimen size is further increased as can be seen from In the above simulations, the W specimens are perfect without any artificial imperfections. To verify the argument that the decrease of the W strength with the increase of specimen size is mainly due to the fact that a larger specimen offers more opportunities for dislocation to occur, the effect of artificially introduced defects in single crystal W block on the stress–strain relation is investigated. Different numbers of vacancies are artificially implemented into Simulation 2 with other simulation conditions being kept the same. The stress–strain curves of W blocks with zero, one, two and four vacancies distributed in the same x–y plane (which is initially located 2.152 nm away from the top end of the active zone) are demonstrated in . As can be seen from the figure, all stress–strain curves are initially the same until failure occurs. The strength of W decreases as the number of vacancies increases, since more vacancies offer more opportunities for bond breaking and dislocation to occur. However, the reduction rate of strength is decreasing with the increase of number of vacancies.To study the effect of the vacancy distribution in the z-direction on the stress–strain relation of single crystal W block, four cases with zero, one, two and four vacancies, respectively, located at the center of x–y plane but different positions in the z-direction, are simulated with other simulation conditions being kept the same as those in Simulation 2. The corresponding stress–strain curves are presented in . As can be seen from the figure, all stress–strain curves are again initially the same until failure occurs, and the strength decreases as the number of vacancies increases, which is similar to the previous simulation with vacancies distributed in the same x–y plane. It seems that increasing the number of defects regardless of their positions in single crystal W block would increase the possibilities for dislocations to occur and thus reduce the strength of W, which is very similar to the effect of increasing specimen size on the strength of W. Therefore, it is reasonable to argue that larger specimens offer more opportunities for dislocations to occur which in turn reduces the strength of W.Since the artificially introduced defects would cause the decrease of the simulated W strength, it is therefore important to investigate the effect of machine precision on the simulation results. In the previous simulations, the default setting, i.e., double precision, is used for all the variables defined as real numbers. To study the effect of machine precision, Simulations 2, 4 and 5 are re-run by setting all the real variables to single precision with all other simulation conditions being kept the same. The MD program is written in C. All the simulations were run on an SGI workstation with Intel Pentium 4 processor and Linux operating system. illustrates the stress–strain curves of W blocks in Simulations 2, 4, and 5 by using single precision and double precision for all real variables in the program, respectively. As can be seen, there is no difference between the curves obtained by using single precision and those by using double precision before failure occurs, although failure occurs slightly later in the single precision case than does in the corresponding double precision case. Hence, the imperfection caused by machine precision is very small and may be neglected as compared to other imperfections or defects in the system.It is well known that loading rate could considerably influence the material properties, such as strength, ductility, etc., at the continuum level. To investigate the effect of the tensile strain rate on the stress–strain curve of a single crystal W block at the atomic level, Simulations 6, 8 and 9 are performed with the initial strain rate of 2 × 109
s−1, 2 × 108
s−1 and 2 × 1010
s−1, respectively. shows the corresponding stress–strain curves. As can be seen from the figure, the initial elastic modulus of W is almost independent on the strain rate, but the peak stress increases with the strain rate. The dependence of decohesion initiation on the strain rate is mainly due to the dynamic wave effect that impedes the motion of dislocations (In order to determine material properties for elasto-plasticity and decohesion at different scales, a power scaling law is proposed. In the proposed approach, the dependence of the strength and decohesion energy of W on the spatial size is established by combining the MD simulation of single crystal W block under tension and the available experimental data.Power scaling in absence of characteristic length has been used to identify the material properties at different scales. By considering geometrically similar systems, the power scaling law takes the general form of (where λ
=
D1/D2 with D1 and D2 being the characteristic sizes of two similar structures, respectively, f(λ) =
Y1/Y2 is a dimensionless function with Y1 and Y2 being the material properties at sizes D1 and D2, respectively, and exponent m is an unknown constant.To determine exponent m, a suitable failure criterion must be chosen. For elasto-plasticity with a fixed yield surface which is expressed only in terms of stress or strain, one finds that m
= 0 when the material property Y represents the stress or strain. This is known as the case of no size effect on material strength, which is however only true when the size of the structure is within certain range. Indentation tests on single crystal W () have shown that there is certain dependence of material hardness on crystal orientation, but the size-dependence is the predominant effect. However, indents on W with diagonals longer than about 100 μm cease to display any hardness-dependence on the size. Since the material hardness is directly related to the strength, the effect of structure size on the material strength exists when the structure size is smaller than about 100 μm, namely, m
≠ 0 when D
< 100 μm. No size effect would occur as the structure size is beyond about 100 μm, namely, m
= 0 when D
⩾ 100 μm. It seems that the exponent m will change from nonzero to zero when the structure reaches the critical size of about 100 μm.Since there is an effect of strain rate on the strength of crystal W when the strain rate is high, a factor is needed to approximately account for the influence of the strain rate. MD simulations of sheared single crystal metals conducted by have demonstrated some qualitative features: (a) strain rate independence at low strain rate, and (b) an increase in the critical strain rate, under which rate-dependence disappears, with a decrease of specimen size. Their simulation results have shown that there is no strain rate effect on nickel’s yield strength with specimen size smaller than 28 nm when the strain rate is in the order of 108
s−1. It is therefore assumed in this study that the strength of W obtained with the strain rate of 2 × 108
s−1 is rate-insensitive since the specimen sizes are smaller than 28 nm. As can be seen from , the strength of W in Simulation 6, decreases from 24.8 GPa at the rate of 2 × 109
s−1 to 22.2 GPa at the rate of 2 × 108
s−1 in Simulation 8 with a factor of 22.2/24.8 = 0.895. For the sake of simplicity, all the strengths obtained in Simulations 2, 4–7 with the strain rate of 2 × 109
s−1, as shown in , will be multiplied by a factor of 0.895 to approximately calculate the rate-independent strengths at different structure sizes under strain rates in the order of 108
s−1.By combining the MD simulation data and the available experimental results, a multi-scale strength model for W is proposed here based on the assumption that the exponent m in the power scaling law must change smoothly when the structure size increases from atomic-scale to macro-scale. presents the MD simulation data for the rate-independent strength of a single crystal W block at different structural sizes, the strength of W at the macro-scale from experiments, and the proposed multi-scale model prediction of W strength. The model proposed to predict the multi-scale strength of W takes the form ofσN=σPD⩽DPlgσN-lgσMlgσP-lgσM=1-sinπ2×lgD-lgDPlgDM-lgDPDP<D<DMσN=σMD⩾DMwhere D is the characteristic size of W specimen, DP is the maximum atomic-scale size of W specimen at which the ultimate tensile strength of W is reached, DM is the minimum macro-scale size of W specimen where the tensile strength of W ceases its dependence on the size, σN is the nominal strength of W at size D, σM is the strength of W at size DM, and σP is the ultimate tensile strength of W. Based on the MD simulations of single crystal W block under tensile loading, σP
= 34.9 GPa atDP
= 1.6 nm, which is in a reasonable agreement with the maximum tensile strength of 29.5 GPa as reported by using pseudopotential density functional theory, is applied. According to , DM
= 100 μm is assumed. As a common material property for W, σM
= 1.5 GPa is adopted in this study. presents the effect of specimen size on the decohesion energy of single crystal W with crystal orientation of (x[1 0 0],
y[0 1 0],
z[0 0 1]) under tension. The decohesion energy can be estimated based on the area under the corresponding stress–strain curve within the softening regime in , with a factor of 0.895 being multiplied to approximately account for the rate effect on the strength. As can be seen from , the failure of the W block is an averaged process since the breaking of the bonds across the failure surfaces cannot occur at the same time. When the specimen size increases, more bonds need to be broken before the complete separation of the specimen can occur, which would extend the whole failure evolution process and thus increases the simulated decohesion energy. However, the size-dependence of decohesion energy would diminish as the specimen size is decreased. Hence, the simulated data based on a smaller specimen could provide a more accurate estimation of the decohesion energy of W. Thus, the decohesion energy of W is chosen to be 0.835 N/m based on Simulation 4, as shown in For the bifurcation-based decohesion model defined by Eq. , U0, τnf, q and Cm are the only four model parameters to be determined. If the size-dependent strength of W is obtained by using Eq. , τnf can then be calculated based on Eq. through bifurcation analysis for a given failure mode. Since the reference surface energy U0 is defined as u¯0τ¯0 instead of 0.5(u¯0τ¯0), U0 is chosen to be 1.67 N/m because the simulated decohesion energy of tungsten is 0.835 N/m. If a linear decohesion–traction relation, namely, q
= 1 in Eq. , is assumed and Cm is determined through well-designed experiments, a multi-scale decohesion–traction model can then be established for W.Based on the proposed multi-scale simulation procedure, as shown in , a plane-strain problem for simulating the thin film delamination process is designed. The problem configuration is shown in . The demension of specimen is given as L
= 10 μm, ht
= 2.5 μm and hs
= 5 μm, respectively. The strength of tungsten is σp
≅ 2.3 GPa based on Eq. by considering the effect of the film thickness. The corresponding yield strength of W is assumed to be σy
≅ 1.53 GPa. Since the elastic modulus is size-independent, E
= 411 GPa is employed with Poisson’s ratio ν
= 0.28 and mass density ρ
= 15,000 kg/m3. Before the discontinuous bifurcation occurs, the associated von Mises elasto-plasticity model with a linear hardening/softening function is used for W. After bifurcation occurs, the discrete constitutive model is active with U0
= 1.67 N/m, q
= 1.0, and Cm
= 1.0, 10.0 and 0.1 for mixed mode, mode I and mode II failures, respectively. Since the yield strength of Si is much higher than the strength of W, decohesion is not active inside Si and no size effect is thus considered for Si. An elasto-perfectly-plastic von Mises model is employed for Si, with Young’s modulus E
= 107 GPa, Poisson’s ratio ν
= 0.42, mass density ρ
= 3200 kg/m3, and yield strength σy
= 8.0 GPa. A step compressive stress of 1.8 GPa is uniformly applied along both ends of tungsten film at the time t
= 0 to simulate the dynamic failure response.Note that the designed substrate thickness is chosen to be much smaller than that in the real film–substrate problem in order to save computational costs. To reduce the effect of stress wave reflection from the bottom boundary of the substrate on the film failure pattern, a silent boundary is applied along the bottom surface of the substrate (). The MPM is used to discretize the film–substrate problem. The computational grid consists of square cells with each side being 1 × 10−7
m long. Initially, one material point per cell is used to discretize both tungsten and silicon. As a result, the interfacial strength would be the average of tungsten and silicon strengths due to the inherent nature of the mapping procedure in the MPM (). To observe the deformation patterns clearly, the deformation fields are magnified by 10 times in both the x- and y-directions.The effect of failure modes on the deformation pattern of the film–substrate structure is investigated by setting Cm
= 10.0, 0.1 and 1.0, respectively, in the decohesion model for W film. present the failure patterns of the W–Si structure at the time t
= 2.88 μs with mode I failure, at the time t
= 1.92 μs with mode II failure, and at the time t
= 2.88 s with mixed mode failure, respectively. Since the film will be severely damaged at the time t
= 2.88 μs with mode II failure, only the deformation field of film–substrate structure at t
= 1.92 μs is shown for mode II failure. As can be seen from , the decohesion might initiate at the top film surface and evolve deeply into the film until reaching the film–substrate interface with mode I and mixed model failures. However, the complete delamination of the film might occur before the film decohesion reaches the film–substrate interface with mode II failure, as shown in . It appears that the decohesion evolves quicker and the damage is severer if mode II failure is dominant as compared with mode I and mixed mode failures. This might be due to the fact that the von Mises model predicts mode II failure that governs the initiation and evolution of decohesion after the discontinuous bifurcation is identified. Note that the use of a silent boundary along the bottom surface of the Si substrate effectively removes the stress wave reflection from the otherwise fixed boundary, and provides a better simulation of the film delamination process.In this paper, a multi-scale model-based simulation procedure for the film delamination process is proposed via a sequential approach. In the proposed procedure, a bifurcation-based decohesion model is first formulated within the framework of the MPM. A multi-scale decohesion–traction model for W is then established by using MD simulation of single crystal W block under tensile loading and available experimental data with a power scaling law to account for the size effect. The application to the model-based simulation of W film delamination from Si substrate demonstrates the potential of the proposed multi-scale simulation procedure.To calibrate the parameters of the bifurcation-based decohesion model, MD simulation of W block with crystal orientation of (x[1 0 0],
y[0 1 0],
z[0 0 1]) under tension is conducted by using the EAM potential. The effects of boundary condition, specimen size, number of vacancies, machine precision and strain rate on the stress–strain relation curves are investigated at the atomic level. It is found that shrinking of specimen cross sectional area and rearrangement of crystal structure will occur with the FS boundary being applied in either direction, while the evolution of the decohesion and the subsequent separation of W specimen would occur with the use of PBC in both the x- and y-directions. Investigations of the size effect on material properties for W demonstrate that the initial elastic modulus of W is insensitive to the specimen size. However, the peak stress increases as the specimen size decreases, which is mainly due to the fact that larger specimens offer more opportunities for dislocation to occur. The argument is further verified by MD simulation of single crystal W block with artificially introduced vacancies under tension, since the increase of vacancies in W block reduces the strength of W regardless of the distribution of the defects. It is also shown that the influence of machine precision on the stress–strain curve of W obtained from MD simulation is not significant as compared to other factors, and might therefore be neglected. The initial elastic modulus of W is rate-insensitive, while the peak stress increases with the strain rate.A multi-scale model for predicting W strength from atomic to continuum scales is formulated with the use of power scaling law. The model parameters are calibrated by combining the MD simulations of single crystal W block under tension and the macro-scale experimental results for W. By combining the multi-scale strength model and the decohesion energy obtained through the MD simulation, a multi-scale decohesion–traction model for W is developed. Simulation of W film delaminating from Si substrate with the proposed multi-scale decohesion model demonstrates that the decohesion evolves quicker and the damage is severer if mode II failure is dominant as compared with mode I failure and mixed mode failure. As can be seen from , blistering might also initiate at discrete nucleation sites, although it usually initiates in the neighborhood of the film’s edge and propagates towards the center of the specimen.Since the size effect on the strength of W film is considered and the decohesion energy is obtained via MD simulation, the multi-scale simulation of W film delamination from Si substrate could provide a better insight into the mechanisms of the film delamination process. However, the proposed multi-scale model for predicting W strength at different structural sizes is based on the MD simulation at the nano-scale and the experimental data for W at the macro-scale. Hence, an integrated experimental, analytical and numerical investigation on the structures with sizes ranging from nano to macroscales is required to verify the proposed multi-scale simulation procedure. Especially, well-designed experiments are needed to quantitatively explore the film delamination mechanisms at different scales.Isogeometric boundary element analysis for two-dimensional thermoelasticity with variable temperatureThis work is devoted to numerical analysis for two-dimensional thermoelasticity problems with temperature change by using the isogeometric boundary element method (IGABEM). The present IGABEM, which is highly attractive, possesses advantages of the isogeometric analysis with NURBS and boundary element method. We derive the theoretical formulations in terms of the IGABEM and apply it to thermal stress analysis. We examine the performance and accuracy of the proposed approach through numerical test cases which include steady-state uniform and non-uniform temperature change. The computed results are compared with the reference solutions which were derived from analytical or finite element methods. We also investigate the convergence of the present approach in modeling thermal stress problem.Many engineering structures operate under high temperature conditions such as gas turbines, diesel engines, and nuclear power plants. The existence of temperature field could significantly alter material properties of the structures or components and generate thermal stress as the temperature changes. The thermal stress plays a critical role that could lead to the damage of such structures. Investigation of the temperature field and thermal stress affecting the structures under heating has become an important topic in structural analysis.The theory of thermal stress has been well developed in the literature. Although some closed–form analytical solutions are available, advanced numerical methodologies are more effective in solving engineering problems with general geometries and/or boundary conditions. In the past several decades, many numerical methods have been introduced to deal with thermal stress problems, such as finite element method (FEM) The FEM has been widely used in various scientific and industrial communities. However, the existing gap between computer–aided design (CAD) and finite element analysis (FEA) is well-known as a critical issue, and generating computational model in general is time-consuming. In addition, element-based polynomial approximation used in the FEA induces the discretization errors, especially for complex structure. The recently developed isogeometric analysis (IGA) has become a powerful numerical approach, see e.g., In CAD, non-uniform rational B–splines (NURBS) describe the boundaries of structure only, so one of the crucial steps in the IGA is to generate solid analysis models based on boundaries, and at present it is still a difficult task in generating such solid analysis models, especially for complex structures. In contrast, only the boundaries of the domain are meshed in the BEM, it has resulted in a new combined approach between the IGA and BEM (called as IGABEM), and the key issue of creating solid analysis models required in the IGA is no-longer required. Simpson et al. The NURBS control points have been used as design variables for structural shape optimization problems. Therefore, the design model, optimization model, and analysis model can be uniformly described with the NURBS. In that sense, the optimized boundary in general is smooth. Hence, the IGABEM is highly suitable for structure shape optimization. Li and Qian Some major desirable features of the IGABEM can be summarized as follows: (a) it has the exact representation of geometries; (b) a traditional meshing process is avoided; (c) the high accuracy can be obtained because of the use of the NURBS basis; (d) the advantages of the IGA and BEM are possessed simultaneously; and (e) the volume parameterization is not required, which is one of the key issues in the isogeometric finite element method. In this paper, we further extend the IGABEM to solve thermal stress problems with varying temperature. We derive the formulations of IGABEM for thermoelasticity analysis with variable temperature, and present the main numerical implementation. Numerical results confirm high accuracy of the developed IGABEM for thermoelasticity. In addition, the computer codes are provided and that should be helpful for other researchersThe rest of the manuscript is structured as follows. briefly introduces the thermal stress problem. The formulation of IGABEM for thermal stress analysis is described in presents the main numerical implementation. In , several numerical examples are considered and the computed results are compared with the analytical solution or FEM solution. In , we discuss several major conclusions observed from the analysis.In absence of body forces, the equilibrium differential equation in elasticity can be written asAssumed the small deformation, the geometric equation is expressed aswhere εij is the strain tensor, ui is the displacement vector.The elasticity will expand (temperature rise) or shrink (temperature drop) when it is subjected to temperature change. Because of the restraint effect, the expansion or shrinkage will be hindered, and the thermal stress is produced. In thermoelasticity, the strain is composed with two parts, including the strain corresponding to the stress and the strain corresponding to the temperature change. For plane strain problems, the physical equation is expressed as where λ=Eμ(1+μ)(1−2μ) are G=E2(1+μ) are Lame constants, E is the Young's modulus, μ is the Poisson's ratio; α is the coefficient of thermal expansion, and T is the temperature change; δli is the Kronecker-delta function.Considering the steady-state temperature change problems, the temperature change T satisfies the Laplace equation, i.e.,The equilibrium differential equation for thermoelasticity problem can be described with displacements as follows For plane stress problems, the coefficients E, α and μ will be replaced with (1+2μ)E(1+μ)2, (1+μ)α1+2μ and μ1+μ, respectively.The boundary conditions are described as follows where u¯i and p¯i are the prescribed displacements and tractions on the Dirichlet (Γ1) and Neumann (Γ2) parts of boundary Γ (Γ = Γ1∪ Γ2, Γ1∩ Γ2 = ∅), respectively; nj is the outward unit normal vector on Γ, and σije is the stress tensor related to the displacements.NURBS basis functions have been used in the IGABEM as the shape functions for BEM discretization. A brief overview of NURBS basis function is described, and the details can be referred to Ref. In one-dimensional parametric space ξ ∈ [0, 1], a knot vector k(ξ) = {ξ1 = 0,…, ξi,…, ξn+p+1 = 1}T is a set of non-decreasing numbers that are between zero and one, where i is the knot index, ξi is the ith knot, n is the number of basis functions, and p is the order of the polynomial. NURBS basis function Ri,p(ξ) is constructed by a weighted average of the B-spline basis functions where wi is the ith weight, and 0 < wi ≤ 1; Ni,p(ξ) is the ith B-spline basis function of degree p, and is defined recursively as follows Ni,p(ξ)=ξ−ξiξi+p−ξiNi,p−1(ξ)+ξi+p+1−ξξi+p+1−ξi+1Ni+1,p−1(ξ)p≥1According to the NURBS basis functions and the corresponding control points, the NURBS curve can be expressed aswhere Bi is the coordinate of control point. yield the weak-form of thermoelasticity problem as follows:∫∫Ωσij,juidΩ+∫Γ1(ui−u¯i)pidΓ−∫Γ2(pi−p¯i)uidΓ=0where ui and pi* are the weight functions.Applying the Green's formula, the first domain integral in ∫∫Ωσij,juidΩ=∫ΓσijuinjdΓ−∫∫Ωσijui,jdΩ can be rewritten in the following form: into the right domain integral term in ∫∫Ωσijui,jdΩ=∫∫Ω(Aijmnum,n−Eα1−2μTδij)ui,jdΩ=∫∫Ω(Aijmnumui,j),ndΩ−∫∫ΩAijmnumui,jndΩ−∫∫ΩEα1−2μTui,idΩ=∫ΓAijmnumui,jnndΓ−∫∫Ω(Aijmnumui,jn+Eα1−2μTui,i)dΩwhere Aijmnui,j=σmn, Aijmnui,jnn=pm, Aijmnui,jn=σmn,n., the weak-form equation can be written as∫∫Ω(σij,jui+Eα1−2μTui,i)dΩ+∫Γ1piuidΓ+∫Γ2p¯iuidΓ=∫Γ1u¯ipidΓ+∫Γ2uipidΓThe selected fundamental solution ui should satisfy where Δ is the Dirac delta function, x′ and x are the boundary source point and the field point, respectively.The fundamental solutions are selected as the weight functions. ui* and pi* are rewritten as uli* and pli, which are called Kelvin solutions ∫Γuk(x)plk(x′,x)dΓ=∫Γpk(x)ulk(x′,x)dΓ+∫∫ΩEαT(x)1−2μulk,k(x′,x)dΩIn order to obtain the boundary integral equation, it is necessary to move source point x′ to the boundary. Using the boundary extension method, the boundary integral equation of thermoelasticity is obtained Clk(x′)uk(x′)+∫Γuk(x)plk(x′,x)dΓ=∫Γpk(x)ulk(x′,x)dΓ+∫∫ΩEαT(x)1−2μulk,k(x′,x)dΩwhere Clk(x′) is only related to the geometric shape of the boundary of the source point, and its expression isClk(x′)={δlkx′∈Ω12δlkx′∈Γ(smoothboundarypoint)δlk+limε→0∫ΓεplkdΓx′∈Γ(unsmoothboundarypoint) is the domain integral term with respect to temperature. Since the steady-state temperature change satisfies the Laplace equation, i.e., , the domain integral term can be converted into the boundary integral form, thus avoids the body parameterization to calculate the domain integral.The displacement fundamental solution ulk* can be expressed as ulk(x′,x)=Glk,jj(x′,x)−12(1−μ)Glj,jk(x′,x)ulk(x′,x)=18πG(1−μ){[(3−4μ)ln1r−7−8μ2]δlk+r,lr,k}The fundamental solution of surface force corresponding to the displacement fundamental solution is plk(x′,x)=−14π(1−μ)r{∂r∂n[(1−2μ)δlk+2r,lr,k]−(1−2μ)(r,lnk−r,knl)}Bk(x′)=Eα1−2μ∫ΩT(x)ulk,k(x′,x)dΩ=Eα2(1−μ)∫Γ(Gki,ij(x′,x)T(x)−Gki,i(x′,x)T,j(x))njdΓ=∫Γfk(x′,x)T(x)dΓ−∫ΓT,j(x)njgk(x′,x)dΓfk(x′,x)=α(1+μ)4π(1−μ)[(ln1r−12)nk−r,kr,lnl], the boundary integral equation of thermoelasticity under steady-state temperature change can be written as follows:Clk(x′)uk(x′)=∫Γpk(x)ulk(x′,x)dΓ−∫Γuk(x)plk(x′,x)dΓ+∫Γfk(x′,x)T(x)dΓ−∫ΓT,j(x)njgk(x′,x)dΓ that only boundary integrals are required and that fits well the BEM framework.Consider the local support property of the NURBS basis functions, the displacement, stress, temperature, and heat flux on the boundary are written as follows:where uki, pki, Ti and T,ni are the displacement, surface force, temperature, and heat flux density coefficients corresponding to ith control point, respectively.In order to obtain the discrete boundary integral equation, the boundary is discretized into Ne non-overlapping elements, i.e.The displacement, surface force, temperature and heat flux on the boundary are discretized and interpolated. The discretized boundary integral equation can be written as follows:Clk(x′)∑i=1p+1Ri,pe′(ξ^′)uke′i=∑e=1Ne∑i=1p+1[∫−11ulk(x′,x(ξ^))Ri,pe(ξ^)Je(ξ^)dξ^]pkei−∑e=1Ne∑i=1p+1[∫−11plk(x′,x(ξ^))Ri,pe(ξ^)Je(ξ^)dξ^]ukei+∑e=1Ne∑i=1p+1[∫−11fk(x′,x(ξ^))Ri,pe(ξ^)Je(ξ^)dξ^]Tei−∑e=1Ne∑i=1p+1[∫−11gk(x′,x(ξ^))Ri,pe(ξ^)Je(ξ^)dξ^]T,neiwhere ξ^∈[−1,1] is the local coordinate; e′ represents the element number where the source point x′ is located; i is the nodal number of each element; ξ^′ is the local coordinate of the collocation point; Je(ξ^) is the Jacobian of transformation, defined as Je(ξ^)=∂Γ∂ξ∂ξ∂ξ^=(dxdξ)2+(dydξ)2·ξ2−ξ12, where ξ1 and ξ2 represent the values of the both ends of the element in the parameter space; ukei, pkei, Tei and T,nei are displacement, surface force, temperature and heat flux density at local node i on element e, respectively.It should be noticed that the nodal points in the IGABEM, which are referred to as control points, may not be situated on the boundary. According to Ref.with B representing a temperature-related term.Since Tei and T,nei can be obtained from the steady-state temperature field problem, B is a known term. By matrix transformation, All the unknown values on the boundary will be obtained by solving The term including 1r or ln1r exists in the integral of fundamental solution, so singularity will occur when H and G matrices are generated. There are three types of integration format in IGABEM: when source point x′ is outside the integral element and the distance is long, it belongs to the conventional integral and is calculated by Gauss integral; when source point x′ is outside the integral element but very close to it, it belongs to the nearly singular integral. In this study, the nearly singular integral is not considered and calculated with the Gauss integral; when source point is situated in the integral element, it belongs to the singular integral and the conventional Gauss integral can not be calculated accurately.Because of the different integral terms involved, singular integrals can be divided into weakly and strongly singular integrals. For the fundamental solution q, there exists term 1r, and the integral where it resides is called as strongly singular integral; for fundamental solution T, there exists term ln1r, and the integral where it resides is known as weakly singular integral. In this work, the strongly singular integrals are evaluated by subtraction of singularity scheme When the source point is in the domain, the displacement boundary integral equation is expressed asuk(x′)=∫Γpk(x)ulk(x′,x)dΓ−∫Γuk(x)plk(x′,x)dΓ+∫Γfk(x′,x)T(x)dΓ−∫ΓT,j(x)njgk(x′,x)dΓ, the boundary integral expression of stress at the interior point is obtained as follows σij=∫ΓDkijpkdΓ−∫ΓSkijukdΓ+∫ΓFijTdΓ−∫ΓGij∂T∂ndΓ−EαT1−2μδijσij(x′)=∑e=1Ne∑i=1p+1[∫−11Dkij(x′,x(ξ^))Ri,pe(ξ^)Je(ξ^)dξ^]pkei−∑e=1Ne∑i=1p+1[∫−11Skij(x′,x(ξ^))Ri,pe(ξ^)Je(ξ^)dξ^]ukei+∑e=1Ne∑i=1p+1[∫−11Fij(x′,x(ξ^))Ri,pe(ξ^)Je(ξ^)dξ^]Tei−∑e=1Ne∑i=1p+1[∫−11Gij(x′,x(ξ^))Ri,pe(ξ^)Je(ξ^)dξ^]T,nei−EαT(x′)1−2μδijwhere the coefficients Dkij, Skij, Fij and Gij* can be calculated by the following formula:Dkij=14π(1−μ)r[(1−2μ)(r,iδjk+r,jδik−r,kδij)+2r,ir,jr,k]Skij=G2(1−μ)πr2{2∂r∂n[(1−2μ)r,kδij+μ(r,iδjk+r,jδik)−4r,ir,jr,k]+2μ(r,ir,knj+r,jr,jni)+(1−2μ)(2r,ir,jnk+njδik+niδjk)−(1−4μ)nkδij}Fij=αE4π(1−μ)r[∂r∂n(δij1−2μ−2r,ir,j)+r,inj+r,jni]Gij=αE4π(1−μ)[r,ir,j+δij1−2μ(2μ+12−ln1r)]The stresses at the boundary point, as shown in , are computed. Here, p1 and p2 are the surface force components in x and y directions, respectively, while s and n stand for the tangential axis and normal axis of point A. We denote α as the angle between normal axis n and p1. The normal stress σn and shear stress τs at any point on the boundary are computed as follows σs=11−μ[2G(−∂u1∂ssinα+∂u2∂scosα)+μ(p1cosα+p2sinα)]−EαT1−μFor the sake of completeness, major steps for the numerical solution implementation using the IGABEM based on NURBS for the thermoelasticity problems are summarized as follows:Read the CAD data files such as knot vector, control point coordinates, weight coefficients.Read the material coefficients, boundary conditions. The boundary conditions include the boundary conditions of temperature field and elasticity.Generate mesh of model and collocation points.Cyclic selection of collocation points and integration elements.If the collocation point is situated in the integral element, it is singular integral. The strongly singular integral and the weakly singular integral are solved by the singular substraction technique and coordinate transformation method, respectively.If the collocation point is outside the integral element, the Gauss integral is used for the conventional integral.Add the generated unit submatrix to the global matrix to form H and G matrix.Apply boundary condition information of temperature field and calculate solution.Apply thermoelastic boundary condition information, including variable temperature, heat flux, displacement and surface force.Calculate all the unknown displacements and forces on the boundary.Calculate stresses in the interior region and on the boundary.In order to demonstrate the accuracy and performance of the present method for thermoelasticity problems, several 2D steady-state variable temperature problems are considered. In all examples, quadratic order NURBS basis functions are used and 10 Gaussian quadrature points are adopted for the integration of each element The first numerical example deals with a uniform temperature change problem as shown in . Because of the heat flux ∂T∂n=0, only the temperature change integral term needs to be considered.Consider a simply supported square plate with width 2 m as depicted in . The material parameters of the plate are taken as follows: the Young's modulus E = 210 GPa, the Passion's ratio μ = 0.3, and thermal expansion coefficient α=1.2×10−5mm/(mm·oC). It is assumed that the temperature in the domain uniformly raises 1The initial knot vector for generating square plate is k={0,0,0,1/4,1/4,1/2,1/2,3/4,3/4,1,1,1}, the corresponding weight coefficient vector is w = {1, 1, 1, 1, 1, 1, 1, 1}. Five refinements (i.e., each edge is refined into 5 elements) are used. The refined control points, collocation points and NURBS basis functions are shown in According to the plane stress problem and the plane strain problem, the solutions are obtained respectively. The calculated results by the present formulation are compared with the analytical solution . In this problem, σx = σy, the results of the IGABEM are consistent with the reference solution.The same problem is again considered, but its boundary conditions have now been changed to simply supported boundaries at two edges as sketched in . The other conditions of the problem remain the same. The plane stress is used to solve the problem, and the analytical solution of normal stress in the y direction σy is −2.52 × 106 Pa presents the computed values of the stress component in y direction at y = 0m and the relative errors. All the relative errors are less than 1%, which indicate that the present IGABEM offers results with high accuracy.Consider an annulus with outer radius Re = 2 m and inner radius Ri = 1 m. The initial temperature is 0°C at inner boundary and the outer boundary remains 0a. Because of the symmetry of the problem, a quarter of the annulus is used to calculate the problem, and the symmetry boundary is considered as adiabatic boundary, as depicted in b. The material parameters are as follows: the Young's modulus E = 210 GPa, the Poision's ratioμ = 0.3, and the thermal expansion coefficientα=1.2×10−5mm/(mm·oC). The plane strain problem is assumed, and the analytical solution of the circumferential stress is σθ=αETi2(1−ν)[ln(re)−ln(ri)][1−ln(rer)−ri2re2−ri2(1+re2r2)ln(reri)]The initial knot vector used to construct a quarter annulus is k={0,0,0,1/4,1/4,1/2,1/2,3/4,3/4,1,1,1}, the weights are w={1,1/2,1,1,1,1/2,1,1,1}. The initial control points, collocation points, elements and NURBS basis functions are shown in . Again in this example, 5 refinements are used for the analysis. shows the comparison of circumferential stresses calculate by the developed IGABEM and the analytical solution on the symmetrical boundary (y = 0 m). It is obvious that the IGABEM results are in good agreement with the analytical solutions [ represents the L2 relative error convergence curve of the circumferential stress on the symmetrical boundary. shows the deformed configuration after thermal expansion reaches steady state. Because the temperature rises in the domain, the whole body shows the phenomenon of outward expansion. visualizes the circumferential stress contour, the results obtained by IGABEM match well with the analytical solution This example studies a more general thermal stress problem of non-uniform temperature change. The geometry, loading and constraints of the . The initial temperature of the structure is 0°C, the Dirichlet boundary condition with T = 10 oC is applied on the upper boundary (y = 10 m), and T = −10 oC on the lower boundary (y = 6 m). The material parameters are as follows: the Young's modulus E = 200 GPa, the Poisson's ratio μ = 0.3 and the thermal expansion coefficient α=1.2×10−5mm/(mm·oC). The plane stress problem is assumed. Due to lack of analytical solutions, the IGABEM results are thus compared with a reference result which is derived from FEM using ANSYS.The initial knot vector used to construct the geometry isk={0,0,0,1/6,1/6,1/3,1/3,1/2,1/2,2/3,2/3,5/6,5/6,1,1,1}, and weights are w = {1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1}. Each edge is refined into 5 elements. The refined control points, collocation points, elements and NURBS basis functions are shown in , whereas the FEM mesh is represented in shows a comparison of deformed configuration between the developed IGABEM and the FEM using ANSYS. The compared result reveals that the curve by the present IGABEM matches well with that by the FEM, almost completely. represents the comparison of σx contour, which exhibits the feasibility and accuracy of the developed method in solving the stress on boundary and inner points. For this specific problem, stress concentration should take place at the corner, and this phenomenon of the stress concentration, as shown, is well captured and reproduced by the developed IGABEM. From the stress contour, the stress varies sharply at the right boundary (x = 12 m), therefore the comparison results on this boundary are given in . The stress values calculated by the IGABEM are in good agreement with those calculated by the FEM. The obtained results in this example show that the present IGABEM can be an effective approach to be used to solve the structure with steady-state variable temperature and external tractions.Next, the convergence of the stresses at the corner point is investigated. From , it is found that absolute value of the stress σy at the corner point x = 4 and y = 6 increases with increasing the number of elements at each edge. The stress concentration takes place at the corner, so increasing the number of elements leads to the magnitude of stresses, it accords with the phenomenon of the stress concentration.The last example deals with the thermal stress problem of a complex structure with non-uniform temperature change, showing the applicability of the present approach in modeling problems with complicated configuration. The initial temperature is 0 oC. A temperature 300 oC is applied at left outer boundary and the right outer boundary remains 100. The material parameters are as follows: the Young's modulus E = 200 GPa, the Poisson's ratio μ = 0.3 and the thermal expansion coefficientα=1.2×10−5mm/(mm·oC). The plane stress problem is assumed. represents the control points, collocation points and NURBS basis function of the initial geometric boundaries. In order to enhance the accuracy of the solution, the original elements are refined into 10 new elements, which are shown in . The deformed configuration and von Mises stress distributions obtained with the present IGABEM are plotted in . As expected, relatively large stresses are generated near the support.In this contribution, we have addressed further developments of the hybrid isogeometric analysis-boundary element method (IGABEM), which takes benefits of both the IGA and the BEM, for modeling 2D steady-state uniform and non-uniform variable temperature problems. The NURBS basis functions are employed as shape functions for both geometric description and field approximation. Major desirable features of the IGABEAM lie in the exact representation of geometries, without a meshing process, high accuracy, and avoiding the discretization of the interior domain. Four thermoelasticity examples have been analyzed using the present method. The computed numerical results are compared with analytical solutions or the FEM solutions. Through our numerical experiments, it has been shown that the present IGEBEM offers remarkable results.In addition, the computer codes of the IGABEM developed for two-dimensional thermoelasticity with variable temperature can be accessed via Shear behavior of full-scale reinforced concrete T-beams strengthened with CFRP strips and anchorsNine tests were conducted on 1220 mm deep T-beams strengthened in shear using Carbon Fiber-Reinforced Polymer (CFRP) strips and CFRP anchors. The use of anchors resulted in most CFRP strips reaching fracture, but not simultaneously. The shear contribution of FRP was larger in beams with less transverse steel reinforcement. Because CFRP and steel reinforcement have different material and bond properties, interactions between the two materials need to be taken into account when determining the shear capacity of a strengthened member.Carbon Fiber-Reinforced Polymers (CFRPs) can be quickly applied in retrofit or repair applications, with a minimum of functional disruption and with virtually no change in the geometry of structural elements. Many studies have been conducted on the application of externally bonded FRP in strengthening reinforced concrete bridge members (NCHRP report 655 Although there have been numerous experimental studies on shear strengthening using FRP materials, relatively few included mechanical anchorage of external FRP to concrete members, and even fewer used CFRP anchors (e.g., Nine tests were conducted on 1220 mm deep T-beams strengthened in shear using externally applied CFRP strips and CFRP anchors. Beam depth and overall dimensions were selected to represent full-scale bridge sections. The specimens tested constitute the largest reinforced concrete beams strengthened in shear using CFRP strips anchored with CFRP anchors tested to date. The tests were further designed to investigate the effects of the following key variables on the efficiency of CFRP shear strengthening: (1) the amount and spacing of steel stirrups; (2) the amount, layout, and inclinations of CFRP strips; and (3) the layout of CFRP anchors.T-beams with an overall depth of 1220 mm were tested with a shear-span to depth (a/d) ratio of 3.0. The a/d ratio was selected based on findings of a previous study , the cross-section of the 1220 mm beams used in this study is shown. Two stirrup spacings were considered to evaluate the effects of the transverse reinforcement ratio. Stirrups were 10 mm diameter bars spaced at either 457 or 254 mm on center. The flexural strength of test specimens was designed to exceed the expected shear strength. Skin reinforcement was also provided on the side of the beams in the flexural–tension region.Measured concrete compressive strength at time of testing was approximately 27 MPa. Transverse steel was ASTM Grade 60 with a measured yield stress of 476 MPa. The manufacturer specified thickness of CFRP laminates was 0.28 mm. Ultimate stress and strain of the CFRP laminate used in this study were 1062 MPa and 0.0105 respectively based on manufacturer’s specifications. The specified modulus of elasticity of CFRP laminates (Ef) was 102,000 MPa. Although the rupture stress of the CFRP laminates is much higher than the yield stress of the steel, the elastic stiffness of CFRP was roughly half that of steel, which implies that large strains must be developed in order to effectively utilize the full capacity of the CFRP materials when anchors are provided. In addition, CFRP is a brittle material for which stress is linearly proportional to strain up to fracture. Effective (average) CFRP strains across the critical shear crack are therefore needed to estimate the contribution of CFRP to shear strength., typical details of the CFRP strips and CFRP anchors used in this experimental study are shown. The design of CFRP anchors was based on previous studies and recommendations by Kobayashi et al. For most tests, two CFRP anchors were installed for each 254 mm wide CFRP strip. Orton et al. , in which tests are divided into two series depending on their transverse reinforcement ratio. Tests with 10 mm diameter stirrups spaced at 457 mm are labeled “L(ow)”, while tests with 10 mm diameter stirrups spaced at 254 mm are labeled “H(igh)”. In each test name, the designation “C” is for control tests with no CFRP strengthening. The variables associated with strengthening are shown in bold letters in . The layout of CFRP strips was 254 mm wide at 508 mm on center except L-S-W and H-S-2. The shear contributions of each material were estimated based on shear design provisions of ACI 440.2R Except for test L-S-I, all CFRP strips were oriented vertically along web sides. In test L-S-I, inclined CFRP strips were applied on each side of the web and the ends overlapped on the bottom of the beam. The shear strength of both L-S-W and L-S-I were designed to be identical based on the shear-strength provisions in ACI 440.2R. It is noted that the length of CFRP strips was larger in test L-S-I than in other tests due to the 45 degrees inclination from vertical of the CFRP strips. In test L-S-W, the width of CFRP strips was wider by 41% but shorter by 41% than in test L-S-I. Consequently, the same amount of CFRP material was applied in tests L-S-W and L-S-I. After test H-C, cracks in the specimen were injected with epoxy and U-shaped CFRP strips and anchors were applied. The repaired specimen was labeled H-S-R. In test H-S-M, the effective length of the CFRP strips was reduced by installing intermediate anchors at the mid-height of CFRP strips. In test H-S-2, two layers of CFRP were used to evaluate the effect of the amount of CFRP material., two tests were conducted on each beam specimen. An external clamping system consisting of pre-stressing rods was used to increase the shear capacity of the span not being tested. Elastomeric bearing pads were used at supports to minimize horizontal restraint at the reactions.Specimen deflections were monitored by linear voltage displacement transducers (LVDTs) placed at the reaction points and under the loading point. Shear strain was calculated using Mohr’s circle from deformations measured by LVDTs arranged in a triangular formation. As shown in , six LVDTs were used to provide redundancy and improve shear–strain measurements. Further information can be found in Kim Internal strain gages were mounted on stirrups and longitudinal bars. Most gages were placed on one side of test specimens with a few redundant gages placed on the opposite side to provide a symmetry check. Most of the strain gages on steel stirrups were placed where the critical inclined crack was expected to occur. Multiple gages were mounted on certain stirrup legs to maximize the chance of intersecting the critical crack. The spacing between two adjacent gages on a stirrup leg was 152 mm. Gages were also placed on the longitudinal steel to monitor flexural response of beams. Several gages were mounted on the surface of CFRP strips. Multiple gages were mounted across the width and length of CFRP strips as the CFRP strain distribution was expected to vary along both directions.Several significant observations described below are helpful in evaluating the test results.As flexural deformations tend to govern beam deflections and all specimens contained the same amount of flexural reinforcement, there was little variation between tests in the deflection versus applied load responses (a). However, there were large differences in the shear strain responses as shown in b. Curves are not labeled since the intent of the two figures is to illustrate that beam deflections were not sufficient to describe the behavior of the beams. Consequently, shear strain was determined to be more appropriate for comparing shear responses of the tests.In tests L-S, L-S-I, H-S-R, the LVDT arrangement for determining shear strains did not intersect the critical shear crack (). In such cases, the shear strain is under-estimated after the critical shear crack forms and will not provide an accurate indication of the test response.The critical shear-crack angle governs the number of steel stirrups and CFRP strips contributing to shear strength and is essential for determining beam shear-strength. Conventional shear design equations are based on an assumed 45 degrees crack angle. However, as shown in , the critical angle (measured from horizontal) decreased as the applied load increased, and was generally less than 45 degrees at failure. As a result, more steel stirrups or CFRP strips contributed to shear strength as can be seen in b. The change in crack angle helps to explain the higher-than-estimated shear strengths., the strains between gages along the same stirrup leg were quite different depending on relative distance from cracks. Once cracks formed, the tensile strain of the gages located at those cracks (D2 and D3 in ) increased abruptly, but gages away from the cracks (D1) showed little change in strain until debonding between the steel and concrete spread along the stirrup., CFRP strain responses were different not only along the direction of fibers, but also across the width of strips. The strains at FD1 and FD2.2 increased abruptly at a shear of 445 kN and the strain at FD3 increased suddenly at 712 kN. At 890 kN, the strains of FD2 and FD2.1 increased so that all of the strains were similar. A crack formed near gages at FD1 and FD2.2 initially followed by another crack near FD3. At 890 kN, the CFRP strip debonded from the concrete surface and all strains were nearly the same.Several observations can be made based on trends observed in . As the applied load increased, crack patterns, reinforcement strains, and the flow of shear forces across a beam section changed. For shear contribution of steel, the strain value from gages indicates yielding, and once yielding occurs, the stresses do not change appreciably. However, the shear contribution of a CFRP strip depends on the strain value until fracture occurs. Furthermore, there was no compatibility between the strains in steel stirrups and CFRP strips at the same location, even though the same crack passed through both materials, because the debonded length of each material was different. Therefore, the interaction between steel and CFRP is difficult to evaluate.. Because estimates based on the ACI 440.2R design equations are generally conservative, the measured ultimate strengths were greater than design values. CFRP strips ruptured in all tests except for test H-S-2, which was strengthened with two layers of CFRP and had CFRP anchor failures. In order to test both shear spans of a specimen, the first test conducted on a specimen was stopped at a load near ultimate strength. Tests were stopped when all stirrups crossing the critical shear crack reached yield or the maximum measured CFRP strain reached the specified fracture strain of the material.Test L-C was a control test that provided the shear strength of the specimen without CFRP strengthening. Loading was stopped at a shear of 654 kN to avoid damage that would prevent testing the other span of the beam. At that load, the maximum crack width was about 4.8 mm. Maximum strain in the stirrups was 0.009 and all stirrups crossing the critical crack yielded as shown in . Although the estimated nominal shear strength of L-C was 481 kN, measured shear strength of test L-C was 36% greater than estimated. For this reason, the control test represented the member shear strength before strengthening.Test L-S had 254 mm wide CFRP strips spaced at 508 mm on center with the same steel stirrup layout as test L-C. Loss of bond between the CFRP strips and concrete started at strip A at a shear of about 668 kN. As debonding spread along the strip, the tensile force in the strip was transferred to the anchors. After reaching the maximum shear strength of 1006 kN, shear decreased to 992 kN when the explosive rupture of several CFRP strips triggered shear failure (). Strip B ruptured first causing the applied shear to drop to 930 kN and then strips C and D ruptured violently. As shown in , one steel stirrup fractured after the CFRP strips ruptured.Stirrup fracture was not reported in the 610 mm deep beams tested in the previous study , indicates that CFRP strengthening increased beam shear strength by about 50%. Similar gains in shear strength were observed in the study on 610 mm deep beams. The effects of transverse steel ratios can be observed by comparing the behaviors of tests H-S and H-C with those of tests L-S and L-C. In , the difference in shear strength between strengthened (-S) and un-strengthened specimens (-C) is highlighted for beams with low (L) and high (H) transverse steel ratios.Both beam types were strengthened using the same CFRP layout. Although tests H-S and H-C were stopped before reaching ultimate strength, it was observed that the increase in shear strength generated by CFRP was substantially greater for beams with the lower transverse steel ratio. Because CFRP strips act similarly to steel stirrups in a truss mechanism, the shear force is shared between the two materials in proportion to the effective stiffness of each material. As a result, the shear strength increase due to the CFRP is expected to be greater in beams with lower transverse steel ratios. It is noteworthy that the critical crack angle was steeper in beams with more transverse reinforcement. Consequently, fewer CFRP strips and steel stirrups intersected the critical shear crack and the effectiveness of the CFRP strips in those beams was reduced as the transverse reinforcement ratio increased.Comparing the estimated and measured strengths of L-S and L-S-W (), an increase of about 110 kN was expected with a 40% increase in strip width from 254 to 356 mm. However, the measured increase in shear strength of L-S-W from L-S was about half of the expected increase or 58 kN. These comparisons indicate that the increase in shear strength is not the same proportionally as the increase in CFRP material.The performance of an inclined layout of CFRP strips was evaluated through tests L-S, L-S-I, and L-S-W. A CFRP strip that is perpendicular to inclined cracks is more efficient at resisting shear forces than one that is oriented perpendicular to a member’s axis. Moreover, more inclined strips intercept a critical shear crack than vertical strips spaced at the same horizontal spacing. Therefore, even though strips in test L-S-I were 10 in. wide and strips in test L-S-W were 14 in. wide, the tests had the same calculated shear strength () and the same surface area of CFRP installed. The inclined strips on L-S-I were longer than the vertical strips on L-S-W, which compensated for the difference in width to produce equal CFRP surface areas.In test L-S-I, the ultimate shear strength of 1050 kN was reached when part of strip B ruptured (). No anchor failure was observed. Yielding of the stirrups was noted at 617 kN. After partial rupture of several strips, the applied shear dropped to 859 kN and then 828 kN. Eventually strips B, C, D, and E ruptured violently and the beam lost nearly all shear strength. Fracture of steel stirrups was also observed when the specimen failed. In test L-S-I, ultimate shear strength was 27 kN lower than the recorded shear strength in L-S-W. The performance of L-S-I and L-S-W was nearly identical, as seen in . However, vertical strips were easier to install and are more practical for field installations.To conduct test H-S-R, the cracks in test H-C were epoxy-injected and the beam was strengthened with CFRP strips having the same layout as test H-S. The maximum applied shear force of H-S-R was 1455 kN; a value much greater than the ultimate shear applied to specimen H-S. In test H-S-R flexural yielding occurred with strains in the bottom layer of flexural steel reaching 0.0073. Shortly after the peak load was reached, the explosive rupture of CFRP strips occurred at a shear of 1304 kN. The shear stiffness of H-S-R shown in was much greater than that of H-S, but is not an accurate indication of the shear deformation because the critical crack occurred outside of the region monitored by LVDTs.Test H-S-M was identical to test H-S except for the use of intermediate anchors at mid web-depth to anchor CFRP strips. As shown in , the fans of the intermediate anchors were spread vertically in both directions. Although intermediate anchors were expected to increase the stiffness of individual CFRP strips by decreasing their debonded length (distance between anchors), the shear stiffness observed in tests H-S and H-S-M was not much different as shown in Test H-S-2 was conducted with two layers of CFRP sheets in each strip to evaluate the effect of the amount of CFRP material. The maximum shear in test H-S-2 was 1135 kN and it was sustained as beam deflection and shear strains increased. As shown in , shear strength was only 58 kN higher than H-S, which had one layer of CFRP in each strip. The failure was triggered by the fracture of several anchors as shown in . The CFRP strips did not rupture. The maximum recorded strain in the CFRP strips was 0.0048 at ultimate shear (point A in ) and was 0.0079 at fracture of CFRP anchors (point B in In test H-S-2, the amount of CFRP in the strips and anchors were twice those of test H-S. For design, the anchors should be stronger than the strip being anchored. Results of H-S-2 indicate that a larger-than-proportional increase in CFRP anchor material is needed for a given increase in CFRP strip strength.Nine full-scale T-beams were tested to evaluate the effectiveness of U-wrapped CFRP strips and CFRP anchors in shear strengthening of reinforced concrete beams. Observations and conclusions from these tests are as follows:CFRP anchors developed the full strength of the CFRP strips in all tests except where two layers of CFRP material were used for each strip. CFRP anchors increased the useable strain in CFRP strips from what could be achieved through bond between CFRP and concrete alone. CFRP anchors were therefore able to maximize the shear strength contribution of CFRP strips.At ultimate shear capacity, which typically occurs at fracture of the first CFRP strip, strains in neighboring CFRP strips were significantly lower than the fracture strain. An effective strain in the strips crossing the critical shear crack was about 1/2 of the fracture strain of the CFRP.The contribution of CFRP strips to shear strength was greater in beams with a lower transverse steel ratio. Interactions between steel and CFRP shear reinforcement were evident in the test results.For the same surface area of CFRP material, there is no significant strength benefit derived from inclining CFRP strips from the normal to a member’s axis.Although the area of CFRP anchors was doubled when doubling the CFRP material in strips, the strength of the strips was not developed. A larger-than-proportional increase in CFRP anchor material is needed for a given increase in CFRP strip strength.Analysis of seabed instability using element free Galerkin methodWave-induced seabed instability, either momentary liquefaction or shear failure, is an important topic in ocean and coastal engineering. Many factors, such as seabed properties and wave parameters, affect the seabed instability. A non-dimensional parameter is proposed in this paper to evaluate the occurrence of momentary liquefaction. This parameter includes the properties of the soil and the wave. The determination of the wave-induced liquefaction depth is also suggested based on this non-dimensional parameter. As an example, a two-dimensional seabed with finite thickness is numerically treated with the EFGM meshless method developed early for wave-induced seabed responses. Parametric study is carried out to investigate the effect of wavelength, compressibility of pore fluid, permeability and stiffness of porous media, and variable stiffness with depth on the seabed response with three criteria for liquefaction. It is found that this non-dimensional parameter is a good index for identifying the momentary liquefaction qualitatively, and the criterion of liquefaction with seepage force can be used to predict the deepest liquefaction depth.In recent years, wave-induced seabed responses have engrossed growing interests not only in coastal engineering but also in geotechnical engineering. This is because seabed instability may have caused the damage and destruction of some coastal and offshore installations, such as breakwaters, piers, pipelines and so on (). Two types of seabed instability may occur in a sandy seabed: momentary liquefaction and shear failure. Wave-induced momentary liquefaction was reported in laboratory tests () also revealed the potential of momentary liquefaction. If momentary liquefaction occurs routinely in shallow waters, serious stability problems have to be confronted for the structures laid on a cohesionless seabed. Because momentary liquefaction and shear failure are directly related to the excess pore pressure and effective stresses within seabed sediments, prediction of seabed responses and evaluation of seabed instability have become important issues in coastal and ocean engineering.Liquefaction and shear failure are produced by different mechanisms (). The liquefaction is a state that effective stress in any direction becomes zero. For example, quick sand or boiling is closely related to vertical seepage flow. When water wave propagates over a seabed, the fluctuation of water pressure exerts on the seabed surface, causing pore fluid in the seabed to flow out or into and producing frictional force on soil skeletons (this frictional force is called as seepage force). The wave train generates the fluctuation of pore water pressure, and thus the transient fluctuation of effective stress in soil masses. If the effective stress momentarily becomes zero, soil skeleton loses its structural strength and the seabed becomes momentarily liquefied. In addition, shear stresses in a seabed may be big enough to overcome its shear resistance, resulting in another type of seabed instability, shear failure. A shear failure refers to a state that stress level reaches to shear failure envelope which is usually described by Mohr–Coulomb criterion.Wave-induced seabed response can be evaluated by Biot consolidation theory (). Analytical and numerical methods have been employed to solve the Biot consolidation equation. Analytical solutions are usually available for those problems with simple boundary conditions. For example, investigated a hydraulically anisotropic and partially saturated seabed, whilst studied an isotropic seabed with infinite thickness. used the compatibility equation under elastic conditions and reduced the sixth-order governing equation of fourth-order differential linear equation. developed a semi-analytical solution for a non-homogeneous layered porous seabed. Later, further extended the framework to a finite-thickness seabed as well as a layered seabed (Several numerical algorithms were proposed to accumulate complex geometry and physical conditions. For example, developed a semi-analytical one-dimensional finite element model to simulate the wave-induced stresses and pore water pressure. This method was later extended to 2D and 3D wave-seabed interaction problems ( developed a simplified finite element model for an isotropic and saturated permeable seabed. Recently, a meshless EFGM model was developed for the analysis of transient wave-induced soil responses (). In order to improve the computation efficiency, a radial PIM method () was extended for wave-induced seabed responses by introducing repeatability conditions (). This radial PIM considers not only sinusoidal waves but also other nonlinear waves such as solitary wave. These numerical meshless methods provide a useful tool for further analysis of seabed instability.Seabed instability is a complicated topic in marine geotechnics (). Past studies have revealed that both soil characteristics and wave properties play a dominant role in the wave-induced seabed responses (). Some parameters are proposed to assess the potential of momentary liquefaction. For example, proposed two parameters to justify the occurrence of liquefaction based on a boundary layer theory (). They concluded that the maximum depth of liquefaction is about half the wave height for surf conditions. However, no single parameter is available to evaluate the momentary liquefaction. Furthermore, the parameters so far are obtained for a homogeneous porous seabed. Is it suitable for a non-homogeneous seabed? Seabed is usually non-homogeneous and its shear modulus of seabed increases with soil depth such as Gibson soil (). This paper will also explore the effect of depth-variable modulus on seabed responses.This paper proposes a non-dimensional parameter to study the most critical condition governing seabed instability due to momentary liquefaction. This single parameter includes both wave characteristics and seabed properties. Numerical examples are studied to verify its effectiveness through a meshless EFGM model as well as three criteria of liquefaction. It is noted that this EFGM model has been critically examined against available analytical and/or semi-analytical methods (). A parametric study, in the perspective of wave-induced soil instability, is carried out to examine the sensitivity of soil and wave properties on seabed responses. The shear failure in one-wave period is briefly discussed, too. The focus is mainly on the potential of wave-induced momentary liquefaction and liquefaction depth. This paper is organized as follows: The criteria of seabed instability, momentary liquefaction and shear failure, are first discussed in . Then Biot consolidation equation and its EFGM meshless method are briefly introduced in . A non-dimensional parameter which includes both soil and wave properties is proposed to identify the potential of momentary liquefaction in , and this parameter is validated with a finite-thickness seabed and three criteria for liquefaction in . Parameters include wavelength, fluid compressibility or degree of saturation, soil permeability and Young's modulus, as well as variable shear modulus along depth. Mohr cycles of effective stress status within one wave period and shear failure mechanisms are discussed in . Finally, the conclusion and remarks are given.Wave-induced momentary liquefaction and shear failure are caused by different mechanisms. When a sandy seabed is subjected to cyclic wave loading, the effective stresses and pore water pressure fluctuate with the propagation of waves. When the effective stress attains to some critical value, momentary liquefaction or shear failure may occur. This section will discuss the criteria of liquefaction and the shear failure.As discussed in the Introduction, liquefaction is a state where a soil loses its structural strength and behaves like a fluid, producing large deformation and the evolution of seabed such as ripples (). Three criteria have been proposed in various reports to assess momentary liquefaction.Criterion 1: Soil is liquefied when vertical effective stress becomes zero (where σzz′ stands for wave-induced vertical effective stress, γb=(γs-γw) is for the effective unit weight of soil and z denotes the soil depth beneath seabed surface, in which γs and γw are the unit weights of soil and pore fluid, respectively. Eq. indicates that liquefaction occurs when seepage force lifts above soil column and soil particles are no more in contact.Criterion 2: Liquefaction occurs when wave-induced effective volumetric stress in soil becomes identical or larger than the initial in situ effective volumetric stress (where σvol′ is the wave-induced effective volumetric stress, and σvol0′ the initial in-situ effective volumetric stress. These stresses are defined as σvol′=13(1+ν)(σzz′+σxx′),σvol0′=13(1+ν)(1-ν)γbz,where σxx′ stands for wave-induced horizontal effective stress and ν is the Poisson ratio.Criterion 3: Liquefaction may occur if upward seepage force is equal or larger than overburden load. This criterion is mathematically expressed as (where Pz is the pore pressure at the depth z and P0 the pore pressure amplitude at the seabed surface.The ratio of shear stress to normal stress is an important parameter for investigating the potential of wave-induced shear failure. Shear failure occurs when stress angle φ becomes equal to or greater than the angle of internal friction φu (For sandy soils, the stress angle φ is calculated byφ=sin-1(((σxx-σzz)/2)2+σxz2((σxx+σzz)/2)).The effective stress has two components: initial in situ effective stress and wave-induced effective stress. That is, σzz=σoz′+σzz′, σxx=σox′+σxx′. σxz is the shear stress. Initial in-situ effective vertical stress is σoz′=γbz, and initial in situ horizontal effective stress σox′ is related to vertical effective stress σoz′ byA seabed soil is assumed to be elastic, isotropic and homogeneous. Biot consolidation equation () have been applied to describe the wave-induced response of a mixture of compressible pore fluid and compressible porous seabed. These two equations are expressed as follows:where u is the displacement, p the pore water pressure, b the body force vector, n the porosity of soil skeleton, k the soil permeability, and γw the unit weight of pore fluid, and t as real time. The constitutive law of soils is given byFor a plane strain problem, the material matrix D, and operators ∂s and ∂ are given byD=E(1+ν)(1-2ν)[1-νν0ν1-ν0001-2ν2],∂=[∂∂x00∂∂z∂∂z∂∂x],∂s=[∂∂x∂∂z].The compressibility of pore fluid β is a function of the degree of saturation Sr, the bulk modulus of fluid Kf, and the absolute fluid pressure Pa, such as (The repeatability conditions are used to implement periodic temporal and spatial conditions (). Incorporating these virtual boundaries together with physical boundary conditions, a modified variational formulation was proposed for the EFGM model whose final discrete system equation is asA Crank–Nicholson scheme is adopted to discretize the time domain in Eq. gives the definitions of various coefficient matrices in Eq. Excess pore water pressure and displacements in the Biot consolidation theory are approximated by moving least square (MLS) approximants (). The MLS approximant uh(x¯) for a function u(x¯) has the following form:where n is the number of nodes I in the neighbourhood of x¯ for which the weight function w(x¯)≠0, and uI is the nodal index of u at x¯=x¯I. The shape function φI(x¯) is obtained as where A=sTw(x¯)s and B=sTw(x¯). For a linear basis, sj(x¯) is asThen the shape functions can be expressed asWeight function usually takes radial function as wI(x¯)≡w(x¯-x¯I)=wI(dI), where dI=‖x¯-x¯I‖ is the distance between two points x¯I and x¯. The size of the influence domain of x¯l is defined as dmI=dmaxdI, where dmax is known as support size factor (usually taken as 2.5). In this study, cubic spline is used to express the weight function for different ranges within an influence domain:w(x¯-x¯I)={23-4(dIdmI)2+4(dIdmI)3for(dIdmI)⩽12,43-4(dIdmI)+4(dIdmI)2-43(dIdmI)3for12<(dIdmI)⩽1,0for(dIdmI)>1. has no property of Kronecker delta functions, Lagrange multiplier method is employed to implement essential boundary conditions (Wave-induced effective stresses at any point reach their extremes when wave crest or trough goes directly over. Momentary liquefaction is likely to occur under a wave trough due to uplift seepage force on the soil skeleton. We propose a non-dimensional parameter to assess the liquefaction potential for given soil and wave properties:where h is the thickness of seabed. ω is the wave frequency. This non-dimensional parameter κ is the ratio of the slopes for one-dimensional depth-wise effective stress profile to the initial in-situ effective stress. It can be derived from the analytical solutions of wave-induced soil responses for one-dimensional and two-dimensional problems (). In situ soil condition is presented by α and αvol as follows:A 2-D wave-induced transient problem is defined in . The meshless model for soil domain is shown in . This domain is discretized with regular distributed nodes (441 nodes) for function approximation and regular background cells for integration. Domain integrals use 4×4 Gauss points in each background cell and 4 Gauss points in each boundary integral cell. The bottom of the soil domain is assumed to be rigid and impermeable:Ignoring the relative acceleration between water and soil skeleton, the boundary conditions at the seabed surface are:where ϑ=2π/L is the wave number, ω=2π/T the wave frequency, x the horizontal coordinate, and t is the time. L is the wavelength, and T the wave period. The amplitude P0 is obtained from the linear theory of a monochromatic wave (where H is the wave height and dw water depth. The dispersion equation determines the relationship among ω, ϑ and dw:Unless otherwise specified, parameters used in the computation are given in this section. In the fluid domain, the wave conditions for a 5 s wave with height H=0.5 m in water depth dw=4.86m; such given P0=1.656kN/m2 and wavelength L=30m. In the soil domain, the parameters of seabed soil are for soil thickness h=20m, Young's modulus E=2.5×105N/m2, Poisson ratio ν=0.3, porosity n=0.4, and isotropic permeability k=2.5×10-2m/s. The density of the pore fluid and sea water is γw=10kN/m3 and the fluid compressibility of β=3×10-3m2/kN(Sr=0.97). Time step size taken is 0.0625 s for the whole wave period of 5 s in the computation. In order to better express the results, a linear normalization procedure as shown in is carried out. The effective stresses and excess pore water pressure are normalized by P0 while the depth is normalized by the seabed thickness h. It is noted that the seabed condition is ‘finite’ when h<L (When the line representing effective self-weight (called as α-line) intercrosses with the effective stress lines, the soil above the intercrossing point is regarded as liquefied and the depth of crossing point is the liquefaction depth because the liquefaction criterion of Eq. is satisfied in this zone. At this time, the κ⩾1. The parameter κ is obtained through changing fluid compressibility (degree of saturation), Young's modulus, and permeability of seabed soil, respectively, based on those parameters in shows that all liquefaction criteria (Eqs. ) are satisfied if the value of κ is equal to or greater than unity. In other words, the seabed soil is liquefied if κ⩾1. Ideally, when κ<1, the liquefaction may not occur and precaution for protection may not be necessary for the seabed or offshore structure against possible damage induced by liquefaction. show the variations of soil responses with κ at the depth of 1.5 m. The soil response enhances exponentially with κ. Therefore, the condition κ⩾1 can be used as a criterion to predict the vulnerability of momentary liquefaction without the details of the wave-induced soil response. Detail analysis reveals that the three criteria mentioned in Eq. perform slightly different in the assessment of liquefaction potential. Criterion 2 always predicts the occurrence of liquefaction at the seabed surface because it is expressed by volumetric effective stress including horizontal effective stress. The parameter κ is obtained from a one-dimensional formulation, thus it does not take the effect of horizontal effective stress into account, consequently, the condition that κ⩾1 might overestimate the liquefaction zone at seabed surface.Experimental results of two centrifuge tests) are used to verify the numerical algorithm in this paper. lists the computational parameters obtained from experiments. These parameters are used for meshless method, and the analytical solutions. is the comparison of excess pore water pressure predicted by meshless method, Madsen's solution (1978), and Hsu and Jeng's solution (1994). The experimental data obtained by Centrifuge tests are also plotted for comparison. They generally agree well in the whole seabed whether the seabed soil is fine sand or coarse sand. It is noted that the pore water pressure predicted by meshless method is between those of Madsen's solution and Hsu and Jeng's solution.This section reports the effect of wavelength on soil response. Wavelength varies from site to site. For example, took the design wavelength for North Sea as 324 m, while used the value of 200 m in his analysis. In this study, the wavelength is assumed to vary from 10 to 180 m which corresponds to a reasonable range of wave periods () according to the dispersion equation of Eq. at the water depth of 4.86 m. Typical seabed response for wavelengths of 40–100 m is shown in for vertical seepage force. These curves have almost the same slopes before maximum values, and the slopes are not affected by the variation in wavelength L. further compares the vertical effective stress for one-dimensional and two-dimensional conditions with three wavelengths (20, 40, and 160 m). Take vertical effective stress as an example for detailed analysis. The wave-induced maximum vertical effective stress occurs at 0.08 h for L=10m, 0.143 h for L=20m and 0.23 h for L⩾40m. obtained the maximum soil response at 0.15L depth if the seabed is deep enough, i.e., h≫L. Yamamoto compared the North Sea data with his analytical solution for a seabed in infinite thickness. He concluded that the most unstable bed thickness varied between 0.20L (). For a finite seabed, our results show that maximum soil responses are more likely one-dimensional within some depth near surface. The depth increases with wavelength until some value. When wavelength exceeds this value, for example two times of seabed thickness in our study, the maximum response is independent of wavelength. As indicated in , the maximum liquefaction depth is determined by taking the intersection of the stress profile (σzz′, σvol′ or (Pz–P0)) with the initial effective stress line (α-line or αvol-line). Therefore, one-dimensional analysis may suffice to identify seabed liquefaction, especially when Criteria 1 and 3 are considered. Because volumetric effective stress σvol′ includes the horizontal effective stress and is difficult to obtain accurately close to seabed surface, Criterion 2 always predicts the liquefied status at the surface. Within the zone close to seabed surface, both momentary liquefaction and shear failure may occur, and the later mechanism may turn out to be more important.The degree of saturation has been recognized as a dominant factor for the wave-induced seabed response. Pore water in seabed soils is compressible due to gas bubbles (). The structure of an unsaturated marine soil can vary significantly depending on the relative size of gas bubbles to soil particles. The in-site degree of saturation of unsaturated marine sediments normally lies on the range of 85–100% ( is assumed to vary from 0 to 1×10−2
m2/kN which corresponds to Sr=1.0–0.9.The maxima of σzz′, σvol′ and (Pz–P0) increase as the degree of saturation (Sr) decreases. indicates the effect of the degree of saturation on vertical seepage force. It reveals that unsaturated soil is more vulnerable to liquefaction. The mechanism for this fragility to liquefaction is complicated. Fluid compressibility increases the absorbing rate of wave energy in this surface zone. This prevents the pore fluid pressure from infiltrating easily into subsurface layers and produces a phase lag in pore pressure response near the surface zone (see ). This phase lag increases when degree of saturation decreases. Due to this phase difference, the soil response at any given time could be greater than the initial load, thus enhancing the possibility towards liquefaction. Therefore, wave-induced soil response is sensitive to the fluid compressibility or degree of saturation. Numerical results again reveal that Criterion 2 overestimates liquefaction potential, and that Criterion 3 or (Pz-P0)⩾γbz predicts deepest liquefaction zone. Therefore, Criterion 3 is the most critical one.Soil permeability is assumed to vary between 2.5×10-1m/s (gravel) and 2.5×10-7m/s (clay). The effect of permeability on seepage force, (Pz−P0), is shown in . It indicates that the seabed response is sensitive to the permeability κ. The seepage force decreases with permeability. When the permeability is low, the seabed is more vulnerable to liquefaction. The maximum response of pore water pressure occurs at deeper position when soil permeability is higher. Again, Criterion 3 predicts the deepest liquefaction zone.Young's modulus is assumed to vary between 2.5×104 and 2.5×108
N/m2 but keeps constant along depth. This range is suitable for a wide range of soil masses (. In the shallow zone, Young's modulus E has almost no effect on vertical effective stress σzz′ and vertical seepage force (Pz−P0). The maximum effective stress increases with Young's modulus E. This implies that the seepage force becomes higher and the soil mass may become more susceptible to liquefaction when E increases. When Young's modulus E is very large (>5×107N/m2 such as gravels), the maximum response (σzz′, σvol′ or (Pz−P0)) is not affected. At this stage, a seabed can be regarded as rigid porous medium for the analysis of liquefaction. Again, Criterion 3 is the most critical one because it predicts the deepest liquefaction zone.Variable shear modulus along depth is a feature of seabed soil in ocean engineering and has been studied by many researchers (). A typical distribution of shear modulus along depth is shown in . Here the effect of variation of shear modulus on seabed response is studied. For comparison, an equivalent constant modulus (called constant modulus), which has the same area over the entire thickness, is also used. The meshless method approximates this variable shear modulus with stepwise constants over background cells. Typical response is shown in for excess pore water pressure. The contours of effective stresses are compared in , where solid lines are for the variable modulus and dashed lines are for constant modulus. Vertical effective stress is larger for variable modulus than for constant modulus, and horizontal effective stress is more sensitive than vertical effective stress. The maximum response occurs at deeper zone for variable modulus, and the liquefaction depth is larger for variable modulus.Shear failure may occur in the seabed. The stress angle φ is used to describe the mobilization of soil shear strength. Seabed is only stable when φ<φu. It is noted that the angle of internal friction φu is between 20° and 30° for sandy seabed (). The stress angle at each node is computed with Eq. . Typical Mohr circles within a wave period are shown in . The line AOB (φu* line) passes through the crown point of the Mohr circle, and φu<φu. When the crown envelope crosses the line AOB, part of the seabed may be subject to shear failure. However, a soil is liquefied when the instantaneous stress at the horizontal plane reaches the point O or the stress crown is on the line COD, i.e. σ3′=0 for Criterion 1 and 0.5(σ1′+σ3′)=0 for Criterion 2. Because a liquefied soil behaves like fluid, the stress status cannot be obtained by Biot's consolidation equation. Theoretically, the crown envelope cannot go beyond the line COD as indicated in the current elastic analysis of . The wave-induced seabed instability may be induced by a complex coupled process combining shear failure with momentary liquefaction. Once shear failure occurs, seabed soil becomes highly nonlinear and the current theory is inappropriate to deal with the situation. Mohr circles are also drawn at two particular depths for different degrees of saturation as shown in . The wave and seabed parameters are the same as those in with α=4. These Mohr circles correspond to the maximum vertical effective stress at that point. If Criterion 1 is used, a soil is liquefied because the minor principal stress is zero or negative. shows a typical relationship of shear failure depth and liquefaction depth when α=4. It can be seen that shear failure occurs at the surface and is shallower than that for the liquefaction (). Shear failure occurs before liquefaction if internal frictional angle is φu=30°. According to Criterion 2, a seabed soil is always liquefied near seabed surface, and thus protection work for seabed surface, such as covering the seabed by a layer of concrete blocks or rubble, is necessary (Wave-induced seabed instability, both momentary liquefaction and shear failure, is studied under various soil and wave properties. A non-dimensional parameter is proposed to evaluate liquefaction potential. The response of a seabed with finite thickness is numerically studied when a two-dimensional progressive wave is applied on the surface of seabed. Parametric study on soil and wave properties is carried out and their effects on the seabed responses and liquefaction potential are analyzed. From these studies, following conclusions can be made.Momentary liquefaction may occur within the shallow zone of a seabed and the non-dimensional parameter κ can be used to identify the momentary liquefaction. The seabed is likely liquefied if κ⩾1 for any one of the three criteria of liquefaction. Three criteria of liquefaction, which are based on vertical effective stress, effective volumetric stress and dynamic excess pore pressure or seepage force, respectively, are discussed for the identification of soil liquefaction. For the same soil and wave properties, Criterion 3 (for seepage force) predicts the deepest liquefaction zone and Criterion 2 is the least critical one. Criterion 2 always predicts soil liquefaction at the seabed surface. Therefore, Criterion 3 becomes the most critical condition for liquefaction.The sensitivity of wave and seabed properties is different in the evaluation of liquefaction potential. Within the shallow zone, wavelength has almost no effect on the maximum seabed response. Seabed response is similar to that in one-dimensional case within the shallow depth near seabed surface. As an approximation, one-dimensional analysis suffices for the identification of soil liquefaction. However, seabed characteristics have dominant effects on wave-induced seabed response. Among all the soil parameters described, compressibility of pore fluid (degree of saturation) is the most critical one. The higher the fluid compressibility is, the more vulnerable condition for the occurrence of soil liquefaction. The coefficient of permeability also plays an important role. The lower the permeability is, the more vulnerable to soil liquefaction. In the shallow zone near the seabed surface, Young's modulus of soil skeleton has almost no effect on vertical effective stress and excess pore pressure, but has some effect on effective volumetric stress. If Young's modulus is very high (>5×107N/m2), the effect on soil response may be ignored and the seabed can be regarded as a rigid one. Such simplification can predict vertical effective stress and excess pore pressure with reasonable accuracy. However, the predicted effective volumetric stress is slightly larger. Variable shear modulus predicts bigger maximum response and deeper liquefaction zone. Therefore, variable shear modulus along depth has to be considered.Stress angle is another important parameter leading to seabed instability due o shear failure. Shear failure may occur near and at the surface. The stress angle of soil has nothing to do with the liquefaction except for causing shear failure. Elastic analysis indicates that shear failure takes place before momentary liquefaction. Once a soil failed in shear, soil deformation becomes highly nonlinear. Therefore, the present linear theory would not be appropriate for the prediction of further failure. It is then necessary to employ the transition mechanism from shear failure to liquefaction as a progressive process.[R]=[KLG0(Gvl-Gvr)0LT-(M-θΔtH)0θΔtG′0(G′vl-G′vr)ΔtθGT000000G′T0000(GvlT-GvrT)000000(G′vlT-G′vrT)0000],[Q]=[000000LT-(M+Δt(1-θ)H)0-Δt(1-θ)G′0-Δt(G′vl-G′vr)(1-θ)000000000000000000000000],The superscript (t+1) denotes the current time (t+Δt). The repeatability conditions create two virtual boundaries at both ends, as denoted by Γνl and Γνr (uνl=uνr and pνl=pνr). Other notations in Eqs. KIJ=∫ΩBITDBJdΩ,LIJ=∫ΩφIAJdΩ,MIJ=nβ∫ΩφI.φJdΩ,HIJ=kγw∫ΩAIT.AJdΩ,GIK=∫ΓuN¯KφIdΓ,GIK′=∫ΓpN¯′KφIdΓ,GIKvl=∫ΓvlN¯KφIdΓ,GIKvr=∫ΓvrN¯KφIdΓ,GIK′vl=∫ΓvlN¯K′φIdΓ,GIK′vl=∫ΓvrN¯K′φIdΓ,fuI=∫Γσt¯.φIdΓ+∫Ωb.φIdΩ,fpI=∫Γϕϕ¯.φIdΓ,BI=∂(φI)=[φI,x00φI,zφI,zφI,x],AI=[φI,xφI,z],N¯K=[Nk00Nk],N¯K′=[Nk].Following boundary conditions are also used during the variational formulation:u(x,t)=u¯(x,t)onΓuandp(x,t)=p¯(x,t)onΓp,σ.n^(x,t)=t¯(x,t)onΓσandkγw∂p∂n^(x,t)=ϕ¯(x,t)onΓϕ,ϕ¯ and t¯ indicate pore water flux and traction, respectively. n^ is the unit normal to boundary Γσ, Γu, Γp, Γσ and Γϕ are the boundaries where displacement, pore water pressure, total stress and flux of pore water are prescribed. Obviously, they satisfy the following relations: Γu∪Γσ=Γ and Γu∩Γσ=∅; Γp∪Γϕ=Γ and Γp∩Γϕ=∅.Chapter 9 The role of particle size reduction, liberation and product design in recycling passenger vehicles The quality of recycling intermediate products created during shredding and physical sepa- ration is of critical importance to ensure that the feed to metal producing processes permits the economic production of quality metal products. The liberation of materials during shred- ding plays an important role in the composition and quality of the intermediate recycling streams. The degree of liberation of the materials present in the car as well as the particle size reduction during shredding are of major influence on the separation efficiency of phys- ical separation processes. Moreover it affects the purity of the material streams produced by separation and thus the metallurgical process efficiency, and hence the ultimate material recovery and therefore the recycling rate. Therefore, it is essential to capture the particle size and degree of liberation in the recycling models, which provide a fundamental framework for the optimization of the recycling rate as well as for the calculation and prediction of the recycling rate. Since particle size reduction and liberation are closely related to the design of the product (material combinations and connections) it should be included in the models in order to link design to recycling. Two different models are developed to describe the influence of liberation and particle size reduction on the recycling (rate) of end-of-life vehicles. These models have been developed based on the knowledge of traditional mineral processing. It is illustrated that the modelling of traditional minerals processing systems can be applied in the new field of (design for) recycling of complex consumer products. From the various simula- tions presented it can be concluded that the modelling of the breakage behaviour for modern consumer products differs fundamentally from traditional minerals processing. Moreover var- ious theoretical simulations will illustrate the effect of changes in product design and hence particle size reduction and liberation on the recovery rate for the various materials in the car and therefore on the recycling rate of end-of-life vehicles. This chapter illustrates that the development of fundamental models is indispensable to build the bridge between the material combinations and connections in design and the recycling of cars in order to increase recycling rates as well as to provide a framework to link design to recycling. Liberation and particle size reduction during shredding is the link between design and recycling. 9.1 Introduction from mines, from which the composition is well known, does not change drastically from a par- ticular mine site or even between mine sites. The simulation of classical minerals processing is often not easy due to incomplete descriptions of mineral properties, making the calibra- tion of fundamental models difficult. Modern society 'minerals' are complex, so diverse and changing so rapidly making a fundamental description extremely difficult. It can be stated that liberation during shredding is the link between design and recycling operations. Particle size reduction and liberation of materials during the shredding of modern end-of-life products are closely related to the design of the product (Technology cycle, see Figure 9.1) and play an important role in the composition and quality of the intermediate recycling streams and the ultimate material recovery and therefore the recycling rate (Resource cycle, see Figure 9.1). In this chapter the development of two different recycling optimization models will be discussed, in addition to the recycling optimization model developed in Chapter 8, describing the relationship between product design ('mineralogy'), mechanical separation efficiency and metallurgy as a function of: 9 liberation during shredding, and; 9 the combination of particle size reduction and liberation during shredding; which will affect the recycling rate of cars. The three different recycling optimization models as discussed in respectively Chapters 8 and Chapter 9 each focus on a different aspect of the intersections between the three cycles (see Figure 9.1), which all affect the recycling rate and optimization of end-of-life vehicles. The main focus of each of the recycling optimization models is briefly described below. The first recycling optimization model as discussed in Chapter 8 describes the recycling system and the calculation of the recycling rate of the car as a function of the performance of the various unit operations on the basis of their individual grade/recovery relationship. The calculations and optimization of the recycling system are placed within the dynamic framework of the resource cycle of the car as described by the dynamic resource cycle model. The calculations are based on normal plant practice, in which the particle size of the material flows is affecting the material flows throughout the plant. The assumption is made that the different particles after shredding only consist of one component. The second recycling model as will be discussed in the first section of this chapter describes the relation between design (material combinations and connections) and liberation of the materials during shredding. The separation efficiency is modelled based on recovery factors, which are dependent on the degree of liberation of the materials. The third model as will be described in the second part of this chapter calculates and optimises the recycling rate of end-of-life vehicles as a function of both particle size reduction and liberation during shredding. This model provides a first principles technological basis to develop the link between design and recycling. In this model the separation efficiency is described by recovery factors, which are a function of particle size class and the degree of liberation of the material flows. In the first model, the grade is implicitly part of the modelling parameters. In addition, the composition of each of the material flows within the recycling flowsheet can be calculated. For the second and third model, the grade and composition can be calculated from the model, not only based on the general composition of the material streams, but including the effect of the material combinations present in the non-liberated particles. The calculation and control of the grade is crucial for the recycling rate to be achieved, in view of the quality control of (intermediate) recycling products being the input for metallurgical processing. The second and third recycling optimization models, which will capture the role of liberation (and particle size reduction) will be developed partly based on the modelling 284 Material liberation ~z product design techniques applied in traditional minerals processing demonstrating how classical theory can be applied to solve modern problems. The inseparable relationship between product design, product mineralogy, and liberation of materials in relation to mechanical separation technology and quality requirements for metallurgical material recovery processes will be captured by the two different system models for the optimization of the resource cycle of passenger vehicles. The development of first principles models is indispensable to build the bridge between the material combinations and connections in design and the recycling of cars. This will illustrate at the same time how the knowledge of traditional mineral processing can be applied in the new field of design for recycling of complex consumer products. On the longer term, this could become the future of minerals processing technology, since legislation and environmental concern will increase the availability of secondary materials, being the mineral ores of the future. The inseparable link between product design (Technology cycle, see Figure 9.1), and the particle size reduction and liberation of materials in relation to mechanical separation tech- nology and quality requirements for metallurgical material recovery processes and hence the recycling rate of the product (Resource cycle, see Figure 9.1) is captured by the models as described in this chapter. This chapter operates on the link between the Technology and the Resource cycle (Figure 9.1). 9.2 Recycling optimization model linking the liberation to the recycling rate of end-of-life vehicles The liberation of materials during shredding plays an important role in the composition and quality of the intermediate recycling streams. The degree of liberation of the materials present in the car is of major influence on the separation efficiency of physical separation processes. Moreover it affects the purity of the material streams produced by physical separation and thus the metallurgical process efficiency. In general an increased complexity of recycling pyrometallurgy has arisen through the development and design of modern consumer products (such as passenger vehicles). Modern products contain a combination of metals that are not linked in the natural resource systems (Figure 1.2) [33]. As a consequence, these materials are not always compatible with the current processes in the metals production network, that was developed for the processing of primary natural resources and therefore, optimised for the processing of the primary metal and all mineralogically associated valuable and harmful minor elements. The formation of complex residue streams or undesired harmful emissions that cannot be handled in the current system inhibits thus the processing and recycling of those products at their end-of-life and will immediately result in decreasing recycling rates of these products. Losses within the recycling phase are e.g. caused by increasing product complexity and changing material combinations (see Figure 1.2), which affect liberation, efficiency of separation and the quality of intermediate recycling streams. Even a small change in product mineralogy (material combinations and connections) due to changing product design can have a significant effect on the final metal recovery and thus on the recycling rate of a product. The final metal recovery is dictated by the prevalent thermodynamics and kinetics of the metallurgical processes, which are the closers of the material cycle [33]. The strict limits to the presence of contaminations present in the input of metallurgical processes (e.g. <0.25% Cu in the ferrous scrap, <0.3% Fe in aluminium for certain alloy types, etc.) indicates that only a small amount of contaminant present in intermediate recycling streams, either due to imperfect liberation and/or separation in combination with a changed product design can lead to a decreased recovery and losses during the recycling of the product. Product 9.2 Recycling optimization model 285 designers, physical liberation and separation plants, waste processors, metal producers and decision makers must cooperate to obtain an optimal material and metal recovery in processing discarded consumer products. High environmental standards and recovery rates can only be achieved and maintained through proper understanding of these complex interactions, which are strongly dominated by continuously changing product design. The assumption has been made in the model as discussed in Chapter 8 that the particles consist of only one material, and are completely liberated during shredding, which is not necessarily the case for all particles. Shredding will not liberate all combined materials. In order to include the influence of product design (mineralogy), liberation, and particle composition in the description and optimization of recycling systems, the model as discussed in Chapter 8 [51] therefore has to be expanded with a liberation model. This recycling optimization model predicts the recovery rate for the various materials present in the car as a function of product design and liberation in relation to the efficiency of the different physical and metallurgical process steps and the quality of the intermediate recycling streams due to imperfect liberation and separation. Product design and liberation will have a direct influence on the realisation of the targets laid down by legislation. The importance of including the degree of liberation in the model and its role in the material quality of the intermediate recycling streams is illustrated throughout the model and the case studies presented. 9.2.1 Phase description of the material streams In order to capture the influence of material combinations determined by design and the degree of liberation (and thus the material combinations in the non-liberated particles) on the recovery rate and recycling of products, the model must be able to describe the first principles of the liberation of the different materials as a consequence of material combinations and joint types chosen during design and as a consequence of shredding. The degree of liberation will be determined by the performance and operation of the shredder, as well as by the material combinations and connections in the car. The developed liberation model describes the degree of liberation of a product (defined as a mineral, which is derived from classical minerals processing) by defining the fraction of the various materials present in the particles for a range of liberation classes. Table 9.1 summarises an example for the definition of the composition of the liberation classes in the model for a mineral A (in this case a mineral with Al-wrought being the major component). Similarly minerals B (Al-cast rich), C (Plastic rich/rest), D (Steel-rich) and E (Cu-rich) are being defined for the example of a five component recycling system. The material combinations in the as given in Table 9.1(c) are a direct consequence of the material combinations defined during design. The material flows in the recycling flowsheet are described based on the various minerals, of which the composition is given over the defined liberation classes based on the elements/materials included in the model. For each of the defined minerals, a similar matrix has been developed. Since data on the composition of the various liberation classes have never been measured up till now, estimations on this had to be made as can be seen from Table 9.1. The transformation of the liberation classes due to the shredding operation is defined in the model based on a transformation matrix. This is similar as defined by Reuter and Van Deventer [309] for milling and flotation plants. The output of the metallurgical processes has to comply with constraints on the alloy composition. Since each element is described separately in the liberation matrices (see Table 9.1) composing the various minerals, the output of the metallurgical operation can be calculated by adding the different materials present in one stream (e.g. the produced aluminium alloy). Aluminium is described in the model as wrought or cast, each with its own specific (average) composition, which is described in a matrix in the model. Together with the 286 Material liberation & product design contaminants or alloying elements ending up in the alloy, the exact alloy composition can be calculated from the model based on the degree of liberation and can be controlled by defining boundary conditions on the output. Primary materials (aluminium and alloying elements) often have to be added to produce a required alloy composition. Input of primary materials must be kept to a minimum, for economical and environmental reasons. This can be realised by including the primary materials in the objective function for optimization. 9.2.2 Formulation of the recycling optimization model The major difference between the recycling optimization model as described in Chapter 8 and the liberation model discussed here, is that the material streams are not defined based on elements k and particle size classes p, but in terms of minerals m, ranging from A to E and liberation classes 1 from 1 to 5 (Table 9.1). The liberation model describes the flow of materials in the recycling system for mechanical separation and metallurgical operations in a different way, similar to the model discussed in Chapter 8. The transformation of the liberation classes 1 due to the shredding operation is defined in the model based on a transformation matrix. The modelling of the different unit operations within the recycling flowsheet is discussed below. Formulation of model for shredding The transition of the liberation class distribution due to the shredding operation is defined in the model based on a shredding transformation matrix. This is similar as defined by Reuter and Van Deventer [309] for milling and flotation plants. It is possible to define a transformation matrix for the transition of the liberation class distribution over shredding Sf'~ 'lI'l~, where I/ is the liberation class of the feed f, whereas ly is defined for the output y. The assumption has been made that all minerals m defined as A1 (cast & wrought), Fe, Cu and rest based minerals (i.e. minerals A to E), break according to the same shredding transformation matrix (for the particle size reduction). This is obviously a simplification, since the various materials will break differently due to their specific mechanical properties, joining method, design, complexity and require therefore different transformation matrices. Separate matrices can however be defined for each mineral, but this was not done in this model. Mass balance over shredder A mass balance can be set up over the shredding operation, which describes the transition of the mass flow over the liberation classes 1 for each mineral m (Eq. 9.1 and Eq. 9.2). Since no separation takes place (the in- and output of the shredder are both defined as one stream distributed over the liberation classes) no separation efficiency equation for the shredding operation is defined. ~ (S f~: . C ~'l'k) ) . fm (~ "s~c~'~'k))~ , . -0 _ y, . ym (9.1) /=1 k/=l with /--5 E smYi 'z =1 (9.2) /----1 9.2 Recycling optimization model 287 Table 9.1: Typical parameters for the phase model as used for simulations. Definition of: (a) input matrix(composition and construction of the car); (b) liberation matrix for shredding m If l~ (Sfi ' ' ); (c) composition matrix of liberation classes (C m'k'l) for mineral A; and also B to E (bold gives the name of the metal/mineral) (a) Mineral (kg) Liberation class IB Ic I D Lib. class 1 15 30 250 700 25 Lib. class 2 0 0 0 0 0 Lib. class 3 0 0 0 0 0 Lib. class 4 0 0 0 0 0 Lib. class 5 0 0 0 0 0 (b) Shredding matrix (S f[ ''z'f ) Lib. class 1 / Lib. class 2 Lib. class 3 Lib. class 4 Lib. class 5 (~[1 , (ill , (if) (l[) Lib. class 1 (lv) o Io o 0 0 Lib. class 2 (Iv) 0.01 0.01 0 0 0 Lib. class 3 (Iv) 0.1 0.05 0.05 0 0 Lib. class 4 (Iv) 0.1 O.O5 O.05 0.05 0 Lib. class 5 (l]~) 0.79 0.89 0.9 0.95 1 (c) Definition of liberation classes C m'k'z Mineral A AI wrought AI cast Fe Cu Rest Lib.class 1 0.60 0.20 0.10 0.05 0.05 Lib.class 2 0.70 0.15 0.10 0.03 0.02 Lib.class 3 0.75 0.10 0.10 0.03 0.02 Lib.class 4 0.95 0.05 0 0 0 Lib.class 5 1 0 0 0 0 Mineral B AI wrought AI cast Fe Cu Rest Lib.class 1 0.30 0.50 0.10 0.05 0.05 Lib.class 2 0.25 0.65 0.05 0.03 0.02 Lib.class 3 0.10 0.75 0.10 0.03 0.02 Lib.class 4 0.05 0.95 0 0 0 Lib.class 5 0 1 0 0 0 Mineral C Al wrought Al cast Fe Cu Rest Lib.class 1 0.02 0.02 0.06 0.1 0.8 Lib.class 2 0.02 0.02 0.04 0.07 0.85 Lib.class 3 0.02 0.02 0.03 0.03 0.9 Lib.class 4 0.015 0.015 0.01 0.01 0.95 Lib.class 5 0 0 0 0 1 Mineral D Al wrought Al cast Fe Cu Rest Lib.class 1 0.01 0.01 0.8 0.08 0.1 Lib.class 2 0.005 0.01 0.855 0.06 0.07 Lib.class 3 0.005 0.005 0.91 0.05 0.03 Lib.class 4 0.005 0.005 0.95 0.02 0.02 Lib.class 5 0 0 1 0 0 Mineral E Al wrought Al cast Fe Cu Rest Lib.class 1 0.01 0.01 0.03 0.8 0.15 Lib.class 2 0.005 0.005 0.02 0.85 0.12 Lib.class 3 0.005 0.005 0.01 0.9 0.08 Lib.class 4 0 0 0.01 0.95 0.04 Lib.class 5 0 0 0 1 0 Material liberation & product design Formulation of model for mechanical separation Mass balance over mechanical separation The mass balance for mechanical separation is based on the defined minerals m and liberation classes 1 over the unit operations i and j (see Eq. 9.3). n f?" + --y?,' = o (9.3) j--1 Separation efficiency of mechanical separation processes (recovery based mod- elling) Since the liberation model describes recycling performance based on material prop- erties, the separation efficiency of the mechanical recycling is defined in terms of only recovery and not in more complicated terms of grade/recovery curves (see Eq. 9.4). (1 R mlx ml ml m,l -Yi ')'Yi ' -RYi ' "xi =0 (9.4) Formulation of model for metallurgical processing A mass balance describes the material flows in metallurgical processing in which the relation between in- and output is given by the recovery for each of the different elements k present in the input for the melting furnace. The mass balance as well as the separation efficiency (recovery) of the metallurgical operations can be described in one equation (see Eq. 9.5). For the mass balance and separation efficiency for metallurgical processing the following equations (Eq. 9.5, Eq. 9.6 and Eq. 9.7) may be derived, representing respectively the mass balance and separation for stream yk, xi k and z k (9.5) m--1 \/--1 Ig 'l . C m'l'k . Rx~ -zi = O (9.6) l.m=l \/=1 (9.7) m--1 \l--1 where: Ry? + + Rz? = 1 (9.8) Eq. 9.5, Eq. 9.6 and Eq. 9.7 calculate the fraction of each element k (A1 wrought, A1 cast, Steel, Cu and rest) present in each mineral class m of the input stream fm,t of metallurgical processing for the sum of all liberation classes l and composition matrix C m,k,l. The mass flows of the elements k (A1 wrought, cast etc.) present in each mineral m are determined from the calculated fractions by multiplication the fractions with the mass flow of the input stream for each mineral m fm,p. A transition from mineral m to element k is being made by adding up element k over all mineral classes m (mineral A becomes A1 wrought, mineral B A1 cast, etc.). The mass balance and separation efficiency over the metallurgical processing for each of these elements k is calculated based on the recovery values Ryki, Rxki and Rzki as given in the model. Since in the output of metallurgical processes the definition of liberation classes make no sense, the recovered elements k are added up over all liberation classes 1 or 9.2 Recycling optimization model 289 just simply alloy classes, the output yk x k and z k are only defined per element k. Therefore Eq. 9.5, Eq. 9.6 and Eq. 9.7 define the mass balance on element basis and not on mineral basis. The recovery values Rye, Rx~ and Rz k can be a fixed value or can be dependent on the concentration of e.g. contaminants in the feed stream. The recovery value is then represented by (Eq. 9.9 and Eq. 9.10): ny k -(ap . If k~,St) -bp = 0 (9.9) where: krest rest i f~..~, : ~ f?,l . cm,k,.,,,,L (9.10) m--1 \/--1 where I f~ a~ ~t,l is e.g. the organic content of the aluminium fraction being the input of the metallurgical process, and ap and b. are plant parameters (where b. is equal to the recovery value for a certain size class p as given in the matrix) that define the variation of recovery as k tl a function of If~ .... . The same applies to Rx~ and Rz~. The recovery values for metallurgical processing are not defined as being dependent on the liberation class. The influence of liberation on the final metal recovery is taken into consideration by including the influence of the other elements, such as organics (=rest stream). 9.2.3 Flowsheet of the model A simplified flowsheet (Figure 9.2) has been derived from the detailed recycling flowsheet for ELV's (Figure 8.3 [324]). This flowsheet forms the basis for the recycling optimization model for aluminium recycling as discussed here. Since the model focuses in particular on the optimization of aluminium, the metallurgical processing of aluminium is described in the model. The model has been developed in Microsoft(~) Excel and AMPL (see Appendix C.2). 9.2.4 Parameterisation of the recycling optimization model As discussed above as well as in the previous chapters (Chapter 7 and 8) the recycling of the car is dependent on various parameters. Most of these parameters will change over time, such as the lifetime of the car, the weight and the composition, (implying the mineralogy) of the car. In Chapter 8 the development of a dynamic model was described, which predicts the behaviour of the resource cycle system over time, based on various distribution functions describing the statistic and time-varying nature of the mentioned parameters [51]. The recycling optimization model predicts the recovery rate of the various materials dependent on these time-varying parameters (design influencing liberation, separation efficiency, etc.). This section will discuss how various parameters were determined for the recycling optimization model. Influence of the choice of materials in the design on the recycling During the design stage, fundamental choices about a product are made, which have to satisfy product requirements for the different stages of its life cycle (production, use and recycling). As mentioned, design decisions on the product mineralogy (material combinations and con- nections) are of significant influence on the end-of-life phase of the product. Liberation of materials is never perfect during the shredding of the car. The combination of materials and in particular the way they are connected in product design will affect the degree of liberation, 9.2 Recycling optimization model the composition of the material streams after shredding and mechanical separation, and the amount as well as the composition of the non-liberated particles. Consequently mineralogy and liberation will affect the possibilities of material recovery as well as the recycling rate of the product. The material stream produced by the shredder consists of a complex mixture of materials, which are present as liberated (pure) and non-liberated (contaminated) particles. The materials in the stream have to be separated by mechanical recycling in order to create high quality material flows for the various elements (materials) present in the car. This will however lead to losses within in the different material cycles, since based on the interrelation between grade and recovery of a mechanical separation process, it can be concluded that the recovery of materials will always be lower than 100%, if the quality of recycled materials has to be increased by mechanical separation. However, the different materials locked up within the non-liberated particles can never be separated from each other by mechanical separation. A high quality feed is a prerequisite for producing high quality metal products after (s)melting, the recovery of which is constrained by the prevalent thermodynamics and kinetics. The con- taminations present may lead to a degradation of material properties and moreover to the loss of valuable materials. Material combination matrix In order to apply a systematic approach to select desired and avoid problematic material com- binations in product design and intermediate recycling products, a decision tree was developed, based on the separation and recycling technologies available nowadays and on metallurgical and thermodynamic properties of the materials [299, 335]. The decision tree is shown in Figure 9.3 and is self-explanatory. This decision tree must be read in conjunction with a selection matrix (Figure 4.9) describing which metal combinations are desirable for recycling and which are not. For example the matrix highlights the sensitivity of the lightweight metals (here aluminium and magnesium alloy families) to contaminants. It means that these metals should either be dismantled from the end-of-life product, carefully separated by mechanical processes, or the contamination of these materials with others should be avoided in product design. In Figure 4.9, also the components of an average passenger car, described by Castro et al. [336], are analysed, as an example of application of the matrix. The data behind Figure 4.9 on the limitations of contaminations in the input for metallurgical processing are included in the simulation model by imposing constraints on the output composition of the mechanical separation units (being the feed for metallurgy). Only three categories to control the input of metallurgical processes are distinguished, which can be translated to the model by eliminating the presence of unwanted components on the input composition of metallurgical processes by constraints on the system (red category). For the green category no restrictions have to be imposed onto the model. However a more detailed approach is required to describe the yellow category. Based on the prevalent thermodynamics and kinetics of the metallurgical processes (on the basis of which Figure 4.9 has been developed), fixed constraint values (or ranges) for the percentage of different contaminants allowed in the feed stream, can be included in the model. The matrix can be expanded by other materials. Lemmers [337] studied the compatibility of polymers for mechanical recycling. In summary this matrix determines the constraints on the various mineral and class flow rates as well is used to estimate the liberation classes and liberation matrix as described by Table 9.1. Graedel and Allenby [39] discuss that pure metals are supremely recyclable, but that metals recycling is complicated by the use of mixed metals from different basic extraction processes. Graedel and Allenby [39] show the metals that commonly occur together and for which common extraction and purification processes have been developed. This is described 292 Material liberation &: product design Color In matrix II m B Value Points Decision DOn'T @ separate TN N ATTENTION ~ I to losses/cost Y MUST separate Question 1. Is there a routine refining method for the troubling component in the industrial stream ? 2. Cantroublingcomponentberecovered aftertherefining? 3 -Is the content of troubling component below concentration limit values? I Inputs eam: I I Indus a, s oam: I Figure 9.3: Decision tree for the selection of metal combinations during design interacting with Figure 4.9, which directly affect the liberation classes in Table 9.1. This has been developed for the average passenger car analysed on present material combinations in various car parts [335] and modelled in much more detail by Verhoef et al. [7], showing the interconnectedness of the various metal cycles (see Figure 1.2). Instead of simply avoiding the mixing of material streams, the knowledge on possible (beneficial) material combinations as well as on problem- atic combinations is required in design for recycling, as also illustrated by Figure 4.9. This emphases the crucial importance of the recycling optimization model as developed in this Part (and recycling practice) to be able to calculate and control the grade of the recycling (intermediate) products. 9.2.5 Simulations on the optimization of product design, liberation and metallurgy The recycling optimization model calculates the recovery of the different elements present in the car dependent on the objective of the optimization. The examples below will present the results of the recycling optimization model in particular for the optimization of the recycling of aluminium in the car. The simulations will show the interrelation of car design (product mineralogy), liberation and the quality of the intermediate recycling products, as well as their influence on material recovery (in particular for aluminium). The various simulations and their results will be described below. Data for the recycling optimization model The values for separation efficiencies (recovery values for model constraints as described above) are derived from experimental and industrial data as far as available. Since most of the data 9.2 Recycling optimization model 293 on the performance of the various unit operations appear to be incomplete or even lacking, estimation for the process efficiencies had to be made. As mentioned the same applies for the description of the composition of the liberation classes, which have never been measured up till now. Data have been collected by sampling and analyzing from industrial experiments and shredder plants. The theoretical, model based approach lays down a solid framework for data collection when setting up or performing recycling experiments. It makes clear what type of data have to be collected on different steps in the recycling of products, in order to describe and optimise the recycling of end-of-life vehicles, and in particular the inseparable link between product design and mineralogy, liberation, mechanical separation and metallurgical recovery. These fundamental insights on the importance of proper collection of data and the corresponding statistics and how this should be performed when carrying out experiments or auditing a plant have been lacking up till now[ The data assumptions made in the model affect neither the usability of the system approach used to describe and optimise recycling systems nor the validity and applicability of the developed model as discussed above, since the model is based on prevailing mass balance and separation efficiency equations. Data assumptions only replace the calibration of the parameters and composition matrices in the model. Software for optimization For the optimization of aluminium recycling in ELV's, as discussed here, more than 400 variables with regard to the different material streams are defined. Furthermore, 9 variables describing the structural parameters (~ij are added (values (~1, a2, (~3,/~1,/~2, "~1, 72, 51, 52 in Figure 9.2) in order to optimise the structure of the network [51]). The software application used to perform this optimization is Frontline Systems' Premium Solver Platform, extended with the Large-Scale GRG Non-linear Solver [328], implemented in Microsoft@Excel [327], which is capable of handling this large scale, complex, non-linear optimization problem. The recycling optimization model as programmed in Microsoft(~) Excel and AMP L is depicted in Appendix C.2. Definition of simulations Various simulations have been performed in order to illustrate the influence of product design (material connections and combinations), liberation, on mechanical recycling performance and metallurgical recovery as discussed above. The objective for all of the simulations is to maximise the recovery of the aluminium minerals (A and B) coming from mechanical processing, while minimising the other mineral flows (C, D and E) in order to optimise the quality of the produced aluminium alloy, this according to Figure 4.9. The various simulations will vary the different parameters in the link between design, liberation and metal recovery in order to illustrate the role of each parameter separately in the recovery of materials from the car and the achieved product quality. Base case scenario (simulation 1) The first simulation (simulation 1) optimises the recovery of mineral A and B (while minimising the others) based on a defined input definition of the car, a liberation matrix for shredding and the definition for the composition of the various liberation classes for the different minerals in the car. This simulation serves as the base case scenario, to which the results of the other simulations will be compared. Table 9.2 depicts the settings of the model for the first simulation. Liberation (simulations 2 and 3) As discussed above the liberation of materials is di- rectly related to the recovery of materials, since it determines the purity (or impurity) of the Material liberation & product design material streams in the recycling flowsheet. The influence of liberation is simulated in the model by defining different values for the liberation matrix for shredding in the model. The results of these simulations are presented in simulation 2 (increased liberation) and simulation 3 (decreased liberation). Table 9.2 represents the changed liberation matrices for shredding. Material combinations in the car (simulation 4 and 5) Based on the matrix of Figure 4.9, design choices can be made to avoid unwanted material combinations in the design of the product. Redefining the composition of the various liberation classes simulates the effect of these design choices, e.g. less Fe is present in the various liberation classes of the A1 containing minerals (A and B) (simulation 4). Table 9.3 gives the changed definition of the composition of the liberation classes for all minerals. In simulation 5, it is assumed that the particles are completely liberated (perfect design). In the definition of the liberation classes, all classes for a mineral will only consist of its main component (mineral A contains 100% Al-wrought in all classes, mineral B contains 100% Al-cast in all classes, etc.). Table 9.2: Definition of liberation matrix for shredding for simulation 2 (a) and simulation 3 (b) Shredding matrix Classl Class2 I lass3 Class4 Class5 Class 1 (a) I(b) 0.05 0 I(~1 0 (b) 0 (a) 0 I(b) 0 (a) 0 (b) 0 (a) I (b) 0 Class 2 0.01 O.05 0.01 0.01 0 0 0 0 0 0 Class 3 0.05 0.10 0.05 0.05 0.05 0.05 0 0 0 0 Class 4 0.05 0.20 0.05 0.05 0.05 0.05 0.05 0.05 0 0 Class 5 0.89 0.60 0.89 0.89 0.9 0.9 0.95 0.95 1 1 Construction of the car (simulation 6) The data from Figure 4.9 can also be applied to change the construction of products. The influence of a decrease in connected materials in the design of the car on the final material recovery and on the output quality of the end product is simulated by defining the input of the recycling optimization model over more liberation classes (simulation 6). Table 9.4 describes the changed input definition. 9.2.6 Simulation results The results for the various simulations are described below. The objective function for all the simulations is to maximise the recovery of the aluminium minerals (A and B) coming from mechanical processing, while minimising the other mineral flows (C, D and E) in order to optimise the quality of the produced aluminium alloy. The defined recovery constraints (upper and lower limits) will remain constant for the various simulations. For each of the simulations, the changed settings are given above. For all the simulations, the boundary condition on the A1 content in the produced alloy was defined to be at least 85.0%. Table 9.5 shows the results of the various simulations. The recovery of mineral A and B (recovery from mechanical separation) is given, being the objective of the optimization. Mechanical separation operates on the optimization of mineral recovery. The recovery of the element aluminium (over the whole flowsheet) is depicted as well, which shows completely different values from the recovery on mineral basis, due to incomplete liberation. When maximising the recovery of minerals (A and B) coming from mechanical 9.2 Recycling optimization model Table 9.3" Definition of composition of liberation classes for simulation 4. Definition of liberation classes C m'k' ~ Mineral A Al wrought A1 cast Fe Cu Rest Lib.class 1 0.60 0.20 0.1C 0.05 0.05 Lib.class 2 0.70 0.15 0.1C 0.03 O.O2 Lib.class 3 0.75 0.10 0.1C 0.03 O.O2 Lib.class 4 0.95 0.05 0 0 0 Lib.class 5 1 0 0 0 0 Mineral B A1 wrought Al cast Fe Cu Rest Lib.class 1 0.30 0.50 0.1G 0.05 0.05 Lib.class 2 0.25 0.65 0.05 0.03 O.O2 Lib.class 3 0.10 0.75 0.10 0.03 O.O2 Lib.class 4 0.05 O.95 0 0 0 Lib.class 5 0 1 0 0 0 Mineral C A1 wrought A1 cast Fe Cu Res Lib.class 1 0.02 0.02 0.06 0.1 0.8 Lib.class 2 0.02 0.02 0.04 0.07 0.85 Lib.class 3 O.O2 0.02 0.03 0.03 0.9 Lib.class 4 0.015 0.015 0.01 0.01 0.95 Lib.class 5 0 0 0 D 1 Mineral D A1 wrought A1 cast Fe Cu Rest Lib.class 1 0.01 0.01 0.8 D.08 0.1 Lib.class 2 0.005 0.01 0.85 D.06 0.07 Lib.class 3 0.005 0.005 0.91 3.05 0.03 Lib.class 4 0.005 0.005 0.95 3.02 O.O2 Lib.class 5 0 0 1 D 0 Mineral E A1 wrought A1 cast Fe Cu Rest Lib.class 1 0.01 0.01 0.03 0.8 0.15 Lib.class 2 0.005 O.0O5 0.02 0.85 0.12 Lib.class 3 0.OO5 0.005 0.01 0.9 0.08 Lib.class 4 0 0 0.01 0.95 0.O4 Lib.class 5 0 0 0 1 0 Table 9.4: Definition of total input 1025 kg (composition and construction) of the car for simulation 6. Mineral (kg) Liberation class A{B Ic D {E Lib. class 1 5 10 100 400 5 Lib. class 2 5 10 50 200 5 Lib. class 3 5 10 50 100 5 Lib. class 4 0 5 50 0 5 Lib. class 5 0 0 0 0 0 ..... Material liberation & product design Table 9.5: Simulation results Recovery mineral Recovery A1 content Input primary A+B (%) A1 (%) in alloy (%) A1 (kg) Simulation 1 93.9 60.6 85.4 Simulation 2 94.3 61.6 86.1 Simulation 3 91.3 57.3 85.0 3.4 Simulation 4 93.9 70.1 86.0 Simulation 5 93.9 92.9 87.0 Simulation 6 94.2 66.6 86.0 processing, while minimising the other mineral flows (C, D and E) aluminium will be lost in these mineral streams. Moreover the A1 content of the produced alloy is given to illustrate the influence of changes in product design and liberation on the final alloy quality (which is obviously influenced by the objective of the optimization as well, which was however the same for all simulations). The results for the various simulations give a clear indication of the influence of the various parameters on the results of recycling. The results are discussed below briefly for the different simulations. 9 Simulation 1 is the base case scenario. For the given objective function and constraints imposed on the model (and the parameters as defined in Table 9.1) the recovery of mineral A and B, the aluminium recovery as well as the aluminium content of the produced alloy is calculated. The results of the other simulations due to changing liberation and design parameters will be compared to this simulation. 9 In simulation 2, the liberation of the minerals during shredding was improved by chang- ing the shredding matrix (see Table 9.2). Simulation 2 clearly indicates that an increased liberation will lead to a higher mineral recovery (since the recovery of the more liber- ated particles is defined as being higher in the model). The final aluminium recovery increases and consequently an improvement in alloy quality can be observed. 9 Simulation 3 illustrates the opposite. Due to decreased liberation of the materials, the recovery of the minerals A and B is decreasing, as well as the aluminium recovery. Obviously this trend can be observed in the output alloy composition as well. In this simulation, it was necessary to add primary aluminium in order to comply with the required constraint on the aluminium content of the alloy. 9 Simulation 4 shows the result for a better-designed product; in which undesired ma- terial combinations were reduced. As can be expected, this will be of no influence on the mineral recovery. However, the recovery of aluminium increases significantly. The output alloy composition also shows increased aluminium content. The same applies for simulation 5. In this simulation, the recovery of aluminium in- creased to almost the same value as the mineral recovery, due to the completely liberated particles. The small difference between mineral and aluminium recovery is caused by a small amount of organics present in the input for the metallurgical plant, due to im- perfect mechanical separation, causing losses. The recovery has however not reached a value of 100% due to the limitations of mechanical separation and losses during the metallurgical smelt operation. 9.3 Modelling of particle size reduction and liberation in recycling of ELV's 297 9 Due to the decrease in material connections in the design (input defined over more liberation classes) both the mineral as well as the aluminium recovery show an increased value in simulation 6. Consequently, this results in a higher purity of the produced alloy. 9.3 Modelling of particle size reduction and liberation in recycling of ELV's Models for the simulation and optimization of the recycling of passenger vehicles have been developed as discussed in Chapter 8 and in the previous paragraphs [51, 338] on the basis of particle size and liberation classes respectively. The first recycling optimization model discussed in Chapter 8 [51] defines the (separation of the) material streams based on particle size classes p and elements k (k --A1 wrought, A1 cast, Rest, Steel, Cu). The second model as discussed in the previous paragraphs [338] describes the material streams in terms of m minerals A to E (representing respectively Al-wrought, Al-cast, Rest, Steel and Cu based metals/minerals) and 1 liberation classes. The degree of liberation of a product is described by defining for each of the minerals A to E the fraction of the various elements k present in the particles of the material flows within the different liberation classes 1. In the first model the separation efficiency of the various physical separation steps is defined in terms of grade/recovery curves, whereas the second model describes the separation in terms of recovery only. The grade (based on metals/minerals m) and the exact composition of the streams (based on the elements k) can be calculated from the model. What is to date not been modelled for recycling systems is the combination of particle size distribution (size classes) and liberation classes in one model to investigate the interrelation between product design and recycling rate. Although the first and second model in a simplified manner disconnected particle size and liberation and therefore could give an indication of recycling rate, the mentioned combination gives a truer formulation of reality. The third model, which will be discussed in the next section, combines both the particle size and liberation. This approach also gives a good insight into what the breakage matrix for liberation looks like, revealing that classical minerals processing thinking cannot be applied directly to recycling systems [6]. 9.3.1 Design for recycling and design for environment Design for recycling and design for environment are the topic of many studies in literature as well as in industry. Graedel and Allenby [39] discusses that the concept of Industrial Ecology is one in which the cyclization of materials at their highest possible purity and utility level is of highest importance. This cyclization can only occur if materials from products that have reached the end of their useful life reenter the industrial flow stream and become incorporated into new products [39]. Graedel states that the efficiency with which cyclization occurs is highly dependent on the design of products and processes; it thus follows that designing for recycling (DfR) is one of the most important aspects of industrial ecology . It is discussed that Design for Recycling (DfR) should focus on a small number of rules defined by Graedel as given below[39, 40]: 9 minimise the use of materials; 9 minimise the materials diversity, i.e. the number of different materials used; 9 choose desirable materials, considering manufacturing, use characteristics, and recycling; 9 make it modular; 298 Material liberation ~ product design 9 make it efficient to disassemble; 9 make it easy to recover. These simple rules are part of many studies and discussions on Design for Recycling e.g. by Henstock [43], and Keoleian et al. [42] and have also been adopted by automotive industry [44, 45], although the latter focus in particular on design for dismantling. This will however lead only to a very small improvement in the recyclability; since dismantling is only beneficial to a certain extend due to its high labour costs. Design for Recovery has also been part of a EUCAR program (European council for automotive R&D) [339], which discusses design for recovery guidelines based on a combination of dismantling, shredding and PST processing (post shredding technology). Coppens et al. [340] discusses a design for recycling software tool developed by PSA Peugeot-Citron. This DFR methodology (software) focuses on dismantling. Although the design for recycling or design for recovery rules (e.g. EUCAR [339]) presented could be in principle correct, these are not supported by detailed knowledge of the behaviour of the recycling system and its material flows and will therefore never result in the total optimization of recycling based on improved design. The detailed technological knowledge, which is required to capture the complex interaction of processes and material and energy flows within the interconnected recycling system is lacking in these approaches. The crucial role of the quality of recycling (intermediate) products in the realisation of high recycling rates as well as the role of product design and its complex interaction with the liberation and recycling of end-of-life vehicles is not addressed. This implies that recycling cannot be optimised something that is often suggested in these studies without a fundamental basis. Design for recycling can never be realised, when the technological framework of recycling is represented in a too simplified manner and will therefore only result in very general and trivial guidelines. A comprehensive overview of the methods and tools supporting Design for Recycling/Environment is given by Bullinger [341]. Bullinger distinguishes three different categories in the existing tools; (1) literature/events, such as standards, guidelines, consulting, etc.; (2) conventional means of support in which a distinction can be made between tools focused on disassembly and materials (material compatibility matrices) and holistic tools; and (3) computer based means of support, focused on either disassembly, materials or on a holistic solution. However these methods are not supported by a sound technological and mathematical basis optimising the total recycling system (and not just dismantling orientated) in close link to the design of the product, e.g. the material compatibility matrices are not included in a the discussed recycling tools, linking liberation, separation efficiency to the grade of the intermediate recycling streams produced as is done in this Part. Only then the use of a material compatibility matrix makes sense. Most of the computer based tools are focused on design for environment, in which a solid technological description of the recycling system and its complex interaction to the design of the car is lacking. A design for recycling tool, Ecoscan-Dare has been developed by TNO [342]. This tool focuses mainly on WEEE (Waste from Electronic and Electronical equipment) and calculates environmental impact scores on the basis of the Eco-indicator '99 methodology. Although some technological insights in the recycling system are integrated in this tool, it does not capture the crucial role of liberation in relation to separation efficiency and recycling rate, making its application for design for recycling therefore debatable. Nagel and Meyer [343] discuss a method for systematically analysing and modelling end-of-life networks. However, this method, which focuses mainly of waste of electronic and electrical equipment (WEEE), covers in principal only the logistics of take-back schemes for WEEE, which is not really translated into a model. Any technological data on end-of-life processing (and process networks) is not included in the approach, although this plays a crucial role, also in view of the logistics of recycling networks. The recycling 9.3 Modelling shredding and liberation 299 optimization models as presented in this Part, which has its focus on the recycling phase, in relation to the dynamics of the resource cycle, could be adopted by Design for Recycling approaches and could fill in this lack of detail based on technological knowledge of recycling systems. This could lead to the improvement and refinement of Design for Recycling within Industrial Ecology and the automotive industry. Furthermore, by placing this work into a larger framework as e.g. described by Industrial Ecology (design for) recycling, based on a fundamental basis, would be placed into the broader scope of Design for Environment, in which the total life cycle impact is addressed. Although Graedel emphasis the effect of fastening parts together in the design of the car, this is only done from the perspective of efficient disassembly. The fastening of parts and combination of materials have not been linked to shredding, liberation and therefore the separation efficiency and quality of recycling (intermediate) products. 9.3.2 Particle liberation modelling of ELV's in relation to minerals processing The particle size reduction and the liberation of materials during shredding, which is among others determined by product design, will both affect the recycling of end-of-life products as is indicated by the two different models as discussed [51,338]. This is a well known fact from minerals processing technology [334]. In order to define the effect of both particle size and liberation on the separation efficiency, the composition of the intermediate recycling streams and the final metal/material recovery, it is essential to combine these two parameters (parti- cle size reduction and liberation) into one model, a fact that was not previously considered. Therefore, the two different models as discussed previously [51, 338] are combined into one final model, which includes the particle size reduction as well as the liberation of the mate- rials to describe the influence of product design and material combinations and connections (mineralogy), particle size of the product and material flows, and liberation (product/particle composition) on the (optimization of) recycling end-of-life vehicles [6]. This model is devel- oped using the knowledge available from the modelling and simulation of minerals processing systems [334] and integrating this into simulation models as defined by Reuter and van De- venter [309]. King [334] discusses the quantitative modelling of the unit operations of minerals processing, for which the modelling of particle size and liberation are essential. The modelling of both particle size and liberation is based on combined distributions as well as population balance methodology. The modelling is based on the definition of the distribution of particles in a size-composition space (matrix). Liberation is modelled only to the extent that is neces- sary to provide the link between comminution and mineral recovery. In spite of a difference in comminution behaviour of mineral ores compared to man-made products, the same principle for the definition of the relation between particle size and liberation (expressed as grade in minerals processing) can be applied to describe the particle size related to the liberation for the modelling of the comminution and separation of any end-of-life consumer product. It is discussed by King [334] that during comminution of mineral ores there is a natural tendency towards liberation and particles that are smaller than the mineral grains that occur in the ore can appear as a single mineral. This happens when the particle is formed entirely within a mineral grain, but is impossible when the particle is substantially larger than the mineral grains in the ore. However, King [334] discusses that the distributions of particles with respect to the composition do show some regular features particularly with respect to the variation of the distribution with particle size. This is however not necessarily the case for the comminu- tion of modern consumer products of which the design and the related particle size reduction and liberation behaviour is much more complex than that of mineral ores. This is often the Material liberation &: product design case due to the metals/mineral not being finely divided in the consumer products as is the case for geological ores. Due to the design and construction of the car it is difficult to define a grain size of the 'minerals'/elements in the product. The grain size of any metal/mineral in a modern consumer product such as the car is not defined by natural mineralogy, but by continuously changing design, composition, size and connection of the various elements created by man and can differ from car to car as well as over time. This implies that what is true for classical grinding i.e. the finer the grind the more liberated particles become is not necessarily true for shredding of end-of-life consumer goods. The models for liberation as described by King [334] are specific to mineralogical textures that consist of only two minerals -a valuable species and all the other minerals that are present and which are classified as gangue minerals. Although the techniques that are used can be applied to multi-component ores, King [334] discusses that the details of a suitable analysis are not yet worked out and are therefore not discussed. The modelling of the comminution of consumer products such as cars can however not be performed on a two component system, but requires the description of all (major) elements present in the car. Many elements building up the car have to be considered as economically valuable and/or environmentally relevant species. The contamination of one element flow, even with a low quantity of other elements, due to e.g. incomplete liberation could have direct implications for the final recovery rate to be achieved (e.g. the maximum concentration of Cu allowed in steel is 0.25%). It is discussed by Gay [344] that it is essential to model multi-phase particles, instead of binary particles on which most research effort in minerals processing has focused, since: 9 particles are multi-phase; 9 scparation efficiency is determined by mineral association; 9 particle breakage is not controlled by the mineral of interest but by the presence of all minerals. It is clear that the same applies for the liberation of the various materials composing the car, for which most of the materials represent an economic value as well, this in contradiction to traditional minerals. Gay [344] defines the multi-phase particles as particle types, in which particles with very similar composition properties are grouped. Hence modelling is applied to particle types rather than individual particles. Metha [345] also developed a liberation model for multi-component minerals. However due to the fundamental difference in the breakage behaviour as well as the complexity of materials between minerals and complex time-varying consumer products such as the car, these models cannot simply be applied for the modelling of car recycling. Gay [344] discusses a liberation model for communication of multi-component particles based on probability theory to determine the relation between the feed and the product particles. Since the design of the car is in essence defined on a completely different basis than the car after shredding, consisting of liberated and un-liberated particles, it can be stated that modelling and predicting the relation between the feed 'particle', which is in fact the car, and the product particles is complicated and differs from modelling this relation for minerals and ores. In order to increase the degree of liberation, particles need to be broken as fine as possible [344]; however by decreasing particle size, energy costs substantially increase, and it becomes more difficult to separate particles. The same principle applies for the shredding of the car. There is a practical limitation to which the car can be shredded and particle size can be reduced, not only due to shredding process costs, but as well as due to a restriction of physical separation processes to process fine materials. In current recycling practice, the 0-10 mm fraction after shredding is in most plants still being land 9.3 Modelling shredding and liberation 301 filled. The effect of particle size on the recovery (or particle throw) of non-ferrous metals is mentioned by Van der Beek et al. [346], Rem [347], Zhang et al. [348] and Maraspina et al. [349]. Moreover some types of joints cannot be destroyed by shredding (e.g. surface type connections such as hylite, Castro et al. [176]). Additionally, the degree of liberation of metal particles could also decrease during shredding due to the intensive plastic deformation these particles undergo in the shredder [350, 351]. As a consequence, materials that were not connected in the design can become attached in particles after shredding. This reveals the fundamental difference between the comminution of minerals, which are all brittle, and the shredding of cars, of which most of the materials or ductile. This leads to a fundamental difference in the breakage behaviour of minerals and consumer goods. In addition, a smaller particle size due to intensive shredding means an increase of particle specific surface area, what could lead to oxidation losses (decrease of metal yield) in reactive metals such as aluminium and magnesium [352]. As indicated by King [334], the simulation of multi-component/mineral liberation is difficult. This work and developed model attempts a first step into the direction of simulating multi-component/mineral liberation systems. The model remains on the system level and uses simplified liberation models. 9.3.3 Flowsheet of the model for recycling end-of-life vehicles A simplified flowsheet (Figure 9.4) has been derived from the detailed recycling flowsheet for ELV's as depicted by Figure 8.4 [324]. This flowsheet forms the basis for the particle size and liberation based recycling optimization model as discussed here, and is also an expansion to the flow sheet discussed previously (above and in Chapter 8). This flowsheet includes not just the metallurgical processing of aluminium as was discussed in Chapter 8, but also of steel and copper. This makes it possible to include the recovery of all metals defined in the models, as well as their quality (of the in-and output of the metallurgical processes) in the modelling and optimization, as well as in the calculation of the recycling rate [6]. The flow sheet of Figure 9.4 is very similar to that of Figure 9.2, however the model includes the particle size classes and mixing operations in order to model both particle size and liberation. 9.3.4 Phase description of the model Mineral classes (m) /Particle classes (p) The mass (kg) of the material flows ym,p in the recycling flowsheet (Figure 9.4) is described in the model based on the minerals A to E, distributed over the defined particle size classes p (see Table 9.6(a)). Element classes (k)/ Liberation classes (1) For each of the particle size classes in a specific material flow Yim'P a discrete 'distribution' of material over the liberation classes l -1 to 5 is defined in the liberation/particle size rap/ matrix Ly~ ' ' (see Table 9.1(b)), which is in principle similar to the definition of the particle ,.mpl distribution in the size-composition space as discussed by King [334]. This matrix Ly i ' ' defines thus for each mineral m the fraction of material present in liberation classes l -1 to 5 for the different particle size classes p for the material stream Yi after each unit operation i. This matrix is also defined for the model input (being the car), describing in this way the particle size classes and liberation classes determined by the design of the car. The composition matrix C m'l'k defines for each mineral m the composition of the different liberation classes 1 for the elements k (see Table 9.6(c)) as discussed previously in this chapter [338]. Table 9.6(c) 9.3 Modelling shredding and liberation summarises an example for the definition of the composition of the liberation classes in the model for a mineral A (in this case a mineral with Al-wrought being the major component). Similarly there are minerals B (Al-cast rich), C (Plastic rich/rest), D (Steel-rich) and E (Cu-rich). Table 9.6: Typical examples of the phase model as used for simulations for mineral A. Defi- nition of: (a) mass based particle size distribution of the input (y~n,p); (b) liberation/particle size matrix L"Yirn,p,l ; (c) composition matrix of liberation classes (C m,kJ) for mineral A; and also B to E (bold gives the name of the metal/mineral) (a) Particle size class A IB Mineral (kg) i D E Part. size class 1 15 30 , 250 700 25 Part. size class 2 0 0 Io 0 0 Part. size class 3 0 0 0 0 0 Part. size class 4 0 0 0 0 0 Part. size class 5 0 0 (b) 0 0 0 Lib. cls. Lib. cls. Lib. cls. Lib. cls. Lib. cls. 1 (l[) . 2 (ll) . 3 (lI) . 4 (ll) . 5 (ll) A in ELV Part. sz. cls. 1 0.200 0.200 0.200 0.200 0.200 A in ELV Part. sz. cls. 2 0.000 0.250 0.250 0.250 0.250 A in ELV Part. sz. cls. 3 0.000 0.000 0.333 0.333 0.333 A in ELV Part. sz. cls. 4 0.000 0.000 0.000 0.500 0.500 A in ELV Part. sz. cls. 5 0.000 0.000 0.000 0.000 1.000 (c) Definition of liberation classes Mineral A AI wrought AI cast Fe Cu Rest Lib. class 1 0.5 0.2 0.2 0.05 0.05 Lib. class 2 0.65 0.15 0.15 0.03 0.02 Lib. class 3 0.75 0.1 0.1 0.03 0.02 Lib. class 4 0.87 0.05 0.05 0.02 0.01 Lib. class 5 1 0 0 0 0 Mineral B AI wrought AI cast Fe Cu Rest Lib. class 1 0.2 0.5 0.2 0.05 0.05 Lib. class 2 0.15 0.65 0.15 0.03 0.02 Lib. class 3 0.1 0.75 0.1 0.03 0.02 Lib. class 4 0.05 0.87 0.05 0.02 0.01 Lib. class 5 0 1 0 0 0 Mineral C AI wrought AI cast Fe Cu Rest Lib. class 1 0.04 0.04 0.06 0.06 0.8 Lib. class 2 0.03 0.03 0.04 0.05 0.85 Lib. class 3 0.02 0.02 0.03 0.03 0.9 Lib. class 4 0.015 0.015 0.01 0.01 0.95 Lib. class 5 0 0 0 0 1 Mineral D Al wrought Al cast Fe Cu Rest Lib. class 1 0.01 0.01 0.8 0.08 0.1 Lib. class 2 0.01 0.01 0.85 0.06 0.07 Lib. class 3 0.01 0.01 0.9 0.05 0.03 Lib. class 4 0.005 0.005 0.95 0.02 0.02 Lib. class 5 0 0 1 0 0 Mineral E A1 wrought Al cast Fe Cu Rest Lib. class 1 0.01 0.01 0.03 0.8 0.15 Lib. class 2 0.005 0.005 0.02 0.85 0.12 Lib. class 3 0.005 0.005 0.01 0.9 0.08 Lib. class 4 0 0 0.01 0.95 0.04 Lib. class 5 0 0 0 1 0 9.3.5 Alloy types The output of the metallurgical processes has to comply with constraints on the alloy composi- tion. Since each element is described separately in the composition matrices C m'l,k composing the various minerals, the output of the metallurgical operation can be calculated by adding 304 Material liberation 8z product design all elements present in the various material flows, being the input for metallurgical processing (see Figure 9.4). This implies that elements must be added from the different size classes p, mpl of which the composition is defined by combining the liberation/particle size matrix Ly i ' ' and the composition matrix C m'l'k. The grade of mechanical separation can also be calcu- lated from the model. Aluminium is described in the model as wrought or cast, each with its own specific (average) composition. To be able to calculate the produced alloy type, the composition of the wrought and cast aluminium is described in a separate alloy matrix in the model. Together with the contaminants or alloying elements ending up in the alloy, the exact alloy composition can be calculated from the model based on the degree of liberation and can be controlled by defining boundary conditions on the output i.e. the metal quality. Primary materials (aluminium and alloying elements) often have to be added to produce a required alloy composition due to losses in the system. These primary materials are defined as one of the input streams of the model. The addition of primary materials must be kept to a minimum, for economical and environmental reasons. This can be realised by including negative cost penalties to the primary materials in the objective function of the recycling optimization model. 9.3.6 Separation models Since the performance of an unit operation is related to the particle size and degree of lib- eration of the feed of the processes, the separation can be defined for different ranges of size classes p and liberation classes I. The transformation matrices Ty m'p'~, Tx m'p'~ and Tz m'p'l (see the example in Table 9.7) define the recovery values for each mineral m for each particle size class p and liberation class I for mechanical separation processes i for respectively stream yi, xi and zi. The difference in separation efficiency (recovery) is determined by the size class as well as the degree of liberation. However, the influence of the each individual material present in a non-liberated particle cannot be expressed in the recovery rate for mechanical separation (e.g. the presence of 10% Fe in A1 will have another effect on the recovery rate for Eddy Current separation than the presence of 10% organic materials). An additional distinc- tion should be made for the different material combinations possible in a certain liberation class to be able to model this. This is however not taken into consideration in the defined model in this chapter, but is an important issue. Table 9.7: Example of a transformation matrix Ty m'p'l with the recovery values for each individual particle size class p and liberation class l defined for m = mineral A for separation process i = 5 (Eddy Current separation- Figure 9.4) flowing to the product stream Yi ,,mplTy i '' (m = mineral A) [Lib. Lib. I Lib. I Lib. Lib. class 1 class 2 class 3 class 4 class 5 i=5 Part. sz. cls. 1 0.8000 0.8400 0.8800 0.9200 0.9600 Eddy Part. sz. cls. 2 0.8000 0.8400 0.8800 0.9200 0.9600 Current Part. sz. cls. 3 0.8000 0.8400 0.8800 0.9200 0.9600 Part. sz. cls. 4 0.8000 0.8400 0.8800 0.9200 0.9600 Part. sz. cls. 5 0.2000 0.2000 0.2000 0.2000 0.3000 9.3 Modelling shredding and liberation i--1 ton m ,p ,! m ,p ,I ' "Yi f Unit operation (i) --~ Unit operation (j) ~-~ i Figure 9.5: General overview of mass flows over unit operation i and j for each mineral m in a particle size class p and liberation class l 9.3.7 Formulation of the recycling optimization model From the recycling flowsheet (Figure 9.4) four different types of processes can be defined viz. shredding, mechanical separation, mixing and metallurgical processing. Since these operations are fundamentally different, the model describes the flow of materials in the recycling system for these operations in a different way. The description of these unit operations in the recycling optimization model is discussed below in four separate sections. As discussed in Chapter 8 [51] two types of equations can in principal describe the flow of materials in the system of processes and the structure of the network for each individual mineral/element present in the car viz.: 9 mass balance equations, including structural parameters for each mineral m, element k, particle class p, and liberation class 1 and; 9 separation efficiency models for each of the unit operations for each mineral m, element k, particle class p, and liberation class l; which are both based on: 9 liberation distributions of liberation classes 1 for each mineral m and particle size class p and; 9 the composition of each liberation class l based on elements k for each mineral m. The various parameters playing a role in the efficiency of the material cycle (economy, legislation, etc.) can be translated into constraints imposed onto the model, the equations mentioned and an objective function for optimization. These theoretical equations comprise the basis of the model, giving the constraints imposed on the system. The material flows for the minerals m (defined based on elements k) in different size classes p and liberation classes 1 between the unit operations and interconnections between these processes as depicted in the recycling flow sheet of Figure 9.4 can be simplified and generalised as shown in Figure 9.5. Formulation of model for shredding The transition of the particle size as well as of the liberation class distribution within the particle size classes due to the shredding operation can be defined in the model based on shredding transformation matrices. This is similar as defined by Reuter and Van Deventer Material liberation & product design [309] for milling and flotation plants. However the transitions of particle size and liberation class are defined in separate transformation matrices. It is possible to define a transformation matrix for the transition of the particle size distributions over shredding S]~ n'p:f'p~ , where pi is the particle size class of the feed f, whereas py is defined for the output y. The assumption has been made that all materials defined as A1 (cast & wrought), Fe, Cu and rest based minerals (i.e. minerals A to E), break according to the same shredding transformation matrix (for the particle size reduction). This is obviously a simplification, since the various materials will break differently due to their specific mechanical properties, joining method, design, complexity and require therefore different transformation matrices. Separate matrices can however be defined for each mineral, but this was not done in this model. Since no data is available on the transition of liberation class distributions during shredding no reliable definition for the shredding matrix for the liberation class transition could be presented here. Moreover, the definition of a liberation class transition matrix would require detailed insight into the relation between the particle size and liberation class transition, which is unknown for complex products such as cars. However the modelling of transition of the liberation class distribution can be described sufficiently based on a mass balance over the shredding operation for the elements k building up the liberation classes 1 as defined in the composition matrix for liberation C m'l'k. The shredding matrix for particle size class transition is changing the distribution of the mass flow of the minerals m over the different particle size classes p after shredding. Therefore, the shredding matrix for the liberation class transition would change the definition of matrix Lf~ 'p'z to Ly'~ 'p't due to the shredding operation. It changes the distribution of liberation classes in the different particle size classes p for each mineral m. Mass balance for shredding for i = 2 in Figure 9.4 (shredder -particle size re- duction) A mass balance can be set up over the shredding operation, which describes the transition of the mass flow over the particle size classes p for each mineral m (Eq. 9.11 and Eq. 9.11). Since no separation takes place (the in- and output of the shredder are both defined as one stream distributed over the particle size classes) no separation efficiency equation for the shredding operation is defined. (9.11) \p~--1 with pu=5 E sfm'P"P~ = 1 (9.12) pu:l Liberation during shredding The shredding operation will change the definition of the liberation of the various minerals in the different particle size classes p as given in the particle size/liberation matrix Lf m'p'l. The relation between the liberation class distribution of the in- and output of the shredder can be described by Eq. 9.13 and Eq. 9.14. (9.13) p--1 p=l \/=1 with /--5 y: Lyy = 1 (9.14) /--1 9.3 Modelling shredding and liberation Formulation of model for mechanical separation processes Mass balance mechanical separation The mass balance equations define the flow of the material streams between the different unit operations and the structure of the network of processes. For the two unit operations i and j as represented in Figure 9.5 the mass balance constraint defined by Eq. 9.15, Eq. 9.16 and Eq. 9.17 may be derived. The mass balance for mechanical separation is defined here for a single input stream, since the mixing operation (see Figure 9.4) will transform a multiple input for mechanical separation into one stream and is therefore defined and modelled as a different process type. The mass balance for mixing must therefore hold for a multiple input stream (if the mixing step was not defined, this must also hold for mechanical separation). Iy ,~ -y7 ~,, -~7 ~,~ -zy,~ = 0 (9.~5) and y?'" = ~,j. y?'" (9.16) n 0<c~ O_<1 and ~ o~ 0 =1 for all j (9.17) i--1 Although in the model, the mass balance is calculated based on particle size classes, the mass balance over the mechanical separation must also close for the mass flows over both particle size and liberation classes. Since during mechanical separation no transformation of particle size classes as well as liberation classes will take place, the following mass balance equation (Eq. 9.18 to Eq. 9.21) also holds for mechanical separation: fm,p,l ,. m,p,l .l i -Yi -x'~ 'p'4 -z'~ 'p'4 --0 (9.18) and fm,pJ _ ~0 " y~. ,p,l (9.19) with yy,,,~ = Lyy,., ~ . yy,~ (9.20) and 4--5 Lyy ,~,~ = 1 (9.21) 4--1 Separation efficiency of mechanical separation processes (recovery based mod- elling) The recovery of a mineral during mechanical separation is determined by both the influence of particle size as well as liberation on the separation efficiency. Therefore it is essential to describe the separation efficiency equation based on both particle size as well on liberation. Eq. 9.22 to Eq. 9.25 define the separation efficiency equations for mechanical m p 4 m p,l m p l separation in the model. The transformation matrices Ty i ' ', Txi ' ' and Tz i ' ' (see Table 9.7) define the recovery values for each mineral m for each particle size class p and liberation class l for mechanical separation processes i for respectively stream yi (Eq. 9.22), xi (Eq. 9.23) and zi (Eq. 9.24). (1 - .,mplTui ' ' )" y,~,p,l _ Ty~,p,l . xm,P,l _ Ty,~,p,l . zm,p,l _ 0 (9.22) (1 -Txm'P'l) 9 x'~ 'p'l -Tx m'p'l . y,~,p,l _ Tx,~,p,l . zm,p,Z = 0 (9.23) (1 - Tz'~'P'4) " z'~ 'p'4 -Tz~ 'p'4 " y,~,p,4 _ Tzm,p,4 . x,~,p,4 = 0 (9.24) Material liberation/~ product design where: Ty m'p'l + Tx m'p't + Tz m'p'l = 1 (9.25) During mechanical separation, the definition of the distribution of materials within particle size class p over liberation class l will change, due to the fact that for each mineral the recov- ery values can differ per particle size and liberation class. The defined particle size/liberation matrix will therefore change after each mechanical separation step, according to the defined recovery values in the transformation matrix for mechanical separation efficiency. The trans- formation of the particle size/liberation matrix L ~ yirn,p,l due to redistribution of the material streams during mechanical separation is defined by Eq. 9.26. Ty i m ,p,l .L L m ,,p l = Ly~ 'p't (9.26) /--5 E (TY~ 'p't" Lf m'p't) /=1 fm,p,l of unit where: L.f~ 'p't is the particle size/liberation matrix of the feed stream Ji operation i (see Figure 9.5). Dividing by the summation in Eq. 9.26 is required to normalise the particle size/liberation class distribution. Similar equations hold for the streams x~ 'p'l and z m'p'L. Formulation of model for mixing A mixer is being defined in the model in order to convert multiple input streams, with each their own corresponding particle size/liberation matrix Lf m'p'l to one stream, with its cor- responding new particle size/liberation matrix, determined by the ratio between the various input streams. The mass balance holding for the mixing unit operations is given by Eq. 9.27 and Eq. 9.28. FS 'p -uS'" = o (9.27) where: n FS, = ym, + U?,, (9.28) j--1 Since no transformation of particle size and liberation classes takes place during mixing, the following equation can also be defined for the mixing operation (Eq. 9.29)" F~,p,l _ y,~,p,l ._ 0 (9.29) where: n FS ,',' = y?,',' + y?,',' (9.30) j----1 Since no separation takes place, no separation efficiency has to be defined for mixing. The transformation of the particle size/liberation matrices Lye. 'p'l and Lf m'p'l of the various input streams aij 9 y~'P and f~'P of the mixing operation to a new particle size/liberation matrix Lyr~ 'p'l of the output of the mixer is defined by the following equation (Eq. 9.31). 9.3 Modelling shredding and liberation fm,p m p l n ym,p m,p,l 9 Lf~_ ' ' + V'~o~ij. j 9L"yj j=l n fS'" + E j=l n fg'P" L f? 'r''t + E aij " y~. ,r,. Ly,~,r,,t 3--1 mpl m,p = Ly i '' (9.31) Formulation of model for metallurgical processing The mass balance as well as the separation efficiency (recovery) of the metallurgical operations can be described in one equation (see Eq. 9.32). For the mass balance and separation efficiency for metallurgical processing the following equations (Eq. 9.32, Eq. 9.33 and Eq. 9.34) may be derived, representing respectively the mass balance and separation for stream y~, x i k and z/k . --\m--'l \l-'-1 n f?'P'l " cm,k,l . fm,p . Ryk,p _ yk i ~. 0 (9.32) p~l LI2,p, l . cm,k, Z . f~ m,p 9 Rxk,P _ X i k _. 0 (9.33) ---\m---1 = (9.34) where" (9.35) Eq. 9.32, Eq. 9.33 and Eq. 9.34 calculate the fraction of each element k (A1 wrought, A1 cast, Steel, Cu and rest) present in each mineral class m of the input stream f~ mpl' ' of met- allurgical processing for the sum of all liberation classes based on the particle size/liberation matrix of the input Lf~ 'p't and composition matrix C m'k't. The mass flows of the elements k (A1 wrought, cast etc.) present in each mineral m are determined from the calculated frac- tions by multiplication the fractions with the mass flow of the input stream for each mineral m fm,p. A transition from mineral m to element k is being made by adding up element k over all mineral classes m (mineral A becomes A1 wrought, mineral B A1 cast, etc.). The mass balance and separation efficiency over the metallurgical processing for each of these elements k p k,p k p 9 9 k is calculated based on the recovery values Ry i ' , Rx i ' and Rz i ' as gwen m the model. Since in the output of metallurgical processes the definition of particle size classes make no sense, the recovered elements k are added up over all particle size classes or just simply alloy classes, the output Yk, xk and Zk are only defined per element k. Therefore Eq. 9.32, Eq. 9.33 and Eq. 9.34 define the mass balance on element basis and not on mineral basis. The recovery values Ry k'p, Rx k'p and Rz k'p can be a fixed value or can be dependent on the concentration of contaminants in the feed stream. The recovery value is then represented by (Eq. 9.36): Rye'; --= 0 (9.36) 310 Material liberation gz product design where: If k'v is e.g. the organic content of the aluminium fraction being the input of the metallurgical process, and a v and bp are plant parameters (where bp is equal to the recovery value for a certain size class p as given in the matrix) that define the variation of recovery as a function of If k'p. The same applies to Rx k'p and Rz k'v. The recovery values for metallurgical processing are only defined as being dependent on the particle size class, but not on the liberation class. The influence of liberation on the final metal recovery is taken into consideration by including the influence of the other elements, such as organics (- rest stream). Alloy composition The control and therefore the modelling of the alloy quality (composition) of the produced alloy are of utmost importance for the economic production of high quality metal products and the minimisation of waste production. The output composition of the metallurgical operation can be calculated by adding all elements present in the various material flows. The input to metallurgical processing (see Figure 9.4) is in the form of different size classes p, of which ,,mpl the composition is defined by combining the liberation/particle size matrix Ly i ' ' and the composition matrix C m'l'k. The different aluminium alloys (wrought and cast), each with their own specific (average) composition is described by an alloy composition matrix in the model. The matrix defines the pure alloying elements for the defined aluminium alloys. 9.3.8 Parameterisation of the model During product design, materials are chosen, and its combinations and connections among them are defined. These decisions will determine the mineralogy of the products and liberation attained by shredding, affecting the quality of intermediate recycling streams, the possibilities of material recovery and therefore the recycling rate of the product. Some connections between materials cannot be broken during shredding due to characteristics such as shape, size and strength of the connections, and ultimately due to the intrinsic randomness of the fracture paths originating from this comminution process [353]. This may result into the incomplete liberation of the materials connected. The two or more materials that remain attached in the non-liberated particles will end up in intermediate and product streams as dictated by the properties of the incompletely liberate particles after mechanical separation. These particles may therefore introduce foreign materials in the recovered stream that cannot be economically treated in the current thermal processing and/or pyrometallurgical systems as a function of thermodynamic limitations [33]. Data on liberation and particle size reduction during shredding Data on the liberation of materials during shredding and data on the composition of the various liberation classes have never been measured up till now. Therefore estimations on this had to be made to set up the models. However the theoretical, model-based approach as presented in this and the previous chapter lays down a solid framework for data collection when setting up or performing recycling experiments. From various industrial experiments and shredder plants, which all involved a large number of car wrecks that were shredded and subsequently separated, data on both particle size reduction and liberation have been collected by sampling the various material flows within the shredder plants and analysing the composition, liberation distribution and the characteristics of the un-liberated particles. In Figure 9.6 to Figure 9.12 an impression is given from the appearance and material combinations encountered in the un-liberated particles/fractions. The different images given in Figure 9.6 to Figure 9.12 reveal 9.3 Modelling shredding and liberation 311 (a) (b) Figure 9.6: (a) Hose clamp (steel) with rubber hose and copper; (b) Fragment of engine block -cast aluminium and steel 0 (a) (b) Figure 9.7: (a) Drive shaft -steel and rubber; (b) Fragment of cylinder head -cast aluminium, steel and copper (valve guide) immediately the influence of design, i.e. material combinations and types of connections, on the liberation and therefore on the maximum achievable quality of recycling (intermediate) products. Moreover Figure 9.6 to Figure 9.12 illustrate the complexity of describing the liberation and capturing the composition of the liberation classes in a model as discussed above. The data as represented by the different images of Figure 9.6 to Figure 9.12 have been structured in order to function as a calibration for the developed models as discussed above as well as to be used as a basis for the further development and improvement of the models as developed up till now. These data are presented by Figure 9.13 to Figure 9.31. Due to the complexity of the data (see the diverse liberation properties in Figure 9.6 to Figure 9.12) it is difficult to define the composition matrix of liberation classes C m'l'k as discussed above, which captures all possible two-and multi-component material combinations in the un-liberated particles. Figure 9.13 gives the distribution of the liberated and un-liberated fraction over the four different particle size classes of the non-ferrous fraction after shredding, air suction and magnetic separation. Figure 9.14 presents the distribution of the "mineral" combinations in the un-liberated fraction for each particle size class as given in Figure 9.13, whereas Figure 9.15 312 Material liberation & product design (a) (b) Figure 9.8: (a) Rubber with cable tree (copper and plastics); (b) Fragment of engine block- cast aluminium and steel bolts (a) (b) Figure 9.9: (a) Hose clamp (steel) on rubber hose; (b) 1 -Coils-copper and soft iron, 2 -Fragment of engine block-cast aluminium and steel bolts, 3 -Electronics-plastics and copper (a) (b) Figure 9.10: (a) Radiator-copper, brass, tin; (b) Radiator-copper, aluminium, plastics 9.3 Modelling shredding and liberation 313 (a) (b) Figure 9.11" (a) Cylinder head-cast aluminium with steel insert; (b) 1 -Steering house-cast aluminium and steel, 2 -Cylinder head-cast aluminium and steel e, (a) (b) Figure 9.12: (a) Fragments of cylinder heads -cast aluminium and steel, valves -steel, and valve guide-copper; (b) Fragment of gear box housing-cast aluminium with steel bolts 314 Material liberation & product design Liberation non-ferrous fraction Frequency OH Un-liberated aLibemted ] 0-20 nun 20-50 nun 50-100 nun > 100 mm Psrdcle size cltu~ Figure 9.13: Distribution of liberated and non-liberated particles in the non-ferrous fraction for different particle size classes (after shredding, air suction and magnetic separation) DJmtrJbutlonof minerub in the un4beruted fr~'tiom per particle size chum Figure 9.14: Distribution of the various minerals in the un-liberated fraction for each particle size class in the non-ferrous fraction (after shredding, air suction and magnetic separation) to Figure 9.31 illustrate for each mineral the various material combinations occurring in the un- liberated fraction for the different particle size fractions. The liberation data as represented in Figure 9.13 to Figure 9.31 is subject to a standard deviation on the measurements and analyses from the plant data, which is 0.3% for the mass flows and 5% for the analyses (material combinations in the un-liberated fractions). Figure 9.32 [354] depicts the particle size/liberation matrix f m,p,l for the mineral alu- minium in the NF fraction (see Figure 9.13). Figure 9.33 illustrates the composition matrix (Cm'l'k) representing the mass distribution of the different elements in the different liberation classes of aluminium in NF 20-50 mm (see Figure 9.32). Figure 9.34 depicts in detail the various material combinations in the un-liberated particles (liberation classes of Figure 9.33) for aluminium in NF 20-50 mm. For each particle type, in each liberation class, the mass per- centage of the different elements composing the particle is represented. Different connection types have been defined in order to predict the breakage and liberation during shredding as a function of design choices on materials associations and the type of connection (see Figure 9.35). 9.3 Modelling shredding and liberation 315 Mad ~mabmmmakmmhmu-.~.~ nm~ ~F 0-20 mm) n~r~n~ GOtham mole, [ i'--NT~ im ,, m imp-...am.mss m m m m m-mco~., Dlvlliimd~ auml~makm,hmu-~.~--..i.~ mm~mlml~m(l~ e-~$ ram) , mm~r~mm i tom--. i P~ i IIP~ i =~m~ l==i .~ mc~ (~) (b) Figure 9.15: Material combinations in (a) un-liberated steel; (b) un-liberated A1-NF fraction 0-20 mm ~ mwm mob,.. NOn--- mwoo~ iT~lliam mFom mPl.,~. m. ma,.. m.-.- mt..d ru~m.em.mm Im^hmmmmmm m~..n (~) (b) Figure 9.16: Material combinations in (a) un-liberated copper; (b) un-liberated zinc-NF fraction 0-20 mm mo,~,. mole m,~,~ NF.. m~ ~ cuik,u,l kmu-Ukrm~m m~ma~m~mre-z$ ram) 03 .. ol i o ill,n, (a) (b) mw,,. mO,h.. mo,-- mw,,~ ml'~,.. ml,m mK.,.,. m~ m~,.. m.-- m,--, mc~iplM. Clm~ mm^hn,amm msm.l Figure 9.17: Material combinations in (a) un-liberated brass; (b) un-liberated plastics-NF fraction 0-20 mm 316 Material liberation & product design Mmr~Ud amnmimmeUah ue-mmtrmNdhlmimerOqlm'~ m'--) .... m m m m m mmm.. m Mamwhm amdmdmmlkm m~r.,. mo,m-- mo~., mwo,~ m'r~aikm mF.. mlt,,m.,. ml.u.,k~ m~ mm-- mz~ mr..,, mc~mm- rm~ m~,-,,--- ma~l (a) (b) Imo~ Imw~ NF~ Im~ Im~ mc~ m~ Figure 9.18: Material combinations in (a) un-liberated rubber; (b) un-liberated textiles-NF fraction 0-20 mm Figure 9.19: Material combinations in un-liberated glass-NF fraction 0-20 mm Mmrg~ ~uu~uud~u b ~ I~0 (l~r SO-SOmi) 1 I ............ v,] 0, o., n os 07 o 7 0.6 mm ....... ~~ ~.... 04 O3 N -- 9I o2 o o, MM in o --- ~ ee//~m b ,m.ienw d~hl~ (~ ~Se mm) m .... m ...... _....=m___ (a) (b) nw~e IICXlm~ Ib IlWood iFmm \| 7~,.. NL~I n~ D~ m^~ Figure 9.20" Material combinations in (a) un-liberated steel; (b) un-liberated A1 -NF fraction 20-50 mm 9.3 Modelling shredding and liberation 317 l 09 os o7 "roe O4 O3 O2 0.! 0 ~lilii~il iiilI~lll~ll IlI ill-III~ Ill,If (~lI ~l-~I i ) liB\|B lllr~ lOllxml lOllm lWmxl l're~dm IF~ lR~bb=r ml'b,~ lBnm IW mr-~m~ D M,~mT---.--- (a) (b) Figure 9.21: Material combinations in (a) un-liberated copper; (b) un-liberated lead-NF fraction 20-50 mm i 1 nil 1///./ ! 2 ) 4 IOd~n lolllWood ITnulm iI~\| IMimcslSS Ih IZJl~ II~ml U~ II^~ lSw~ (a) (b) Figure 9.22" Material combinations in (a) un-liberated zinc; (b) un-liberated brass-NF fraction 20-50 mm 0.3 i I w--e.~-1Texuim IFcmm i i 1R~ O2 IP~ mss momm i"-~ n. mc~ Q~ _. m~l (a) (b) Figure 9.23: Material combinations in (a) un-liberated SS; (b) un-liberated plastics-NF fraction 20-50 mm 318 Material liberation & product design MmrW ~ m~ierm4 rdd~ (NF 2e-S$----) O.5 -mw',,,, I -" B~ 04 IWood ilTeou~ks o 3 ~ _ meo,mi m "-O.2 IlSS I-:..I "'-o.i lllLmel\| "~" ! 09 0.8 07 ~'06 O.4 0.I O.2 0.1 0 (a) (b) Figure 9.24: Material combinations in (a) un-liberated rubber; (b) un-liberated glass-NF fraction 20-50 mm Figure 9.25: Material combinations in un-liberated wires NF fraction 20-50 mm o7 06 o, ~o. m )0, m o, m o, m .~ mo~,, ......... ~ ildl~ Iml'a,m imm~w, imPu,,u~ ...... m~ m i\|t.~ me.op~ E__ __!1 ~ ......... u.,, os ot 06 i o,04 03 O2 0! 0 Mmrlel ~ a-m~UkrNd akmdmkm (I~P'se..lee ~) ,, m m m m m m m _ m m m-_J~-J mod~ molm mwood mTeaUiw ~mPl~ Rss ]lBmm jm~ IL~ \|^~,-- ~.~__. ~..~ ~.~-,~ (a) (b) Figure 9.26: Material combinations in (a) un-liberated steel; (b) un-liberated A1 -NF fraction 50-100 mm 9.3 Modelling shredding and liberation 319 O8 mm O.6 m =~ m )" m ~ m ~ m m ~ m m Mm~mm ~ kmu~.~,--.,~ cqmp~ (l~r ~m-mltram) m m m~rrml iOIml iOilu m~ mTm~l~ l ,~_-~. m,~.,, m~'m~.~ m~ ma,,,, mz~ iw mc~ mAIm~m~ msl~l (a) (b) Figure 9.27: Material combinations in (a) un-liberated copper; (b) un-liberated lead-NF fraction 50-100 mm Mjm~ll climllllll b im-m.nlmd brm ~lr SI-III --,-) v~ mwrmm mollmn m(~m m "~ mF~ i m m "-- m~ l n m -mzmc miami m m m m m-am~imim,m,-m ............. m~,,.,,m (a) (b) Figure 9.28" Material combinations in (a) un-liberated zinc; (b) un-liberated brass-NF fraction 50-100 mm Mlwmtll j kl II-IIm~lllr IdllWt (l~lr SI-III Ira) u,,i .................. IlWrnm motm,i l "- IFm,. 1.2 m ~-,..~,~ n "--, _ m 9 ,,_ m .urn.m, mc~ o n I Q~m~ (a) (b) Figure 9.29" Material combinations in (a) un-liberated SS; (b) un-liberated plastics-NF fraction 50-100 mm 320 Material liberation gr product design 9.3.9 Linking design to recycling Figure 9.13 to Figure 9.31 illustrate the wide range of material combinations present in un- liberated materials as a function of the various particle size fractions after shredding. This reveals that the composition matrix C m'l'k of the liberation classes for each mineral A to E (steel, aluminium, copper, etc.) as defined above do not give the possibility to describe each random combination of materials within the different liberation classes as present after shredding (see Figure 9.13 to Figure 9.31). However, this definition provides a first and crucial step to incorporate design, particle size reduction and liberation in the description and optimisation of recycling systems. The recycling models as developed provide a first principles basis to link design and recycling as is required by the automotive industry at this moment. The developed models provide the basis to further develop this theory; collect and incorporate data as e.g. given in Figure 9.13 to Figure 9.31, which is essential to improve the description of liberation. This is required in order to link particle size reduction and liberation with the joints and material combinations as defined in the CAD of product design. The recycling optimisation models define the effect of liberation and material combinations on the recycling system. In order to make it possible to ultimately link design to recycling, knowledge from the recycling system (as provided by the models as well as by the data of Figure 9.13 to Figure 9.31) should be applied to define car design (being the input of the shredder), in view of material combinations and connections. In order to realise this, the description of the composition matrix C m'l'k and therefore liberation classes has to be improved. A basis for this is provided by the data of Figure 9.13 to Figure 9.31, however more detailed information on individual particle composition should be collected in addition to the data provided by Figure 9.13 to Figure 9.31. Furthermore, the transformation of particle size and liberation over the shredder has to be modelled; more research and data collection are required to realise this. This must be done in close relation to a proper definition of the car in view of recycling in order to link design properties (material combinations, material connections, type of connections, size of connections, etc.) to the definition of particle size and liberation after shredding. This could be done using the first principles basis of the recycling optimisation model as developed in this thesis work. Castro et al. (2004b)[176] have developed a design simulation tool, which connects product characteristics (composition and material connections) defined during the design phase with liberation of these materials during shredding as a function of joint types. The model shows how design choices affect the feed to recycling systems by the application of a hierarchical decision tree model, which should be combined with the recycling models as described here. The combination of these models could establish a future bridge between the knowledge areas of product design and recycling, hence providing a tool which the designer can use in the process of car design. These models could be used as a basis to translate the detailed knowledge of liberation and recycling to the language and tools of product designers in future. Note that the link between design software and recycling models has not been established yet, although the recycling optimisation models give a clear indication how this link should be realised by using the data as provided in Figure 9.13 to Figure 9.31. By studying the modelling principles of minerals processing systems, a direction could be found to define the design of the car in relation to recycling, which is essential to apply design for recycling. However, the fundamental differences as well as the analogies of comminution modelling in minerals processing and shredding modelling in recycling of cars need further investigation to finally link design and recycling on a proper fundamental basis. 9.3 Modelling shredding and liberation 321 I 09 o., 9 07 9 06 9 i o., II O4 '-' 9 O3 9 O.2 l 0 l ~ l , IlOdm IOl-,- IlWood IT~... IlFom mr.d~ IDSS IZ~ II.~d iCom~ OX~am~ (a) (b) Figure 9.30: Material combinations in (a) un-liberated rubber; (b) un-liberated glass-NF fraction 50-100 mm Figure 9.31" Material combinations in un-liberated wires-NF fraction 50-100 mm 1.00 0.80- ..~ 0.70- I 9 0.60-.,~ '-0.50- 0.40" 0.30- 0.20- Wo. o-mw Q--" o 1 9~-~/~ ~,~/o~,~:~ A Aluminium in NF >1OO mm luminium in NF 50-100 mm Aluminium in NF 20-50 nun Figure 9.32: Particle size/liberation matrix L m,p'l for aluminium 322 Material liberation 8,= product design 0.8-I0.7- 0.6 ~ 0.4 0.3- 0.2- 0.1 0 Steel Brass ~i, Ira, , Rubber Copper Plastics Others 4•S'/I{}~(Lib.class5) W 95-10(P,4(Lib.class4) _ 85-95%(Lib.class 3) 70.85%(Lib.class2) 50.70~ (Lib.Class1) Figure 9.33: Composition matrix for aluminium in NF 20-50 mm I Figure 9.34: Description of particle types showing the compositions of the different un- liberated particles for the mineral aluminium (see Figure 9.33) within the different liberation classes in NF 20-50 mm Material liberation 8z product design 9.3.10 Simulations on the optimization of product design, liberation and metallurgy The developed recycling optimization model was used for four different case studies. The results of these simulations are discussed showing the relationship between the in- and output of the shredder. These simulations will reveal that the breakage behaviour for modern con- sumer products differs fundamentally from traditional minerals processing. Moreover the four different simulation scenarios are applied to calculate the effect of changes in product design and hence particle size reduction and liberation on the recycling of end-of-life vehicles. There- fore also the relationship to recycling rate is discussed. The recycling optimization model is depicted in Appendix C.3. Software for optimization The software application used to perform the modelling of the shredder as well as the opti- mization of the recycling flowsheet as depicted in Figure 9.4 is Frontline Systems'(~)Premium Solver Platform, extended with the Large-Scale GRG Non-linear Solver [328], implemented in Microsoft(~)Excel [327]. This solver platform is capable of handling these large scale, complex, non-linear optimization problems (see Appendix C.3). Simulation of the shredder Scenarios Since data on the relation between particle size reduction and liberation during shredding of end-of-life products is lacking, no model for the transformation of the particle size and liberation distributions during shredding could be developed. However, the relation between the in- and output of the shredding operation is investigated by calculating the liberation distribution of the output of a shredding step, therefore estimating the liberation matrix (Eq. 9.13), based on a fixed particle size reduction (Eq. 9.11 and 9.12) (by defining a shredding matrix Sf m'pl'pu for the transformation of the particle size distribution) for different input definitions fm,p,t (mass based particle size distribution) and Lf m'p'z (liberation distributions) of the shredding step (which are representing differences in product design). The ,.mpl relation between the liberation distribution of the input (Lf~ 'p'l) and the output (Ly~ ' ' ) is calculated based on the optimization of the closure of the mass balances for all elements (Eq. 9.13) over the shredding process, for different starting values for the input distributions defined for the four different scenarios. This relationship illustrated the complexity of the breakage matrix for liberation. The optimization and calculations are performed using Microsoft(~) Excel [327]. As can be seen from Table 9.8 (a) to (d) the liberation distributions of the output are defined as a diagonal matrices in these simulations. However, this does not have to be the case in practice, but is done here for reasons of clarity. Simulations Scenarios i and 2 illustrate the effect of the liberation distribution of the input. The input distribution of the liberation for scenario 1 is shifted to the lower liberation classes (no or poorly liberated materials in the design of the car), whereas simulation 2 calculates the liberation distribution of the output based on an liberation distribution of the input shifted to the higher liberation classes (more/better liberated materials in the design of the car). The particle size distribution of the input is defined for both simulations in class 1 (largest particle size class). The influence of the particle size distribution of the product design (input) on the shredding operation is illustrated by simulations 3 and 4. The definition of the liberation distribution of the input of simulation 3 is shifted to the lower liberation classes (similar to simulation 1), whereas the input of simulation 4 is shifted to the higher classes (similar to 326 Material liberation &: product design Table 9.S: (a) to (d) Particle size class distribution (kg) and liberation class distribution (-) of mineral A for the input and output of the shredder operation for respectively (a) scenario 1; (b) scenario 2; (c) scenario 3 and; (d) scenario 4 INPUT A in ELV A in ELV A in ELV A in ELV A in ELV OUTPUT A in shredded A in shredded A in shredded A in shredded A in shredded INPUT A in ELV A in ELV A in ELV A in ELV OUTPUT A in shredded A in shredded A in shredded A in shredded A in shredded INPUT A in ELV A in ELV A in ELV A in ELV OUTPUT A in shredded A in shredded A in shredded A in shredded A in shredded INPUT A in ELV A in ELV A in ELV A in ELV A in ELV OUTPUT A in shredded A in shredded A in shredded A in shredded A in shredded 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 2 3 4 1 2 3 4 5 1 (a) Scenario 1 15.000 0.158 0.442 0.000 0.381 0.020 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 O.O00 1.000 0.000 0.000 0.000 0.000 3.000 10.63210.36710.00010.00010.000 I 4.500 10.00010.99910.00010.00010.0001 4.500 I 0.000 I 0.000 I 1.001 I 0.000 I 0.000 I 1.5oo Io.ooolo.ooolo.ooolo.9991o.oool 1.500 O. 000 O. 000 0.000 O. 000 O. 999 (b) Scenario 2 O.000 O. 000 O. 000 O. 000 O. 000 O. 000 O.000 O. 000 O. 000 O. 000 O. 000 O. 000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 I 3.000 [ 0.255 [ 0.129 [ 0.240 [ 0.184 [ O. X90 I 4.500 10.00010.16510.31310.28610.2361 4.500 10.00010.00010.461 10.28610.2521 1.5oo I o.ooo I o.ooo I o.ooo I o.~6o I o.441 I 1.500 0.000 0.000 0.000 0.000 0.999 (c) Scenario 3 5.000 0.000 0.623 0.078 0.239 0.060 5.000 0.153 0.427 0.000 0.421 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 l l.000 I 0.000 I 0.999 I 0.000 I 0.000 I 0.000 I 4.000 10.00010.99910.00010.00010.0001 5.5oo IO.OOOlO.OOOlO.9991o.ooolo.OOOl 2.500 IO.O0010.OO010.00010.99910.OO01 2.000 0.000 0.000 0.000 0.000 0.999 (d) Scenario 4 5.000 O. 114 0.019 0.000 0.868 0.000 5.000 0.003 O. 104 0.000 0.894 0.000 5.000 0.018 0.000 0.000 0.756 0.227 0.000 0.000 0.000 0.000 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1.000 1.000 I O.23S I 0.202 I 0.185 I 0.203 I 0.X71 I 4.000 ] 0.000 I 0.042 [ 0.223 [ 0.521 I 0.213 [ 5.500 I 0.000 I 0.000 I 0.4x2 I 0.452 I 0.x35 I 2.500 10.00010.00010.00010.99510.0041 2.000 0.000 0.000 0.000 0.000 0.999 9.3 Modelling shredding and liberation 327 12.00 10.00 i 8.00 6.00 i 4.OO 2.00 0.1)0 / m II lib class 1 I lib class2 I lib class 3 I lib class 4 I lib class 5 Ai wrought Figure 9.37: Mass (kg) of element A1 wrought in mineral A for liberation classes 1 to 5 over all particle size classes p for the input and output of the shredding operation for scenario 2 i r,C ( ( lib class 1 I lib class 2 I lib class 3 I lib class 4 Fe lib class 5 il Input amOutput Figure 9.38: Mass (kg) of element Fe wrought in mineral A for liberation classes 1 to 5 over all particle size classes p for the input and output of the shredding operation for scenario 1 9.4 Discussion Table 9.9: Recovery rate for the metal content and recycling rate of passenger vehicles calcu- lated from the recycling optimization model for the different scenarios (%) Recovery rate Recycling rate metals(%) car (%) Scenario 1 78.5 58.6 Scenario 2 80.1 59.8 Scenario 3 78.6 58.5 Scenario 4 82.8 62.8 of the produced recycling streams, which are the feed to metallurgical processes. Table 9.10: Composition of produced aluminium alloy for the different scenarios given for the fraction of A1, Si, Fe and Cu A1 Si Fe Cu Others Scenario 1 0.60 0.06 0.21 0.12 0.01 Scenario 2 0.69 0.07 0.14 0.08 0.01 Scenario 3 0.67 0.07 0.17 0.09 0.01 Scenario4 0.66 0.07 0.16 0.10 0.01 9.4 Discussion Product design not only influences the use phase of the product, but also has a significant influence on the recycling due to its 'mineralogy' or design. The material connections and combinations in the design of the car determine the particle size reduction and the degree of liberation of the product during shredding, which affects the composition of the intermediate recycling streams (composition and amount of the non-liberated particles) and the efficiency of physical separation. The quality of intermediate recycling products is of critical importance in order to optimise the material recovery in metallurgical processing, which is the closer of the material cycle. 9 Two different recycling optimization models have been developed, in which (1) the liberation of the materials and (2) both the particle size reduction as well as the liberation of the materials were included as modelling parameters. The modelling and definition of the particle size reduction and liberation is developed based on the knowledge available from the modelling of minerals processing systems. 9 The modelling and optimization of the recycling of end-of-life consumer products such as passenger vehicles is closely related to the modelling and simulation of traditional minerals processing systems. It is illustrated in this chapter how the knowledge of traditional fields such as mineral processing technology can be applied in the field of (design for) recycling of complex consumer goods. 9 The modelling of liberation (and particle size reduction) is crucial to lay down a fun- damental basis, which makes it possible to link in future design with final metal and material recovery, therefore, recycling rate. Material liberation & product design 9 The modelling of liberation is necessary in order to optimise the resource cycle as well as to describe the quality of the products, not only due to imperfect separation, but also due to incomplete liberation of the different minerals composing the car. Liberation during shredding is the link between design and recycling. 9 In order to apply a systematic approach to desired and problematic material combi- nations in product design and intermediate recycling products, a material matrix has been developed depicting the consequences of material combinations in intermediate recycling products (achieved by product design, liberation and mechanical separation) on metallurgical process efficiency (losses or contamination of end product). Based on this matrix it becomes clear which material combinations have to be liberated dur- ing shredding, separated during mechanical recycling, or should be avoided in product design. 9 The effect of the product mineralogy, liberation on the quality of intermediate recycling products and as a consequence on the recovery of materials and the quality of the output becomes clear from simulations using the developed recycling optimization model for recycling end-of-life vehicles. From this the following could be concluded: - Modern society minerals are complex, so divers and changing so rapidly making a fundamental description very difficult, since data collection on the relationship between particle size and liberation during shredding has not been considered up till now. However the simulations reveal the complexity of modelling the breakage matrix for shredding modern consumer goods; - The liberation behaviour of modern consumer products differs fundamentally from that of mineral ores. This implies that what is true for classical grinding i.e. the finer the grind the more liberated particles become is not necessarily true for shredding of end-of-life consumer goods; - The modelling of multi-component systems for liberation reveals the fact that dur- ing shredding, the major element composing a mineral will liberate. However, the other elements in this mineral could become less liberated; - The design of a product and the related particle size reduction and liberation efficiency during shredding are of critical importance in achieving a high quality feed to metal producing processes to ensure high recycling rates; - Optimization of the resource cycle of passenger vehicles can never be realised with- out proper understanding of the effect of design, liberation and particle size reduc- tion on the closing of the material cycle, something that is well understood in the processing of mineral ores. 9 Since data on the liberation of materials during shredding and data on the composition of the various liberation classes have never been measured up till now, estimations on this had to be made to set up the models. Recycling systems have never really been analysed systematically as classical minerals processing has done in the past. 9 This chapter discusses the significant influence of product mineralogy, expressed in ma- terial combination as well as construction, and the liberation during shredding on the final material recovery and product quality in recycling modern consumer products, such as passenger vehicles. Optimization of the resource cycle of passenger vehicles can never be realised without proper understanding of the effect of these parameters on the closing of the material cycle. 9.4 Discussion 9 In summary it can be stated that the knowledge built up over many years within the field of minerals processing can contribute significantly to improving the transparency, quality and control of recycling systems and design for recycling and metal recovery. Moreover it should be realised that the future of minerals processing technology could lie in the growing field of recycling consumer products, which are becoming the new mineral ores of the next decades. 332 Material liberation & product design Nomenclature ap, bp Parameters in grade-recovery relationships for a particle size class p aij Structural parameters linking unit operation j with i C m,l,k Composition matrix, defines for each mineral m the composition of the different liberation classes I for the elements k f~,l Feed of mineral m in liberation class l for unit operation i (kg) F~ 'l Sum of feed of mineral m in liberation class 1 for unit operation i (kg) fm,p,t Feed of mineral m in particle size class p and liberation class l for unit operation i (kg) F~ 'p'l Sum of feed of mineral m in particle size class p and liberation class I for unit operation i (kg) /,j Plants, unit operations, transport, etc., with 1 ~ n representing the total amount of units (dismantling, shredding, magnetic separation, non-ferrous separation, metallurgical unit operations, etc.) Organic content of metal fraction fi for element k in particle size class p Elements, metals, compounds originating from the different material streams in the recycling flow sheet of end-of-life vehicles (A1 wrought, A1 cast, steel, copper, other materials such as other non-ferrous metals, organic materials, glass, etc.) l Liberation classes with I = 1 ~ 5 Lx'~,p, l Liberation/particle size matrix, defines for each mineral m the liberation classes l present in the different particle size classes p for the material stream xi after each unit operation i ~mp! Ly i ' , Liberation/particle size matrix, defines for each mineral m the liberation classes I present in the different particle size classes p for the material stream yi after each unit operation i Lz'~,p, ' Liberation/particle size matrix, defines for each mineral m the liberation classes l present in the different particle size classes p for the material stream zi after each unit operation i m Minerals A (A1 wrought based), B (A1 cast based), C (Rest based), D (Steel based), E (copper based) p Particle size classes with p = 1 ~ 5 Rx ki ,p Recovery for metallurgical processing of element k in particle size class p to stream x for unit operation i Ry k'p Recovery for metallurgical processing of element k in particle Rz ,p size class p to stream y for unit operation i Recovery for metallurgical processing of element k in particle size class p to stream z for unit operation i S f? 'pF'p~ Shredding matrix for the transformation of the particle size distribution for mineral m Sf~ 'l Shredding matrix for the transformation of the liberation distribution for mineral m smYi 'l Liberation matrix, defines for each mineral m the liberation 9.4 Discussion Tx m,P, l mpl Ty i ' , X7 ,p'l m,p,l Yi Zm ,p,l classes l present for the material stream Yi after each unit operation i Transformation matrix for mechanical separation processes i defining the recovery for each mineral m for each particle size class p and liberation class 1 to stream xi Transformation matrix for mechanical separation processes i defining the recovery for each mineral m for each particle size class p and liberation class l to stream Yi Transformation matrix for mechanical separation processes i defining the recovery for each mineral m for each particle size class p and liberation class 1 to stream zi Flow rate of mineral m in particle size class p and liberation class 1 to stream x of unit operation i (kg) Flow rate of mineral m in particle size class p and liberation class 1 to stream y of unit operation i (kg) Flow rate of mineral m in particle size class p and liberation class l to stream z of unit operation i (kg) nd control of recycling systems and design for recycling and metal recovery. Moreover it should be realised that the future of minerals processing technology could lie in the growing field of recycling consumer products, which are becoming the new mineral ores of the next decades. 332 Material liberation & product design Nomenclature ap, bp Parameters in grade-recovery relationships for a particle size class p aij Structural parameters linking unit operation j with i C m,l,k Composition matrix, defines for each mineral m the composition of the different liberation classes I for the elements k f~,l Feed of mineral m in liberation class l for unit operation i (kg) F~ 'l Sum of feed of mineral m in liberation class 1 for unit operation i (kg) fm,p,t Feed of mineral m in particle size class p and liberation class l for unit operation i (kg) F~ 'p'l Sum of feed of mineral m in particle size class p and liberation class I for unit operation i (kg) /,j Plants, unit operations, transport, etc., with 1 ~ n representing the total amount of units (dismantling, shredding, magnetic separation, non-ferrous separation, metalChapter 9 The role of particle size reduction, liberation and product design in recycling passenger vehiclesThe quality of recycling intermediate products created during shredding and physical separation is of critical importance to ensure that the feed to metal producing processes permits the economic production of quality metal products. The development of first principles models is indispensable to build the bridge between the material combinations and connections in design and the recycling of cars. This will illustrate at the same time how the knowledge of traditional mineral processing can be applied in the new field of design for recycling of complex consumer products. To apply a systematic approach to select desired and avoid problematic material combinations in product design and intermediate recycling products, a decision tree was developed, based on the separation and recycling technologies available nowadays and on metallurgical and thermodynamic properties of the materials. The recycling optimization model calculates the recovery of the different elements present in the car dependent on the objective of the optimization. The examples below will present the results of the recycling optimization model in particular for the optimization of the recycling of aluminum in the car.An optimistic approach “from hydrophobic to super hydrophilic nanofibers” for enhanced absorption propertiesWater holding capacity becomes essential for hygiene applications including baby diapers. Microfibers of hydrophilic polymers have been useful source for such applications. While, super hydrophilic and stable nanofibers incorporation with functional antibacterial agent are essential to get higher absorption of water along with antimicrobial activity against harmful bacteria. In current work, hydrophobic polymeric nanofibers are transformed to super hydrophilic nanofibers by addition of copper (II) oxide (CuO hereafter) nanoparticles. CuO nanoparticles provided two distinctive properties to existing nanofibers. Firstly, nanofibers surface area was significantly increased, and secondly copper (II) oxide itself is hydrophilic material which imparted hydrophilicity to base polymer. Polyacrylonitrile, crosslinked Polyvinyl Alcohol, and PICT were selected as super hydrophobic polymeric nanofibers. Copper II oxide nanoparticles (same concentration) were added in all polymer solution and electrospun. Surface, morphological, and hydrophilic properties were characterized and it was concluded that copper II oxide is suitable for transforming hydrophobic nanofibers to super hydrophilic nanofibers. Water holding capacity (WHC) was also improved for all prepared nanofiber mats. WHC for PVA/CuO, PAN/CuO, and PICT/CuO were recorded an average of 23 g/g, 21 g/g, and 18 g/g respectively. Combining all useful results from possible characterization of nanofiber mats, it is expected that CuO nanoparticles loaded nanofibers will have potential application as antibacterial, sustainable, and stable replacement of hygiene products.Electrospun nanofibers have covered huge space in advancing fields of life. Application areas of electrospun nanofibers are biomedical [], environmental, energy, filtration, and others as well []. Nanofibers' applications are increasing day by day due to increase in diseases caused by environmental pollution. Resources for overcoming these problems have been also a point of concern for researchers. Super absorbent polymers (SAPs) have contributed well in overcoming a number of environmental problems including reuse of SAPs for sufficient absorption of liquid (water retention), crack healing by SAPs, sanitary diapers (including all types of diapers for babies and adults) []. Water contact or hydrophilicity is an important factor which effects final applications of developed product to an extent. Polymeric nanofibers’ hydrophilicity is dependent on many factors one of which is crosslinking. Crosslinked or heat treated nanofibers usually become hydrophobic in nature []. Although, hydrophobic nanofibers have their own applications areas but hydrophobic nanofibers which are fabricated from hydrophilic polymers need to be converted back to get optimum results. Removal of heavy metal ions from aqueous mixtures also requires enough hydrophilicity to allow some water for absorption and adsorption [Polyvinyl alcohol (PVA) is one of the best example which is used for removal of heavy metal ions from aqueous mixtures and similar applications which require hydrophilic nature []. Uncrosslinked PVA nanofibers are hydrophilic in nature but these are highly unstable in aqueous mixtures and nanofibers’ structure is dissolved immediately, resulting in lower performance. To prevent this problem, PVA nanofibers are crosslinked by glutaraldehyde and resultant nanofibers become hydrophobic in nature []. This gives stability in aqueous mixtures but it reduces the water absorption. We have to trade-off between efficiency and stability. PAN [] nanofibers have also wide range of applications in biomedical and environmental engineering but these are also highly hydrophobic in nature [Baby diapers, and similar products must have some basic features which are high absorbency of liquid, retention capacity of liquid, and lower moisture content after absorption of liquid. Sodium polyacrylates have been used as super absorbent polymer for sanitary diapers, baby diapers, and adult's diapers. In our previous research [] we successfully fabricated copper (II) oxide incorporated polyacrylonitrile (PAN) nanofibers for antibacterial air filter. It was observed that addition of copper (II) oxide nanoparticles enhanced water take-up ability of nanofibers. As PAN nanofibers are hydrophobic in nature but due to addition of 1.00% of copper (II) oxide nanoparticles, nanofibers turned to super hydrophilic with water contact angle of 0° (instantly). Current research is mainly focused on conversion of super hydrophobic nanofibers to super hydrophilic nanofibers by addition of copper (II) oxide. We developed hydrophobic nanofibers and then converted them to hydrophilic nanofibers. Moisture-vapor transport rate, BET surface area, water contact angle, and liquid retention capacity were analyzed. Copper (II) oxide is also an emerging antimicrobial agent. It was confirmed that copper (II) oxide imparted hydrophilicity and improved absorption capacity of intrinsically hydrophobic nanofibers, which will be an appealing application of copper (II) oxide nanoparticles in converting hydrophobic polymers to super absorbent polymers.Current research is focused on development of new SAPs for enhanced liquid absorption. Copper (II) Oxide nanoparticles have already been characterized for antimicrobial properties and exhibited excellent antimicrobial activity against both types of bacteria i.e. gram positive and gram negative []. CuO nanoparticles were incorporated with crosslinked PVA, PAN, and PICT nanofibers. PVA, PAN, and PICT having wide range of biomedical applications, were selected as base polymers. Resultant nanofibers of PVA, PAN, and PICT are considered to be hydrophobic having higher angle of contact. Aim was to develop hydrophilic nanofibers having antibacterial properties. So, CuO nanoparticles did the same. Having higher surface area, excellent hydrophilic properties, and excellent antibacterial properties, CuO nanoparticles transformed hydrophobic polymeric nanofibers to super hydrophilic nanofibers. Further testing showed that resultant nanofibers possess significant water absorption (g/g of nanofibers), improved mechanical properties, and other features required as a SAP for commercial applications.Polyacrylonitrile in powder form with average molecular weight 150,000 was purchased from the Sigma-Aldrich Corporation (Saint Louis, MO 63103, USA). 87–89% hydrolyzed Polyvinyl Alcohol (PVA) with average molecular weight 85000–124000 was purchased from Sigma-Aldrich Corporation. Poly (1, 4 cyclohexane dimethylene isosorbide terephthalate) “PICT” in pallets form was supplied by SK Chemicals, Korea (Republic of). Acetone and trifluoroacetic acid with purity of 99.9% were supplied by Fujitsu pure chemicals (Wako). N,N-Dimethylformamide (DMF) was purchased from FUJIFILM Wako Pure Chemical Corporation (Osaka, Japan). Copper (II) Oxide (nanopowder, <50 nm particle size) was purchased from Sigma-Aldrich Corporation (Saint Louis, MO 63103, USA). Glutaraldehyde (25% solution) was purchased from Wako chemicals. Hydrochloric acid was also purchased from Wako chemicals. Distilled water was used from laboratory.PAN and PAN/CuO nanofibers were fabricated as per our previous research []. PAN (8% W/W) was dissolved in DMF, CuO nanoparticles were added in solution after 12 h of continuous stirring at room temperature. Solution was kept on further stirring for 4 h. Homogenous solution of PAN/CuO was then loaded to electrospinning (syringe capacity 20 ml, nozzle diameter 0.5 mm, voltage of 13kv, and flow rate of 0.5 ml/h) for nanofiber production. PICT was dissolved (10% w/w) in trifluoroacetic acid (99.9%), and electrospun using electrospinning equipment at voltage of 20 kV and distance between tip and collector was kept 17 cm. PVA (8% w/w) was dissolved in distilled water at 60 °C for 6 h 1% glutaraldehyde (25% diluted solution) was added (w/w) in solution before electrospinning. Voltage of 12 kV was applied and distance between tip and collector was kept 15 cm. CuO nanoparticles’ concentration was kept same (1%) for all polymers. Electrospun nanofibers were crosslinked by HCl fumes method [Morphological properties of electrospun nanofibers were analyzed by “Scanning Electron Microscope (SEM), JSM-5300, JEOL Ltd, Japan”, which was accelerated by a voltage of 20 kV. Average diameters of all electrospun nanofibers were calculated by taking mean of 50 readings (randomly) using Image J software. Diameter distribution plot (hexagrams) were plotted by Origin 8.0. Any possibility of peak shift due to reactivity of different functionalities of base polymers and CuO nanoparticles were characterized by Fourier Transform Infrared Spectroscopy (FTIR), “ATR Prestige-21, Shimadzu, Japan”. ATR spectra for pure CuO nanoparticles, polymeric nanofibers with CuO nanoparticles, and polymeric nanofibers without CuO nanoparticles were recorded in set range of wave number 600 cm−1 to 4000 cm−1. Crystal structure of prepared composite nanofibers was analyzed by X-ray diffractions (XRD) spectra which were taken at room temperature (25 °C) using Rotaflex RT300 mA, Rigaku, Osaka, Japan, with angle ranging 5 ≤ 2θ ≤ 70°, and experiment was performed by Nickel-filtered Cu. Ka radiation. Water contact angle was performed to analyze hydrophilic properties of prepared composite nanofiber mats using Digidrop, GBX, Whitestone way, France. Mechanical properties of polymeric nanofibers with and without CuO nanoparticles were measured by Universal Testing Machine (UTM), Tensilon RTC 250A; A&D Company Ltd., Japan. Test was performed under crosshead speed of 5 mm/min and at room temperature (25 °C). Specimen were prepared following ISO 13634 standard. Stress-strain plot was used to calculate mechanical properties i.e. Tensile Stress, Tensile strain, and Young's modulus of polymeric nanofibers with and without CuO nanofibers as per equations Where ε, σ, and E are tensile strain, tensile stress, and Young's modulus respectively. Δl is change in length, l is original length of specimen, F is applied force, and A is cross sectional area of specimen. Surface area of prepared nanofiber mats was measured by Brunauer-Emmett-Teller (BET) surface area and pore size analyzer (SHIMADZU Tri star II 3020, Japan) using nitrogen adsorption method. 1 g of each nanofiber mats was taken for measuring water holding capacity (WHC). WHC was measured using below equation.WHC=weightofwetsample−weightofdrysampleWeightofdrysampleMorphological characterization was performed to analyze fiber diameter and surface properties. represents SEM images of neat PAN, CuO loaded PAN, neat PVA, CuO loaded PVA, neat PICT, and CuO loaded PICT nanofibers. It can be observed that all neat and CuO loaded nanofibers exhibited bead free nanofiber morphology except CuO nanoparticles loaded PVA nanofibers. However diameters were changed due to addition of CuO nanoparticles. Beads formation may be due to non-uniform dispersion of copper (II) oxide nanoparticles in solvent (which was deionized water in case of PVA). Addition of metallic nanoparticles to polymer usually increases diameter of nanofibers. The same mechanism occurred in case of our experimental work. Average diameter was measured by image-J software and values were calculated by taking average of 50 random readings for each type of nanofibers. represents diameter distribution plot of neat and copper (II) oxide nanoparticles loaded PVA, PICT, PAN nanofibers. It can be observed that all three polymeric nanofibers represented uniform morphological properties however addition of copper (II) oxide nanoparticles imparted slight non-uniformity in diameter distribution of polymeric nanofibers. It can also be observed that PAN/CuO and PICT/CuO nanofibers have diameter up to few hundreds of nanometers with increasing fiber counts in higher diameter range. It can be due to possible reason of agglomeration of nanoparticles on the surface of nanofibers which caused increase in diameter of nanofibers. PVA/CuO nanofibers exhibited almost similar diameter distribution as that of neat PVA nanofibers. Which can be associated to uniform dispersion of CuO nanoparticles on the surface of PVA nanofibers.(a–d) represents FTIR-ATR spectra of PVA, PAV/CuO, PICT, PICT/CuO, PAN, PAN/CuO nanofibers, and copper (II) oxide nanoparticles. It can be observed in (a) that PVA/CuO nanofibers exhibited higher absorbance as compared to that of PVA nanofibers. PVA is highly hydrophilic in nature which is due to presence of abundant hydroxyl groups. Presence of hydroxyl groups in main chain causes higher water affection while low water stability to PVA. It is the reason that uncrosslinked PVA cannot be used in applications where there is direct contact of water or aqueous mixtures. However crosslinked PVA can be used in such applications, because of crosslinking, hydroxyl groups can be restricted. It can be shown in (a) that PVA nanofibers exhibited –OH stretching characteristic peak in range of 3000 cm−1 to 3500 cm−1 (precisely at 3239 cm−1). A peak at 2900 cm−1 was also observed which referred to –CH2 asymmetric and symmetric band. While PVA/CuO nanofibers exhibited same peaks as that of neat PVA, except an extra peak at 2300 cm−1 which is referred as characteristic peak of copper (II) oxide. There was no peak shift observed in PVA/CuO nanofibers which indicates that there may not be any chemical interaction between PVA and CuO functionalities. (b & c) represent ATR spectra of PICT, PICT/CuO nanofibers, and PAN, PAN/CuO nanofibers respectively. It can be shown that PICT nanofibers exhibited CH bending peak in CH2 and CH- groups at 1455 cm−1 while CH stretching at 2922 cm−1 respectively, which are considered to be characteristic peaks of PICT polymer. PICT/CuO nanofibers also exhibited same spectra as that of neat PICT while presenting CuO characteristic peak at 2300 cm−1. PAN nanofibers exhibited some prominent peaks at wave number of 1450 cm−1, 1660 cm−1, 2240 cm−1, and 2922 cm−1. Peak at 1450 cm−1 was referred to –CH2, While peaks at 1660 cm−1, 2240 cm−1, and 2922 cm−1 can be associated as stretching of –CN, and –CH bonds respectively. It was also observed that same as PVA and PICT, there was no possible reaction among functionalities of CuO and PAN polymer. As there was no significance peak shift observed in ATR spectra of PAN and PAN/CuO nanofibers. CuO nanoparticles were added in a small concentration (1%), so it can also be possible that due to low percentage of CuO nanoparticles, no significant peak change was observed. represents the main theme of our research. We aimed to attain super hydrophilic nanofibers for enhanced and efficient adsorption of heavy metal ions from wastewater. It can be observed that contact angle of water droplet for neat polymeric nanofibers is in the range of hydrophobic to super hydrophobic materials while addition of copper (II) oxide nanoparticles drastically reduced the contact angle, which is direct indication of changing to hydrophilic from hydrophobic. In our previous research we introduced a unique method to crosslink PVA nanofibers for enhanced adsorption of heavy metal ions. It was also successful to an extent but in our current research we have attained our required results by decreasing contact angle to 0°. It can be observed in that contact angle for neat PAN nanofibers, PVA nanofibers, and PICT nanofibers were 123.3°, 66.8°, and 79.2° while contact angles for CuO loaded PAN, PVA, and PICT nanofibers became 0°, 0°, and 2° respectively. represents vapor transport rate (MVTR) of neat polymeric nanofibers and copper (II) oxide nanoparticles loaded polymeric nanofibers. It can be observed that neat PVA, PAN, and PICT exhibited lower performance as compared to that of PAN-CuO, PICT-CuO, and PVA-CuO nanofibrous membranes. There may be three possibilities of increasing performance. Firstly, average pore size among different nanofibers would be smaller in neat polymeric membranes as compared to that of nanofibers containing copper (II) oxide nanoparticles. Secondly, addition of copper (II) oxide enhanced surface area of nanofibrous membranes. Third and most important possibility of increasing MVTR may be due to strong hydrophilic tendency of CuO nanoparticles.Water holding or water retention capacity is generally used as performance indicator of super absorbent polymers (SAPs). All polymeric nanofiber mats with and without copper (II) oxide nanoparticles were immersed in 100 ml of distilled water for 1 min each, and weighed when water droplets stopped dropping from the nanofiber mats. Then samples were placed for drying at 105 °C for possible removal of moisture content encapsulated within nanofiber mats. It was observed that addition of copper (II) oxide nanoparticles significantly enhanced water retention capacity of polymeric nanofibers. Data of water holding capacity () of prepared nanofiber was also compared to some of commercially available products for better understanding of current research significance.Change in crystalline structures of PVA, PICT, PAN nanofibers after addition of copper (II) oxide nanoparticles was analyzed by wide angle XRD. (a) represents an overlay plot of XRD spectra of PVA, PICT, PAN, PVA/CuO, PICT/CuO, and PAN/CuO nanofibers. It can be observed that copper (II) oxide nanoparticles loaded PVA, PICT, and PAN nanofiber mats exhibited CuO representative peaks at same degree of angle while varying intensities depending on interactions among CuO and different polymers. (b) represents that PVA nanofibers exhibited only characteristic peak at 2θ = 19.6 which is usually referred to amorphous structure of PVA. (b) represents spectra of PICT nanofibers and PICT/CuO nanofibers. It can be observed that PICT nanofibers exhibited a sharp peak at 2θ = 20°. (c) represents that pure PAN nanofibers exhibited a sharp peak at 2θ = 17°, and a small peak at 2θ = 30°, while PAN did not exhibit another peak up to 2θ = 80°. PAN nanofibers showed characteristic peaks of pure PAN. First peak (2θ = 17°) was generally associated with hexagonal lattice of PAN. It was observed that characteristic peak of PAN was decreased after addition of copper (II) oxide in to PAN nanofibers which cleared that crystallinity of pure PAN was decreased and hexagonal lattice of PAN was decentralized. CuO exhibited its characteristic peaks at 2θ = 36° and 2θ = 38°. Occurrence of CuO characteristic peaks imparted crystallinity to PAN/CuO, PICT/CuO, and PVA/CuO nanofiber mats. It was also observed by tensile test that tensile strengths of PAN/CuO, PICT/CuO, and PVA/CuO nanofibers were increased with increasing amount of CuO in polymeric nanofibers. Tensile strength has direct relation with crystallinity of polymers. So, by comparing results of UTM and XRD, it can be concluded that addition of nanoparticles acted as nanofiller as well as imparted crystallinity to polymeric nanofibers.Mechanical properties of PVA, PVA/CuO, PICT, PICT/CuO, PAN, and PAN/CuO nanofibers were characterized by UTM. represents stress-strain curves for neat PVA, PICT, PAN, CuO loaded PVA, PICT, and PAN nanofibers. It can be observed that mechanical properties (especially) tensile strength was increased for all polymeric nanofibers with addition of copper (II) oxide nanoparticles. It is a simple fact that metallic nanoparticles with a very fine diameter impart mechanical stability even though it does not have any chemical interaction between polymers. It can be shown () that tensile strength of pure PAN nanofibers was recorded as 4.03 MPa while tensile strength of PVA/CuO nanofibers was extended to 8.43 MPa. Which is clear indication of a significant increment in tensile strength of PAN nanofibers when CuO nanoparticles were added in PAN polymer. It can be also observed that same trend was observed in case of PICT and PVA nanofibers as well. Values of tensile strength for PICT, PICT/CuO, PVA, and PVA/CuO nanofibers were recorded as 1.63 MPa, 7.28 MPA, 11.06 MPa, and 17.61 MPa respectively. Which represented a significant increase in tensile properties of neat polymers when copper (II) oxide nanoparticles were incorporated with them.Effect of copper (II) oxide nanoparticles on the surface area of polymeric nanofibers was analyzed by BET surface analyzer using 5-point surface area measurement by nitrogen adsorption. 1.0 g of each nanofiber samples were placed in BET standard sample tube (3/8″ tube diameter). All samples were degassed by helium gas before setting for surface area measurement. represents adsorption curves of PVA, PICT, PAN nanofibers with and without addition of copper (II) oxide nanoparticles while insets represent BET surface area plot for all mentioned nanofibers. It can be observed in figure that nitrogen adsorption was significantly increased when CuO nanoparticles were added in polymeric solution for electrospinning. Inset represents that surface area trend was also linear. Surface area of PAN, PAN/CuO, PICT, PICT/CuO, PVA, and PVA/CuO nanofibers were recorded as 11.5856 ± 0.0477 g/m2, 19.2541 ± 0.0914 g/m2, 11.3899 ± 0.0469 g/m2, 17.9917 ± 0.1022 g/m2, 11.2944 ± 0.0489 g/m2, 21.2944 ± 0.0749 g/m2 respectively. It was observed that surface area of all polymeric nanofibers (mentioned above) were increased with addition of CuO nanoparticles. It is well understood fact that nanoparticles have greater surface area as compared to that of nanofibers due to smaller size.From all results and discussions described in above text, it was concluded that all polymeric solutions (PAN, PICT, and PVA) were electrospun with smooth morphological properties which were confirmed by SEM. Our main target was to transform super-hydrophobic nanofibers to super hydrophilic nanofibers and that purpose was fulfilled by addition of copper (II) oxide nanoparticles. Water holding capacity (WHC) was also calculated and it was concluded that all polymeric nanofibers incorporating CuO nanoparticles exhibited excellent water holding capacity which is in the range of SAPs. CuO nanoparticles are hydrophilic in nature, and having higher surface area due to fine particle size, so these nanoparticles were dispersed in nanofibers and imparted hydrophilicity to hydrophobic nanofibers. In our previous research [] we have already characterized antibacterial activity of CuO nanoparticles. Keeping in mind antibacterial, morphological, structural, and hydrophilic properties of prepared nanofibers it is expected that these functional nanofibers will have potential applications as super absorbents.Authors declare no conflict of interest in this research.The following is the Supplementary data to this article:Supplementary data to this article can be found online at Comparison about effects of Sb, Sn and Sr on as-cast microstructure and mechanical properties of AZ61–0.7Si magnesium alloyIn the paper, the effects of Sb, Sn and Sr on the as-cast microstructure and mechanical properties of AZ61–0.7Si magnesium alloy, especially on the modification and/or refinement of Mg2Si phases in the alloy, are investigated. The results indicate that adding 0.4 wt.%Sb or 0.6 wt.%Sn to AZ61–0.7Si alloy can refine the Chinese script-shaped Mg2Si phases in the alloy, but the modification of Mg2Si phases is not obvious. Oppositely, adding small amounts of Sr can obviously modify and refine the Mg2Si phases in the alloy. After adding 0.09 wt.%Sr to AZ61–0.7Si alloy, the morphology of Mg2Si phases in the alloy changes from coarse Chinese script shape to fine granule and/or irregular polygonal shapes. Accordingly, the tensile and creep properties of the Sr-containing AZ61–0.7Si alloy are greatly improved. The difference of Sb, Sn and Sr in the modification and refinement of Mg2Si phases might be related to the effects of these elements on the undercooling degree.Magnesium alloys are the lightest structural alloys commercially available and have great potential for applications in automotive, aerospace industries and others. However, in recent years, improving the elevated temperature properties has become a critical issue for possible application of magnesium alloys in hot component. It has been shown that the Mg–Al–Si-based alloys are a potential-elevated temperature magnesium alloys Due to the above-mentioned reasons, the research about the modification and refinement of Mg2Si phases in Mg–Al–Si-based alloys by microalloying method, has received much attention all over the world, and consequently many researches have been carried out. It has reported that the Chinese script-shaped Mg2Si phases in Mg–Al–Si-based alloys could be modified and/or refined by Sb The modified AZ61–0.7Si experimental alloys were prepared by adding following materials: commercial AM60 alloy, pure Mg, Al, Zn, Sb and Sn (>99.9 wt.%), Al–30 wt.%Si and Al–10 wt.%Sr master alloys. The experimental alloys were melted in a crucible resistance furnace and protected by a flux addition. When the melt temperature was around 740 °C, the 0.4 wt.%Sb, 0.6 wt.%Sn and 0.09 wt.%Sr were added into the melt of different experimental alloys, respectively. After held at 740 °C for 60 min, the melts were homogenized by mechanical stirring and then poured into a preheated permanent mould in order to obtain a casting. The specimens as shown in were fabricated from the casting for tensile and creep tests. As reference, the AZ61–0.7Si alloy without adding Sb, Sn or Sr was also cast and analyzed under the same conditions with the above-modified alloys. The actual chemical compositions of experimental alloys were listed in The microstructure analysis samples were etched with an 8% nitric acid-distilled water solution, and then were examined by Joel/JSM-6460LV type scanning electron microscope (SEM) equipped with Oxford energy dispersive spectrometer (EDS) with an operating voltage of 20 kV. The phases in the experimental alloys were analyzed by D/Max-1200X type X-ray diffraction (XRD) operated at 40 kV and 30 mA. The differential scanning calorimetry (DSC) was also carried out using a NETZSCH STA 449C system. Samples weighted around 30 mg were heated in a flowing argon atmosphere from room temperature to 700 °C for 5 min before being cold down to 100 °C. The cooling curves were recorded at a controlling speed of 15 °C/min.The tensile properties at room temperature and 150 °C were determined from a complete stress–strain curve. The 0.2% yield strength (YS), ultimate tensile strength (UTS) and elongation to failure (elongation) were obtained based on the average of three tests. The constant-load tensile creep tests were performed at 150 °C and 50 MPa for creep extension up to 100 h. The total creep strain and minimum creep rate were respectively measured from each elongation–time curve and averaged over three tests. shows the XRD results of 2–4# alloys. It is well known that the 1# alloy is composed of α-Mg, Mg17Al12 and Mg2Si phases. According to a and b, it is found that adding 0.4 wt.%Sb or 0.6 wt.%Sn to AZ61–0.7Si alloy will cause the formation of small amounts of Mg3Sb2 or Mg2Sn phases, respectively. However, as shown in c, adding 0.09 wt.%Sr to AZ61–0.7Si alloy does not cause the formation of any other new phases, which is consistent to that of Zhao et al. show the SEM images and EDS results of experimental alloys, respectively. As shown in , the Mg17Al12 and Mg2Si phases are detected in the 1–4# alloys, and the Mg3Sb2 and Mg2Sn phases are also detected in the Sb- and Sn-containing alloys, respectively. In addition, it is found from a that the Mg2Si phases in the AZ61–0.7Si alloy unmodified exhibit coarse Chinese script-shaped morphology. However, after adding small amounts of Sb or Sn to AZ61–0.7Si alloy, although the Chinese script-shaped Mg2Si phases are still obvious, they become relatively fine as shown in b and c, indicating that adding 0.4 wt.%Sb or 0.6 wt.%Sn to AZ61–0.7Si alloy can refine the Chinese script-shaped Mg2Si phases in the alloy, but the modification of Mg2Si phases is not obvious. Furthermore, it is found from b and c that the refinement result of adding 0.4 wt.%Sb is better than that of adding 0.6 wt.%Sn. Comparing b–d, it is interestingly observed that, after adding 0.09 wt.%Sr to AZ61–0.7Si alloy, the Mg2Si phases in the alloy become very fine, and their morphology changes from initial Chinese script shape to granule and/or irregular polygonal shapes, indicating that adding 0.09 wt.%Sr can effectively modify and refine the Chinese script-shaped Mg2Si phase, which is consistent to that of Srinivasan et al. The tensile properties including UTS, 0.2% YS, elongation (Elong.) and creep properties of the experimental alloys, are listed in that the tensile and creep properties of the 2–4# alloys, are higher than that of the 1# alloy, indicating that adding small amounts of Sb, Sn or Sr can improve the mechanical properties of AZ61–0.7Si alloy. This situation is possibly related to the modification and/or refinement of Mg2Si phases and the grain refinement of the modified alloys. It is well known that the presence of fine and uniform phases distributed along the grain boundaries is easier to act as an effective straddle to the dislocation motion thus improving the properties of engineering alloys b, the morphology and the secondary dendrite arm spacing of Mg2Si phases in the 2# alloy are different from those in other alloys. For example, the secondary dendrite arm spacing of Mg2Si phases in the 2# alloy is smaller than that of the Mg2Si phases in the 1# and 3# alloys. Obviously, this is beneficial to the improving of mechanical properties. Therefore, as listed in , the tensile and creep properties of the 2# alloy are better than that of the 1# and 3# alloys. However, since the Chinese script-shaped morphology of Mg2Si phases in the 2# alloy is still obvious, the tensile and creep properties of the 2# alloy are poorer than that of the 4# alloy.In general, the Mg2Si phases in Mg–Al–Si-based alloys unmodified are prone to forming coarse Chinese script shape under lower solidification rates a). However, after adding 0.4 wt.%Sb, 0.6 wt.%Sn or 0.09 wt.%Sr to AZ61–0.7Si alloy, the Chinese script-shaped Mg2Si phases in the alloys are modified and/or refined (b–d), especially after adding 0.09 wt.%Sr, the Mg2Si phases change from coarse Chinese script shape to fine granule and/or irregular polygonal shapes (d). Previous investigations showed that, when the microalloying method was adopted, the modification and/or refinement of Mg2Si phases in Si-containing magnesium alloys were mainly related to the forming of nucleus for Mg2Si precipitates ), in the present work adding 0.09 wt.%Sr to AZ61–0.7Si alloy does not cause the formation of any other new phases, indicating that the above-mentioned mechanism is not suitable for the modification and refinement of Mg2Si phases in the 4# alloy. shows the surface scanning results of the 2–4# alloys. It is found from that Sb, Sn and Sr not only exist in the α-Mg matrix but also are incorporated in the Mg2Si precipitates. In addition, it is observed from the cooling curves of experimental alloys () that the effect of adding 0.09 wt.%Sr on the onset crystallizing temperature of AZ61–0.7Si alloy, Tl, is very obvious, decreasing from 608.8 °C to 600.4 °C. Oppositely, the effect of adding 0.4 wt.%Sb or 0.6 wt.%Sn is not relatively obvious, thereinto the effect of adding 0.6 wt.%Sn is least.According to the classic solidification theory, the relationship between the critical nucleus radius and the undercooling degree is given as follows where r is the critical nucleus radius, ΔGr is the variation of volume free energy, σ is the interfacial energy of unit surface area, Tm is the equilibrium crystallizing temperature, Lm is the crystallizing latent heat and ΔT is the undercooling degree, which can be expressed as: ΔT
=
Tm
−
Tl. According to Eq. , the critical nucleus radius decreases with the decreasing of Tl, then the nucleation energy of crystal nucleus reduces and the probability of nucleation increases, which would result in grain and precipitate refinement. Based on the above analysis, the possible reasons for the modification and refinement of Mg2Si phases in the 4# alloy are mainly related to the following two aspects: (1) due to the limited solid solubility of Sr in the magnesium, the redundant Sr would enrich in the liquid ahead of the Mg2Si growing interface, which would restrict the Mg2Si growth during solidification process and (2) the Sr microalloying increases the undercooling degree, which would result in the increasing of effective number of the potential Mg2Si crystal nucleus.Since the solid solubility of Sb in the magnesium is also limited, then the Sb would enrich in the liquid ahead of the Mg2Si growing interface during the solidification process of 2# alloy. In addition, as shown in , the Mg3Sb2 phase which could act as a nucleus of Mg2Si phase ) or other reasons, further investigation would be carried out in our group. In addition, although the solid solubility of Sn in the magnesium is high (≈14.8%) , adding 0.6 wt.%Sn to AZ61–0.7Si alloy results in the formation of small amounts of Mg2Sn phases. Since the crystal structures of Mg2Sn (cF12 type, a
= 0.6761 nm) and Mg2Si (cF12 type, a
= 0.6359 nm) , the effect of adding 0.6 wt.%Sn on the undercooling degree of AZ61–0.7Si alloy is least. Therefore, compared to the adding 0.09 wt.%Sr, adding 0.6 wt.%Sn exhibits relative refinement for the Mg2Si phases, the modification is not obvious. Compared to the adding 0.4 wt.%Sb, the refinement efficiency for the Mg2Si phases is relatively poor. According to the above analysis, it is inferred that the undercooling degree is a very important factor for the modification and refinement of Chinese script-shaped Mg2Si phase in Si-containing magnesium alloys. The difference of Sb, Sn and Sr in the modification and refinement of Chinese script-shaped Mg2Si phases in the AZ61–0.7Si alloy, might be related to the effects of these elements on the undercooling degree. Actually, this situation is similar to the modification and refinement of Chinese script-shaped Mg2Si phases under fast cooling condition such as die casting which results in the undercooling degree increasing Adding 0.4 wt.%Sb or 0.6 wt.%Sn can refine the Chinese script-shaped Mg2Si phases in the AZ61–0.7Si alloy, but the modification of Mg2Si phases is not obvious. Oppositely, adding small amounts of Sr can obviously modify and refine the Chinese script-shaped Mg2Si phases in the AZ61–0.7Si alloy. After adding 0.09 wt.%Sr to AZ61–0.7Si alloy, the morphology of Mg2Si phases in the alloy changes from the coarse Chinese script shape to fine granule and/or irregular polygonal shapes. Accordingly, the tensile and creep properties of the Sr-containing AZ61–0.7Si alloy are greatly improved. The difference of Sb, Sn and Sr in the modification and refinement of Chinese script-shaped Mg2Si phases in the AZ61–0.7Si alloy, might be related to the effects of these elements on the undercooling degree.Optimization of nickel nanocomposite for large strain sensing applicationsA novel large strain sensor has been developed using a silicone/nickel nanostrand/nickel coated carbon fiber nanocomposite system. The effect of conductive filler volume fraction on the piezoresistive response of the nanocomposite sensor has been studied in order to determine the optimal composition for use in large strain/motion sensing applications. Electromechanical testing of various compositions revealed that optimum performance was achieved using 11 vol% nickel nanostrands with 2 vol% nickel coated carbon fiber in the silicone matrix. Initial results indicate that this nanocomposite is capable of sensing strains of over 40% elongation.The sensing of mechanical strain is integral to many engineering applications such as ballistic testing, biomechanics (e.g. advanced prosthetics), haptic interfaces, structural health monitoring, etc. However, at present, most conventional strain gauges can only measure strain reliably up to a few percent Conductive polymer composites (CPCs) have shown promise as inexpensive large strain sensors In previous work, tensile testing of various elastomeric materials filled with NiNs demonstrated the extreme piezoresistive response of elastomer/NiNs composites In traditional percolation theory, a system is represented by an undirected graph of nodes and connecting lines. The lines in this lattice are called ‘bonds’ and the nodes or intersections of the lines are called ‘sites’. For a particular simulation, sites (in the case of site percolation) or bonds (in the case of bond percolation) are either closed or open with a given probability, p. As p increases, clusters of closed sites or bonds will develop and one can define a critical or threshold probability, pc, which is equivalent to the number fraction of closed sites or bonds required to create a cluster that spans the lattice. This percolation threshold is intimately related to the structure of the graph. The graph structure of traditional percolation theory is that of a regular lattice. However, the intrinsic structure of some physical systems does not lend itself well to an ordered lattice representation. For cases of this type continuum percolation theory is used. In continuum percolation theory the locations of sites are not limited to discrete points on the lattice; rather, they are allowed to exist at any point in the continuous domain. This allows for the modeling of random networks, such as the one under consideration.Consider for a moment the problem of electrical conductivity for a CPC in the context of a continuum bond percolation model. In this case the nodes represent the conductive phase and the bonds represent conductive paths through the non-conductive phase (due to, e.g. tunneling, electron hopping, etc.). When a bond is open there is no conduction between adjacent nodes, when it is closed there is conduction between nodes. In the case of Si/NiNs composites this is thought to be due to quantum mechanical tunneling, in which case a bond is open only if the conductive phase particles are within ∼1 nm of each other ) the threshold probability for conduction can be deduced. For a conductive path to exist through a node at least two of the bonds connected to that node must be closed. It would then be expected that the threshold probability be approximately equal to the number of required closed bonds divided by the total number of available bond locations. For the honeycomb lattice in one would expect a critical probability of pc
≈ 2/3, for the square lattice pc
≈ 1/2, and for the triangular lattice pc
≈ 1/3 and indeed these values match well with those reported in the literature also shows a representative ‘unit cell’ for a continuum model where the central node is connected to 6 adjacent nodes, for which we would again expect pc
≈ 1/3. This is to say that by increasing the number of bonds attached to each node the percolation threshold can effectively be lowered. This fact can be exploited to manipulate the critical strain at which Si/NiNs nanocomposites begin to respond piezoresistively. By some means, as this material is strained the spatial distribution of NiNs with respect to one another (which directly corresponds to the distribution of bond lengths in the continuum percolation graph) is altered such that the material passes from a sub-critical percolation regime through the percolation threshold and into a highly conductive super-critical regime. By increasing the initial (unstrained) number of potential paths between conductive phase nanoparticles the threshold (ɛc) can be lowered and the amount of strain required to cross the threshold should be less. Increasing the proximity of conductive phase particles for a static system (i.e. one that is not subjected to mechanical loading) is typically accomplished by increasing the volume fraction of the conductive phase. However, in nanocomposites this strategy can require prohibitively large quantities of expensive nanoparticles. An alternative method to modify the initial bond length distribution is to introduce a second conductive phase of a distinct length scale—effectively superimposing the two respective percolation graphs. The effect of this is to create ‘super-nodes’ or ‘super-sites’ in the composite graph that connect small clusters and create larger clusters at lower volume fractions (The creation of these ‘super-nodes’ significantly reduces the threshold probability as can be seen from , where a ‘super-node’ connecting 50 clusters is schematically represented. The expected threshold for this case would be pc
≈ 1/25.While the introduction of this larger second phase does increase the volume fraction of conductive phase material (with fewer and less expensive particles), the most important effect is that of manipulating the bond length distribution such that the average distance between conductive phase domains is decreased. As the material is mechanically loaded this is what directly causes the consequent decrease in ɛc. There is, however, a competing increase in composite stiffness because of the lower compliance in the larger phase, which is a limiting factor for ɛmax. Therefore, this study is couched as an optimization problem in which simultaneous minimization of ɛc and maximization of ɛmax is sought. The above theory as well as prior work suggests that by finding the ideal volume fractions of the nano-phase and the larger macroscopic phase conductive fillers the spatial distribution of conductive phase particles can be indirectly optimized so as to achieve this objective. In order to ensure the usefulness and applicability of the resulting nanocomposite material as a large displacement strain sensor, the metric of ɛerr is also used to identify the ideal composition. In previous electromechanical testing of Si/NiNs composites there was little to no response manifested with NiNs volume fractions below 7%. Conversely, mechanical instability was observed at volume fractions above 15%. These previous results guided our selection of the following compositions for testing:where filler content was measured in volume percentage. The following compositions were also tested: 7% NiNs + 1% NCCF, 7% NiNs + 2% NCCF, and 7% NiNs + 3% NCCF. However, there was limited piezoresistive response and therefore the data is not included in this study. Three trials were performed for each of the compositions that were tested; however, for both the 9% NiNs + 1% NCCF and 9% NiNs + 2% NCCF compositions the data for one of the trials was too noisy and differed significantly from the other two trials and was consequently thrown out.Small ‘dog-bone’ tensile samples were prepared using an aluminum mold. To accommodate both small and large batches each slot in the mold was made for a set of three dog-bone samples (). Channels were cut into the mold along its length so that copper wires could be cast into the dog-bone samples for improved and consistent electrical contact (). The mold was treated with an aerosol polytetrafluoroethylene (PTFE) mold release in order to facilitate post-cure removal of the nanocomposite samples.The matrix material for the Si/NiNs/NCCF nanocomposite in this study was Dow Corning's® two part silicone elastomer, Sylgard 184. The principal conductive filler that was used was nickel nanostrands. NiNs are high aspect ratio nanoparticles with a unique bifurcated structure The silicone base was mixed with the NiNs in a planetary centrifugal mixer in order to achieve uniform dispersion of the nanoparticles. The Si/NiNs solution was then screened through a 40 gauge mesh to eliminate any large particles that may have infiltrated the solution and to provide some degree of uniform particle size. To this concentrated solution were added the NCCF, additional silicone base, and the cross-linking catalyst. With increasing filler volume percentage it became necessary to add small amounts of solvent as well, in order to decrease the viscosity sufficiently such that proper mixing could occur and to decrease shear stresses that could destroy the unique structure of the NiNs particles. This mixture was then mixed again in a planetary centrifugal mixer.After mixing, the solution was then placed in the mold using a metal spatula. This method of filling the mold introduced air bubbles into the samples. Therefore, in order to prevent porosity in the cured samples, they were degassed under vacuum at room temperature. The samples were then cured at 100 °C overnight.Mechanical testing was performed on the samples using an MTS 880 Material Test System. The metallic clamshell grips that were used were insulated from the rest of the test system using custom made Phenolic spacers. In order to prevent slippage, an abrasive covering was applied to the grips. Each sample was connected in series with a 120 Ω ± 0.01% precision resistor. This voltage divider circuit was shielded and excited by a 10 V DC source. The samples were pulled in tension at a strain rate of 2.5 mm/min until fracture. Strain was calculated from the displacement of the test system cross-head and the gauge length of the samples.As each sample was pulled, the voltage drop across it decreased. The resistivity of the sample was calculated from the change in voltage using the following formula, derived from the voltage divider rule and the definition of volume resistivity:where R1 is the resistance of the 120 Ω series resistor, V0 the measured voltage signal, Vs the excitation voltage, t the sample thickness, w the sample width, and l the distance between the copper contacts.The response of each of the tested compositions is shown in . In all cases the volume resistivity decreased significantly as the material was strained in tension. Averaged over the three trials for each composition, the 9% NiNs + 1% NCCF and 9% NiNs + 2% NCCF compositions dropped about three-and-a-half orders of magnitude in resistivity; the 11% NiNs + 1% NCCF, about three orders of magnitude; the 9% NiNs + 3% NCCF and 11% NiNs + 2% NCCF, about two-and-a-half orders of magnitude; and the 7% NiNs + 4% NCCF almost one order of magnitude.Excepting the 7% NiNs + 4% NCCF composition, all of the tested compositions achieved greater than 40% elongation.The negative gauge factor that was observed shows a diametrically opposite response to that of typical conductive filled polymer composites, but which is characteristic of this nanocomposite system , when NCCF content is increased there is a dramatic corresponding increase in the overall conductivity of the composite. The composite conductivity is increased about an order of magnitude for each additional volume percent of NCCF.Increasing NCCF content also tends to decrease the magnitude of the gauge factor, as can be seen from where the peak gauge factors generally become less and less negative with increasing NCCF content.The critical strain, ɛc, was calculated as the last strain level for which the volume resistivity was within 5% of the maximum volume resistivity. As predicted, ɛc did decrease with increasing NCCF content for both the 9% NiNs and 11% NiNs compositions (). Although there was no comparative sample reported to test this trend for the 7% NiNs + 4% NCCF sample, we note that – as stated previously – lower NCCF content samples were tested at 7% NiNs loadings but there was no response. This is to say that ɛc was never reached at NCCF content lower than 4% for these samples. This corroborates the results of the other samples because ɛc effectively decreased from infinity to a finite value as NCCF content was increased. also indicates a general dependence of the maximum elongation on both NiNs and NCCF content. Increasing the volume percentage of either significantly decreases the maximum elongation of the nanocomposite system before fracture. This is thought to be due to the fact that increased filler volume fraction leads to a larger number of inhomogeneities in the composite material. These inhomogeneities act as stress risers and lead to void formation In order to quantify repeatability between gauges, the maximum and minimum resistivity of all trials was calculated for each composition as a function of strain. The smallest possible strain that a measured resistivity could represent was given by the strain at which the mean resistivity was equal to the maximum resistivity. Similarly, the largest possible strain that a measured resistivity could represent was given by the strain at which the mean resistivity was equal to the minimum resistivity. ɛerr is defined as the difference between these two quantities. This process is illustrated in This represents, in essence, the predicted uncertainty in the strain level indicated by the gauge—based on the uncertainty in the measured resistivity signal. The measurement error profile of each candidate composition is shown in We note that unlike the previously discussed parameters (ɛc, ɛmax, G), ɛerr is not an intrinsic property of the nanocomposite system. It is, rather, a function of process parameters. ɛerr varies with composition only because certain compositions increase the difficulty of achieving ideal spatial particle distribution. As stated earlier, the viscosity of the pre-cured sample mixture increases with filler content. This can lead to difficulty during the mixing phase of manufacture and consequent non-uniform distribution of particles, which negatively affects the repeatability of the sensors. Additionally, the high viscosity of the more heavily filled samples can be an impediment for the degassing stage of manufacture, leading to porosity in the final samples, which can also adversely affect repeatability. In order to compensate for these problems extra solvent was added. However, excessive solvent may lead to particle settling and a similar problem of non-uniform particle distribution. Thus, uniformity of filler distribution and porosity are the limiting factors in maximizing repeatability. Theoretically there is no barrier to achieving uniform particle distribution and eliminating porosity with any given composition; however, achieving ideal process parameters becomes a practical limitation with certain compositions.Although processing is the real culprit, some conclusions may be drawn as to the effect of filler content on repeatability (i.e. ease of manufacture). As filler content increases uniformity of particle distribution becomes easier to achieve. This is usually reflected in a decrease in ɛerr for any given NCCF volume fraction (although at low strains the 11% NiNs + 1% NCCF specimen deviate from this trend). The effect of increasing NCCF content is a similar decrease in ɛerr, though more pronounced than in the case of varying NiNs volume fraction. This is likely due to the disparity in length scale. As the volume fraction of NCCF reaches a level such that uniform distribution of this phase is practically achievable, the ‘super-node’ effect created by this phase dominates the influence of non-uniformity in the distribution of the much smaller NiNs phase. As a result the composition with the smallest ɛerr over the entire tested strain range was found to be the 11% NiNs + 2% NCCF, which had an average of 0.05 mm/mm error.Based on the experimental tests that were performed an empirical optimization was performed. As stated previously, the optimization problem for this study was to maximize ɛmax while simultaneously minimizing ɛc, and ɛerr. As such, an appropriate objective function that satisfies our demands is:f(NiNsvol%,NCCFvol%)=εmaxεc×εerrεmax=εmax(NiNsvol%,NCCFvol%)εc=εc(NiNs vol%,NCCF vol%)εerr=εerr(NiNsvol%,NCCFvol%)And the optimization problem is formulated as:maxx∈7,9,11,y∈1,2,3,4(f)subjecttoεmax≥0.4where x
= NiNs vol %, and y
= NCCF vol %. The optimization algorithm consisted in the following: (1) measure ɛmax, ɛc, ɛerr; (2) compute the value of the objective function, f; and (3) choose the composition which maximizes the objective function. shows the values of each of the parameters as well as the value of the objective function. From it can be seen that the best performing composition was the 11% NiNs + 2% NCCF. The value of f for the 7% NiNs + 4% NCCF composition put it in 4th place numerically; however, the maximum elongation was less than the imposed constraint of 40% and it is therefore thrown out. The 9% NiNs + 3% NCCF also performed well, however the repeatability of measurements as given by ɛerr was about half that of the 11% NiNs + 2% NCCF composition. With improved control of process parameters it is believed that the repeatability for this composition can be enhanced. It is therefore suggested that both of these compositions be further developed for application as a large strain sensor material.The optimized nanocomposite composition of 11% NiNs + 2% NCCF is capable of measuring strains from as little as 1% up to as large as 44% elongation with an average error of only ±2.5% elongation.In this study it has been shown that the piezoresistive material response of Si/NiNs/NCCF can be tuned by varying the volume percentage of NiNs and NCCF. Increasing the volume percentage of NiNs in the composite was found to cause a decrease in ɛc, and improved repeatability between gauges. It was also found that increasing NCCF content caused a decrease in gauge factor magnitude and ɛmax, and an increase in repeatability and bulk composite conductivity.From these results, the composition that showed the most promise for use as a large displacement sensor was determined to be the 11% NiNs + 2% NCCF because of its large maximum elongation (ɛmax), low critical strain (ɛc), and minimal measurement error (ɛerr). This material is capable of measuring strains from 1% to 44% elongation. This is over 8 times greater than the maximum strain measurable using traditional foil strain gauges The results of this study indicate that Si/NiNs/NCCF nanocomposites in concentrations of 11 vol% NiNs + 2 vol% NCCF can be used as simple, inexpensive large displacement sensors that can measure strains over 40% elongation.Oliver K. Johnson is an undergraduate student at Brigham Young University majoring in mechanical engineering. His research interests include multi-functional nanocomposites, visualization of tensor fields, statistical methods for image segmentation, and 3D microstructure reconstruction.George C. Kaschner is a technical staff member of Los Alamos National Laboratory. He earned his Ph.D. in materials science and engineering at the University of California, Davis, with minors in biomedical engineering and electronic materials. He is the co-author of over 35 peer-reviewed publications regarding mechanical properties of actinides and low-symmetry metals.Thomas A. Mason is a Research Engineer in the Weapon Systems Engineering Division at Los Alamos National Laboratory. He holds a Ph.D. in mechanical engineering from Yale University with an emphasis on statistical continuum mechanics. He currently specializes in the design and fielding of experiments that provide statistically relevant data sets that describe the response of complex systems to dynamic loading. He is particularly interested in off-normal environments and accident scenarios.David T. Fullwood is a member of the Materials group in the ME Department. Following his Ph.D. he spent 12 years working for the nuclear industry in the UK. As Head of R&D and Head of Mechanical Engineering he developed high-speed energy storage flywheels based on novel composites for two spin-off companies. The result was the most high-tech flywheel available, with applications on the NY Metro, a Fuji wind farm and other areas requiring energy smoothing. Dr. Fullwood now focuses on composites and computational materials.George Hansen is the Founder and President of Conductive Composites Company, where nanostrands are developed and manufactured. With a B.S. in chemical engineering, his central current interest is in the electromagnetic modification of polymers and composites with nanomaterials. He has been the Principal Investigator for nine major government awards in the field, totaling over $9 million in funding. He is the recipient of an R&D 100 Award, a NASA Nanotech 50 Award and is the 2010 Utah Innovator of the Year. Most recently, he is advancing these materials into full manufacturing.Experimental investigation on the mechanical properties of a low-clay shale with different adsorption times in sub-/super-critical CO2Knowledge of the effect of carbon dioxide (CO2) on the mechanical properties of low-clay shales is essential to shale gas production and CO2 sequestration. In this paper, a series of uniaxial compressive strength (UCS) variable-time experiments were performed on low-clay shale samples saturated in sub-/super-critical CO2. The crack propagation process and micro scale variations were recorded by acoustic emission (AE) sensors with 3D ARAMIS technology and SEM tests together with EDS analysis. According to the experimental results, sub-/super-critical CO2 adsorption weakens the strength and increases the ductility of the shale. The UCS and Young's modulus decrease with the increase of saturation time. Compared to samples saturated in sub-critical CO2, samples saturated in super-critical CO2 present lower strength and Young's modulus. AE results show that samples saturated at a longer time in sub-/super-critical CO2 present a higher number of peak cumulative AE energy. Super-critical CO2 saturation creates more AE energy than sub-critical CO2 saturation. Based on the SEM results, sub-/super-critical CO2 adsorption creates some new pores in shale samples which lead to the strength decreasing. EDS analysis presents that CO2 adsorption increase the C content of the shale which demonstrates the occurrence of chemical reactions in the shale.Due to the advantages of low costs and suitability for fracturing, water is only fracturing fluid applied in commercial shale gas exploitation. Generally, a typical shale gas well needs 7500 to 15,000 cubic metres of water for fracturing []. However, it is challenging for countries like China where water is scarce around shale gas reservoirs. Moreover, the flow-back water which is contaminated with muriatic acid, gelling agents, chemical modifiers and other substances will be difficult to be disposed of []. Therefore, the possibility of using non-aqueous fracturing fluids (e.g., super-critical CO2) instead of water has been received a great deal of attention [CO2 is known as a nontoxic fluid that has been used as high pressure fracturing fluids in about 40% of Canada's horizontal wells []. When the temperature is higher than 31.8 °C and the pressure is higher than 7.38 MPa, CO2 will present a super-critical characteristics which has low viscosity and no surface tension []. Super-critical CO2 offers several significant advantages over water in drilling and fracturing engineering []. The low viscosity and the high density make it possible to present better jetting behaviour than water which can be used as a drilling fluid instead of water []. Super-critical CO2 has low viscosity, which is similar to slick water that can generate complex, multi-orthogonal fracture networks []. The viscosity of super-critical CO2 is easy to be changed by adding CO2-philic species, such as perfluoroether and siloxane []. Meanwhile, the adsorptive capacity of CO2 in shale is 2–3 times higher than methane. This advantage can be used to enhance shale gas production [The injection of CO2 into shale reservoirs leads to sequestration that can help reduce the current emissions of this greenhouse gas to the atmosphere. When shale absorbs CO2, CO2 will move along the shale fracture systems, replace naturally existing CH4 because of the higher chemical potential []. Gas adsorption will influence organic matters swelling []. Although shale has low total organic carbon (TOC), which presents less swelling potential than coal after CO2 adsorption [], the high adsorption capacity will also have considerable influence on its mechanical properties. Some researchers have explored the effect of fluid saturations on shale properties [] investigated the strength of montmorillonitic, illitic and chloritic shale after water saturation. The results showed that shale strength decreased dramatically because of the water saturation. Wong [] investigated the influence of salinities on La Biche shale samples and found that shale swelling caused the decrease of Young's modulus. Ghorbani et al. [] conducted a series of experiments to demonstrate that the dynamic shear modulus of clay-rock samples increased because of the desiccation-driven hardening. Lyu et al. [] investigated the effect of sub-critical CO2 and water with sub- and super-critical CO2 on the mechanical properties of shale. The experimental results showed that all the three fluids decreased the strength of shales. Lu et al. []investigated the swelling of shale induced by CO2 with temperatures between 35 °C and 75 °C and pressures up to 15 MPa. The results showed that the swelling potential of shale first increases then decreases while the pressure increases gradually. Yin et al. []tested the mechanical properties of shale after 10 days of adsorption in different pressure of CO2. The results showed that the saturation of CO2 with different pressure caused the decrease of shale strength. However, the saturation time is too short for highly compact shales. CO2 adsorption also affects the particle size and pore structures of shales, which will directly influence the mechanical properties of shale [In the above studies, researchers mainly focus on the clay-rich shales. However, most resource shales are low-clay shales, which are characterized as low porosity and high stiffness []. For low-clay shales, the organic matters will make it possible to have good sorption potential of CO2 []. The adsorption of CO2 will change the mechanical properties of low-clay shales. In fact, the decrease of shale strength will cause well collapse in the drilling process, make natural and artificial fractures closure whiling fracturing and even reduce long-term trapping of CO2 as the permeability decreases. Therefore, in this study, we further investigate the influence of different sub-/super-critical CO2 adsorption time on the mechanical properties of a low-clay shale. Uniaxial compressive strength (UCS) tests were conducted together with the acoustic emission (AE) sensors and ARAMIS digital cameras to test the strength variation and crack propagations of shale samples. Scanning Electron Microscope (SEM) were also used to manifest the micro-scale variations of shale samples after sub-/super-critical CO2 adsorption.Nearly one third of Chinese shale gas is located in Sichuan Basin []. In this study, the shale samples were obtained from the Sichuan Basin, China (latitude and longitude coordinates: N29°52′47.8″, E108°17′06.6″). The mineralogical composition was analysed by Bruker AXS D8-Focus X-ray diffract meter, as shown in . Specimens were cored and polished in the Institute of Rock and Soil Mechanics, Chinese Academy of Science, China. The testing process were performed in the 3G deep laboratory of the Department of Civil Engineering at Monash University, Australia. The samples were cored parallel to the bedding and cut into 30 mm diameter cylinders. The length of each sample was 60 mm. Two round surfaces of each sample were carefully ground to make smooth faces.The experiments were conducted in two steps: (1) sub-/super-critical CO2 adsorption; (2) UCS tests and SEM tests. The arrangements of the experiments were listed in . Because of the limited shale samples, only two samples were used in each adsorption condition. Although samples were chosen carefully before the experiments, the anisotropy of the shale would make some of the samples have unacceptable compression results. Therefore, extra experiments will be done to ensure that each adsorption condition has two samples with minor strength deviation.sub-/super-critical CO2 adsorption. The schematic diagram of adsorption is shown in . Several high-pressure containers are connected in parallel to ensure that all samples were absorbed at the same pressure. Liquid CO2 flows from the cylinder to a cylinder pump. Then CO2 is compressed by a pump controller which has a precision of 1 kPa. When the pressure of CO2 in the pump reaches at 7 MPa for sub-critical CO2 or 9 MPa for super-critical CO2, it will be injected into the high-pressure container. Meanwhile, a resistive heater is covered on the surface of the container. The temperature of the heating system can be adjusted from room temperature to 100 °C. In this study, the temperature was set as 40 °C to make sure that CO2 in the container was in the super-critical phase when the pressure was 9 MPa. The adsorption times for the four containers were 10, 20 and 30 days. The pumps remained opened to maintain the adsorption pressure. Three shale slices (the thickness is 0.4 mm) were used for SEM tests. Two of them were put into the containers together with the samples which were saturated in sub-/super-critical CO2 for 30 days.All shale samples including the control group (two of which without adsorption) were tested in this study. The axial stress-strain, the AE response and the fracture propagation were recorded during the compression process. The experimental results will be discussed with mechanical behaviours, AE results and SEM analysis. shows the values of UCS and Young's modulus for all intact and soaked samples. Variations of UCS and Young's modulus are shown in . Samples soaked in sub-critical CO2 for 20 and 30 days, supplementary experiments have been done due to the outliers., the UCS of shale samples decreases after CO2 saturation. For intact samples, the average UCS value is 56.10 MPa. After 10 days of adsorption in sub-critical and super-critical CO2, the values decrease 8.79% to 51.17 MPa and 12.96% to 48.83 MPa, respectively. When the adsorption time extends to 20 days, the UCS value for sub-critical CO2 absorbed sample is 47.24 MPa, which is 15.79% lower than that of the intact samples. In the super-critical saturation condition, 20 days of saturation causes a reduction of 20.09% and the UCS value reaches to 44.83 MPa. When the adsorption time is 30 days, the UCS values for samples in both two saturation conditions are 43.18 MPa and 39.30 MPa, respectively. According to the study of Middleton et al. [], shale gas was absorbed in natural fractures, porous matrix and kerogen. Super-critical CO2 has 2–3 times higher adsorptive capacity than methane (the major component of shale gas) []. Although samples used in this study are outcrops, shale gas is no longer absorbed in the rock. However, the pores previously filled by shale gas in the samples can be easily occupied by CO2 []. As shale samples adsorb more and more CO2, they will swell, which contributes to the decrease of strength []. When the adsorption time is the same, samples in super-critical CO2 condition have lower UCS values than that in sub-critical CO2. The UCS gap between the two conditions increases with the increase of adsorption time, as shown in (a). This phenomenon is caused by three main reasons. Firstly, samples in sub-critical CO2 and super-critical CO2 have different ambient pressures (7 MPa for sub-critical and 9 MPa for super-critical, respectively). The 2 MPa higher pressure will let CO2 permeate into shale sample more easily and quickly. When the adsorption time is the same, samples in super-critical CO2 have higher saturation percentage than that in sub-critical condition. Secondly, higher ambient pressure will make shale samples absorb more CO2. This will lead to the samples become weaker. More importantly, compared to sub-critical CO2, super-critical CO2 has lower viscosity and no capillary force. This will make it easier for super-critical CO2 to move into shale samples. According to the decreasing trend of UCS values, if the adsorption time is longer than 30 days, the strength of shale samples will continue to decrease. This is mainly because shale sample has an ultra-low permeability []. After 30 days of adsorption, samples are still in unsaturated condition. When the saturation time is much longer, the strength of shale samples will reach to a stable value.The effect of sub-/super-critical CO2 adsorption time on the Young's modulus of shale samples is shown in (b). It can be seen that Young's modulus decreases gradually with increasing adsorption time. The intact samples have the highest Young's modulus of 5.98 GPa. When samples are soaked in sub-critical CO2 for 10 days, 20 days and 30 days, the values of Young's modulus reduce 16.05% to 5.02 GPa, 28.60% to 4.27 GPa and 32.61% to 4.03 GPa, respectively. The Young's modulus for samples in super-critical CO2 present reductions of 20.23% (10 days of adsorption), 33.61% (20 days of adsorption) and 37.79% (30 days of adsorption), respectively. As shale samples used in this study are a kind of highly brittle material (71.4% of brittleness index), the swelling caused by SC-CO2 adsorption will make shale samples more ductile and therefore the Young's modulus will decrease.Some researchers found a linear relationship between UCS and Young's modulus (E) for rocks like sandstone []. Based on the previous study, we can obtain the relationships between E and UCS for intact and CO2 absorbed samples which are shown in Eqs. where UCS is in MPa and E is in GPa. The R-squares for Eqs. Consider the decreasing trend of Young's modulus in (b), the Young's modulus will reach to a constant when the adsorption time is much longer than 30 days. Thus, we fitted the data with an exponential relationship between Young's modulus and adsorption time (t/day) by the curve fitting tool of Matlab R2012a, yieldingE=2.72exp(−0.0.063t)+3.27(super−critical)For which the R-squares are 0.9949 for sub-critical condition and 0.997 for super-critical condition, respectively. According to Eqs. , the Young's modulus will reach to a constant of 3.47 GPa for sub-critical adsorption samples and 3.27 GPa for super-critical adsorption samples when the soaking time is much higher than 30 days., we can obtain the minimum uniaxial compressive strength of sub-/super-critical saturated samples, which are 40.72 MPa and 37.71 MPa, respectively., when the saturation time is long enough, samples in super-critical CO2 has lower UCS and E values than that in sub-critical CO2. This is because of the higher confined pressure of super-critical CO2 than sub-critical CO2 and the different properties of the two phases of CO2. The differences of UCS and E values between samples soaked in sub-critical and super-critical CO2 for an ultra-long time are smaller than that saturated for 30 days. This is mainly because, samples are all fully saturated in both sub-critical and super-critical conditions. The penetration percentage will no longer affect the strength and Young's modulus.Acoustic emission (AE) technology was chosen in this study to observe the crack propagations of shale samples saturated in sub-critical and super-critical CO2. shows the values of cumulative AE energy, axial stress and axial strain for intact samples and samples soaked in sub-/super-critical CO2 from 10 to 30 days. The corresponding cumulative AE energy, axial stress and axial strain are listed in . For each soaking condition we used two samples, the one with higher axial strength was chosen to do the AE analysis. The crack variation during the uniaxial compression of shale samples consist of three stages: crack closure, stable crack propagation and unstable crack propagation, and two main point: crack initiation and crack damage, which is similar to the previous studies [, the cumulative AE energy of all samples at crack initiation varies between 1134 μJ and 6136 μJ except the sample saturated in super-critical CO2 for 20 days which presents a value of 17374 μJ. At the crack damage point, the cumulative AE energy increases to more than 10000 μJ except the one in sub-critical CO2 for 30 days, which is only 3849 μJ. These two unexpected values are caused by the anisotropy of shale samples. This anisotropy also lead to the result that no remarkable trend can be obtained for AE data of all samples at the two points. At the failure point, intact sample has the lowest cumulative AE energy, which is 36473 μJ. For sample saturated in sub-critical and super-critical CO2, this value increases with the increase of saturation time. When the adsorption time is 10 days, 20 days and 30 days, the maximum AE values are 54416 μJ, 60770 μJ and 69016 μJ for sub-critical condition, are 55607 μJ, 63725 μJ and 71437 μJ for super-critical condition, respectively. The increase of cumulative AE energy after adsorption is mainly caused by as flows: (1) the adsorption of CO2 will increase the conductivity of acoustic energy emission; (2) shale sample contains water, the reaction of CO2 with water will create hydrocarbons, which will be crushed and release acoustic energy during the compression; (3) the swelling caused by CO2 adsorption contributes to the occurrence of many artificial cracks, and the propagation of these fractures will produce more AE energy. When the CO2 phase is the same, longer adsorption time creates higher cumulative AE energy. This is because samples in CO2 need a long time to be fully saturated. A 30 days of adsorption presents a higher saturation percentage than a 10 days of adsorption, and therefore has higher AE energy. When keeping the adsorption time the same, it can be seen that the sample in sub-critical condition has lower total AE energy than that in super-critical CO2. This is caused by the difference of CO2 phase and adsorption pressure which will influence the adsorption of CO2. Compared to the peak cumulative AE energy, samples at crack initiation point and crack damage point have very low values of AE energy. This phenomenon is in accordance with the previous studies that AE energy is mainly created at the unstable crack propagation stage [The axial strains of all samples at crack initiation and crack damage points are around 0.6% and 0.7%, respectively. As the compressive strength tests were done at a constant displacement rate, and the crack initiation point and crack damage point are the boundary of the three stages, it can be concluded that CO2 saturation has less effect on the range of crack closure stage and stable crack propagation stage. At the failure point, intact sample has the lowest axial strain among the samples. This means that CO2 adsorption can expand the range of unstable crack propagation stage. At the three points, axial strains of samples in sub-/super-critical CO2 increase with increasing adsorption time. This is mainly because CO2 adsorption makes shale samples more ductile.When shale samples absorb CO2, CO2 will dissolve into the water inside the pores and cracks. The dissolution process can be described as the following chemical reactions,When the temperature is 40 °C and the pressure is 7 MPa, the pH of water saturated with CO2 will be 2.84 []. This kind of strong caustic liquid will lead to the dissolution and precipitation of some minerals of the shale sample, such as carbonates [In consideration of the sample compositions (shown in ), some chemical reactions will occur during the adsorption process [Fe2++Mg2++Ca2++bicarbonate↔mixedcarbonate+3H+ presents the results of SEM tests for intact samples and samples soaked in sub-/super-critical CO2 for 30 days. It is clear that no visible pores can be seen from the images ((a–b)) of intact sample as shale is a kind of highly compact rock. However, images ((c–f)) of saturated samples present some pores at different amplification factors. These pores are created by mineral dissolution. As SEM tests only show the surface of shale slices, it can be deduced that, after a long time of adsorption, CO2 will penetrate into the whole shale sample, dissolve into the water inside and create more pores. These artificial pores will organize a new porosity system which leads to the decrease of strength and Young's modulus []. Compared to the SEM results of CO2-water-shale interaction obtained by Lyu et al. [], samples after CO2 saturation show less pores on the surface than that with CO2+water saturation. This is because samples with CO2+water saturation are surrounded by acid fluids. Chemical reactions will occur everywhere. However, under pure CO2 saturation, only a small part of the shale sample where there has enough water for CO2 dissolution has the possibility of having chemical reactions. As SEM tests only show an ultra-small part of the surface of the shale slice, no convincing conclusion can be obtained by comparing the SEM results between sub-critical saturation and super-critical saturation.EDS analysis has been done based on the SEM results. shows the EDS results of intact samples and samples with sub-critical and super-critical CO2 adsorption. The Chemical element compositions of the three slices obtained by X-ray spectra are presented in . For slices saturated in sub-/super-critical condition, we conducted three times of EDS analysis at three different places. The one with moderate percentage of carbon was chosen in this paper to do the analysis. According to , O and Si account for the first and second highest proportion of the composition among the three slices, which are in accordance with the XRD results (shown in ) that shale samples used in the study contain high percentage of brittle minerals. For slices with sub-critical and super-critical CO2 saturation, C presents the third highest proportion among the elements, which are 6.7% and 7.9%, respectively. For the slice without saturation, the content of C is too low to be detected by the EDS sensors. The difference of the C content between intact sample and saturated samples is mainly caused by the precipitation of carbonates happens in the adsorption process. The influence of CO2 phase on the carbon content cannot be obtained through the EDS data as it only shows a small part of the slice surface. The decrease of the percentage of other chemical elements, such as Al, K and Fe after CO2 saturation, is mainly because of the increase of C content. From we can also see that, the contents of O and Si for samples with sub-/super-critical CO2 saturation are nearly the same as the intact sample. While in Ref. [], the percentage of Si and O varied sharply. It can be deduced that water plays a very important role in the variation of the mechanical properties of shale during CO2 adsorption.The effect of sub-/super-critical CO2 adsorption on the mechanical properties of a low-clay shale has been investigated and some conclusions are drawn as follows:The adsorption of sub-/super-critical CO2 causes reductions of shale strength and Young's modulus. The longer the adsorption time is, the larger decrease of the two values. From a 10-day adsorption to a 30-day adsorption, UCS and Young's modulus of samples with sub-/super-critical CO2 saturation show reductions from 8.79%/12.96% and 16.05%/20.23%–23.03%/29.95% and 32.61%/37.79%, respectively. The fitting results predict that fully saturated shale samples will have reductions of 27.42% for UCS and 41.97% for Young's modulus under sub-critical condition, 32.78% for UCS and 45.32% for Young's modulus under super-critical condition, respectively. The reduction of shale's mechanical properties is mainly caused by the adsorption of CO2 makes shale swell and the chemical reaction between CO2 dissolved water and shale samples. Super-critical CO2 adsorption causes higher reduction of shale strength than sub-critical CO2 when the adsorption time is the same. The reason for this result is because of the difference of phase and ambient pressure during the adsorption process. Longer saturation time also creates higher axial strains for samples before failure. It demonstrates that CO2 adsorption increases the ductility of the shale.AE energy is mainly created at the unstable crack propagation stage. The peak cumulative AE energy increases with increasing adsorption time for both of the sub-critical and super-critical CO2 saturation conditions. Intact shale sample has a peak AE energy of 36473 μJ. However, shale samples with 30 days of saturation in sub-critical and super-critical present total AE energy of 69016 μJ and 71437 μJ, respectively. The increase of AE energy after saturation is because of the CO2 adsorption and chemical reaction. With the same saturation time, super-critical condition has more positive effect on the increase of AE energy than sub-critical condition.SEM results shows that new pores appear on the surface of shale slices after sub-/super-critical CO2 saturation. The increase of carbon content after CO2 adsorption which obtained by EDS analysis proves that chemical reactions happen during the saturation process. The change of the shale's microstructure is the real reason for the variation of the mechanical properties of shale after sub-/super-critical saturation.Both the CO2 sequestration and the CO2 enhanced shale exploitation are long-term program. In this paper, the conclusions only presented the influence of CO2 on shale with a short-term saturation experiments. A long time saturation for low-clay shales with CO2 is necessary to the investigation of the effect of CO2 on shale's mechanical properties.Formation of fine cementite precipitates by static annealing of equal-channel angular pressed low-carbon steelsIn this study, a static annealing of low-carbon steels severely deformed by equal-channel angular pressing was conducted. Employment of the processing route on a low-carbon steel containing 0.06% vanadium resulted in the formation of cementite precipitations as well as the refinement of ferrite grains to submicrometer size. During the static annealing treatment, rod-like cementites in the pearlite colonies of the sample decomposed to form spherical cementite precipitates distributed uniformly in ferrite grains. The decomposition phenomenon of the cementite is discussed on the basis of the dislocation–cementite interaction.Precipitation hardening is one of the most frequently used strengthening methods in metallic alloys. The precipitation is usually induced by a conventional heat treatment route, which includes solutionization, quenching and aging treatments. Although the route has been used successfully in various non-ferrous alloys, it has rarely been used in plain carbon steels because a martensitic phase supersaturated with carbon usually results during the quenching, instead of a ferrite phase supersaturated with carbon. As the martensite is relatively stable, precipitation of the cementite phase can only be obtained when tempered just below the eutectoid point for a moderate length of time. The cementite precipitates, however, coarsen significantly during the tempering treatment and provide little contribution to the strengthening effect of the steel As a potential processing method to produce the steel with cementite precipitates, a process of severe plastic deformation followed by static annealing heat treatment was noted. Originally, the process was used to restore the ductility of eutectoid steel after wire drawing The decomposition was attributed to microstructural features generated by the severe plastic deformation. The features include high dislocation density, fine cementite size and high defect concentration in the cementite phase. The high dislocation density should increase the degree of cementite–dislocation interaction On the basis of this assumption, an attempt was made in this study to investigate the cementite decomposition behavior in severely deformed plain carbon steels of different recrystallization temperatures during annealing treatment. When the recrystallization temperature of a steel is increased to above the annealing temperature, the microstructural features in the severely deformed steel might be retained during the treatment. Severe plastic deformation on the steel was imposed by the equal-channel angular (ECA) pressing technique. The technique does not alter the dimension of the sample and has been used mainly in refining the grain size of aluminum alloys and steels to less than 1 μm A severe plastic deformation was imposed on a low-carbon steel having a composition of Fe–0.15 C–1.1 Mn–0.25 Si–0.06 V in wt% (hereafter, CSV steel) using the ECA pressing technique. The vanadium was alloyed in this steel to raise the recrystallization temperature. For the purpose of comparison, a carbon steel of similar composition but without the vanadium addition (hereafter, CS steel) was prepared through the same route. The samples, of dimensions ∅18 mm×130 mm (diameter×length), were deformed by up to four passes in an ECA pressing die. The die geometry was designed to yield an effective strain of about 1 per pass: the inner contact angle and the arc of curvature at the out point of contact between the channels of the die were 90° and 20°, respectively. The ECA pressing was conducted at a temperature of 350°C and a pressing speed of 2 mm/s to prevent surface cracking of the sample. During ECA pressing, the sample was rotated 180° around its longitudinal axis between passes.Annealing of the samples after the ECA pressing was conducted in the range from 420 to 600°C for 1 to 24 h. The microstructures of the two steels thus produced were examined by optical microscopy, transmission electron microscopy (TEM; Jeol JEM 2010) and scanning electron microscopy (SEM; Jeol JEM 6330F). Room-temperature tensile properties of the steels were measured with the initial strain rate of 1.33×10−3 s−1 on an Instron machine (type 4206).Optical micrographs of samples in the as-received condition, after four passes of ECA pressing, and after annealing of the pressed sample at 600°C for 1 h are illustrated in . The microstructure of the as-received CS steel consists of ferrite grains and pearlite colonies (which appear as black phases in the micrograph), of size approximately 30 μm in diameter. The microstructure of the CSV steel in the as-received condition appeared to be similar, but its grain size was approximately 10 μm in diameter. The pearlite colonies and ferrite grains of the CS steel after four passes of ECA pressing became heavily deformed and could not be resolved with an optical microscope []. The microstructure of the CSV steel in the as-pressed condition was similar to that of the CS steel.After the ECA-pressed CS steel was annealed at 600°C for 1 h, a significant fraction of the ferrite grains became recrystallized and the pearlite colony was restored []; a detailed TEM analysis of the sample will be given in a following section of this paper. It is also noted that cementite particles precipitated near the colonies after the annealing treatment. On the contrary, when the pressed CSV steel was annealed at the same condition, the pearlite colonies disappeared completely and cementite particles precipitated uniformly throughout the matrix [The decomposition behavior of the pearlite colonies in the CSV steel was studied by changing the annealing time and temperature. shows SEM micrographs of the sample annealed at 540°C for 1, 4 and 24 h, respectively. When annealed for 1 h, the cementite in the colony retained the rod-like morphology, while fine cementite particles precipitated near the colony []. In the sample annealed for 4 h, the diameter of the rod-like cementite was reduced significantly and transformed into discrete particles []. Further increase of the annealing time to 24 h led to complete disappearance of the pearlite colonies and homogeneous distribution of the cementite precipitations throughout the ferrite matrix []. The decomposition time was increased to 24 h at 540°C, compared with 1 h at 600°C.Although the pearlite colonies in the CS steel were restored after the annealing treatment as shown in , detailed examinations of the microstructure revealed a significant variation in their morphology. In some of the colonies, the rod-like cementites were restored. In others, they transformed into spherical precipitations. shows a TEM micrograph of a pearlite colony consisting of the spherical cementite precipitations. The sample was annealed at 540°C for 1 h. However, the precipitations were limited within the former colonies or neighboring grains instead of being uniform throughout the matrix.The effect of annealing temperature on the decomposition of the rod-like cementite in the CSV steel was also investigated while keeping the annealing time to 1 h. Increase in the annealing temperature led to a faster decomposition of the rod-like cementite and precipitation of spherical cementite particles. TEM observation of the CSV steel annealed at 420°C for 1 h indicated that the rod-like cementite remained in the colony []. The kinetics of the decomposition reaction seems to be slow at this temperature. As the annealing temperature was increased to 540°C, the cementite became discontinuous and partially spherodized []. At this temperature, however, the morphology and size of the cementite phase varied significantly depending on the location of the observation. The cementite became completely spherodized in some pearlite colonies, while the rod-like cementite remained in other colonies. When the annealing temperature was increased to 600°C, the rod-like cementite disappeared completely and spherical cementite particles resulted [The effect of vanadium alloying on the microstructures of the steels was examined using the sample annealed at 540°C for 1 h. In the CS steel, a significant fraction of ferrite grains became recrystallized by the annealing treatment []. The recrystallized grains were approximately 3 μm in diameter. In the CSV steel, however, the grains were not recrystallized [], indicating a higher recrystallization temperature. The effect of vanadium on the increase in recrystallization temperature has been reported in various studies ]. From the TEM micrograph, the dislocation density in the colony was estimated to be of the order of 1016 m−2. The addition of the vanadium resulted in a high dislocation density in the sample, especially in the pearlite colony.Tensile properties of the CS and CSV steels were measured as-received, after ECA pressing, and after annealing at 540°C for 1 and 24 h []. The yield strength of the as-received CS and CSV steels was approximately 310 and 380 MPa, respectively. The strength of the CS and CSV steels in the ECA pressed condition was increased to 930 MPa. Upon annealing at 540°C for 1 h, the strength of the CS and CSV steels decreased to 690 and 870 MPa, respectively. As the annealing time was increased to 24 h, the strength decreased further to 330 and 500 MPa for CS and CSV steel. A combination of the grain size refining and the fine precipitation of cementite in the CSV steel enhanced its tensile properties significantly.Annealing of the ECA-pressed CSV steel led to decomposition of the entire pearlite colonies and uniform precipitation of cementite particles throughout the ferrite matrix. The decomposition reaction occurred not only during the deformation stage but also during the annealing stage. This extraordinary phenomenon demonstrates a potential new processing route of forming fine precipitates by the static annealing of severely deformed steel, instead of the conventional heat treatment route including the solutionizing, quenching and aging treatment., a significant fraction of the rod-like cementite in the ECA-pressed CS steel had transformed to spherical particles after the static annealing. The cementite was observed to coarsen during the annealing treatment. If the decomposition reaction had occurred during annealing of the sample as in the CSV sample, the cementite should have become smaller in size with the progress of the treatment. These results indicate that the transformation is due to the reprecipitation of supersaturated carbon atoms during ECA pressing.Examination of annealed CS and CSV steels indicated that a major microstructural difference between the two steels lies in the dislocation density, especially in the areas of former pearlite colonies []. The other microstructural features that were cited As the formation energy of cementite is relatively low where C0 is the equilibrium concentration in the matrix, b the Burgers vector of the edge component, ν the Poisson's ratio, μ equals E/2(1+ν), E the Young's modulus, vs the atomic volume of carbon and va the interstitial site volume of ferrite steel. As the cementite becomes nano-sized, the experimentally determined C0 value , the ECC value is a strong function of the density and is negligible as the density becomes less than 1014 m−2. When the density is 1016 m−2, the ECC varies from 0.00015 to 0.002 at% in a temperature range from 420 to 600°C. Although the rate constant for the decomposition reaction was not determined, the calculated ECC value, which is 10–20% of the equilibrium concentration, is considered to be large enough for the decomposition reaction to proceed at a reasonable rate. Therefore, the colony of high dislocation density such as in the CSV steel might have promoted the decomposition via the interaction with the dislocations., the decomposition of the rod-like cementite into spherical cementites appeared to be similar to the break-up of a cylindrical liquid jet into spherical droplets, i.e., Rayleigh instability The uniform distribution of the cementite particles indicates that the carbon atoms released from the decomposition reaction must have diffused away from the colonies to ferrite grains and reprecipitated during the static annealing treatment. This phenomenon is considered to be related with the difference in dislocation densities in the CSV steel. As shown in , the dislocation density in the pearlite colony was much higher than that inside the ferrite grain. As the ECC value is very sensitive to the dislocation density as shown in , the ECC value in the colony is relatively high compared with that inside the ferrite grain, which would eventually induce a diffusion flux towards the ferrite grains. As the carbon diffused away from the colony towards the ferrite grain of low dislocation density, the grain would become supersaturated with the carbon atoms, providing a favorable condition for the precipitation.A simple estimation of the diffusion distance of carbon atoms during the annealing at 540°C for 1 h, using the relationship x=(Dt)1/2, indicated that the distance is about 120 μm, which is much longer than the inter-colony distance (in this sample, the distance is approximately 30 μm). The diffusivity of carbon in steel used for the estimation was Static annealing of an ECA-pressed steel led to the formation of uniformly distributed cementite precipitates. The pearlite colonies were completely decomposed and fine cementite precipitates were uniformly distributed throughout the ferrite matrix when a plain carbon steel containing 0.06% V was annealed at a temperature range from 420 to 600°C. The formation is a result of pearlite decomposition during the static annealing. TEM observation of the annealed steel indicated that the dislocation density in the colony remained similar to that in the ECA-pressed condition, providing evidence for a decomposition via dislocation–cementite interaction. The rate of the decomposition reaction was observed to increase with annealing temperature. The decomposition and precipitation reactions appeared to be controlled by the kinetics of the reactions rather than the diffusion of carbon through the ferrite matrix. Available online at www.sciencedirect.com ScienceDirect Materials Today: Proceedings 5 (2018) 3587â€“3594 www.materialstoday.com/proceedings ICMPC 2017 Characterization of Ni-Fe-W matrix alloys in as-cast and heat treated conditions A Sambasiva Raoa*, M.K.Mohanb and A. K. Singha a Defence Metallurgical Research Laboratory, Kanchanbagh P.O., Hyderabad â€“ 500 058, India. b Department of Metallurgical and Materials Engineering, National Institute of Technology, Warangal, Telangana â€“ 506 004, India. Abstract Selection and/or Peer-review under responsibility of 7th International Conference of Materials Processing and Characterization. Keywords: Ni-Fe-W Matrix alloy; Vacuum Induction Melting; Microstructure; EPMA; XRD 1. Introduction: Tungsten Heavy Alloys (WHA) prepared by powder-based liquid phase sintering are a unique class of y h y h g r materials developed for applications where their high density can be used to advantage such as kinetic energ penetrators, radiation shields and counterbalance weights etc [1-3]. WHAs are two-phase composites whic normally consist of nearly rounded hard tungsten grains (bcc) embedded within a Ni-base ductile matrix (fcc) allo [4-6]. In general, the matrix phase is a Ni-based solid solution having Fe, Co and W elements [4]. Owing to the hig melting point of tungsten, the WHAs are typically prepared by powder metallurgy using liquid phase sinterin instead of using conventional ingot melting route [7]. Several authors have investigated the WHAs in powde metallurgy route and optimized processing parameters, which results in better mechanical properties [8-10]. Present work described the detail microstructural characterization of the two matrix alloys (Alloy I: 53Ni-29Fe-18W and alloy II: 43Ni-11Fe-30W-16Co). These alloys are prepared by a combination of powder and ingot metallurgy route display close to theoretical density. Both the alloys exhibit the presence of single fcc phase in as-cast condition. The Alloys I and II demonstrate the presence of single and two phases in heat treated condition, respectively. The present alloys can be prepared using conventional ingot metallurgy route with maximum solubility of W in matrix. The solubility of W in matrix of both the alloys is nearly same although the alloy II displays the presence of Co7W6 intermetallic phase. The intermetallic phase Co7W6 is observed only at the grain boundaries. This has been attributed to enrichment or micro-segregation of Co during solidification. Â© 2017 Elsevier Ltd. All rights reserved. 2214-7853Â© 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of 7th International Conference of Materials Processing and Characterization. Corresponding author. Tel.: +91-9866106144; fax: +91-40-24340681. E-mail address:[email protected] 3588 A Sambasiva Rao et al. / Materials Today: Proceedings 5 (2018) 3587â€“3594 In addition to playing a prominent role on developing WHAs, the matrix alloy containing Ni-Fe-W and Cu- W alloys are also widely used for fabrication of shaped charge warhead liners for defence applications. Shaped Charge Liner (SCL) is a concave metal hemisphere or cone (known as a liner) backed by a high explosive. When the high explosive detonates, the metal liner is compressed and squeezed forward, forming a metal penetrating jet. The high velocity of the jet in combination with the high density of the material forming the jet generates a very high amount of kinetic energy enabling the penetrating jet to pierce the target [11]. It has been reported in U.S.Patent 7261036 that the tungsten is a suitable material for fabrication of shaped charge liners mainly due to its high density, high sound velocity and high ductility [12]. Hanwei He et al. have studied and established direct current (DC) electrodepositing technique to prepare Ni-Cu-W alloys for liners for shaped charges successfully [13]. Bai Xi et al., have worked on the penetration performance of pure W, Ni-Fe-W alloy and Cu-W alloys for SCL against steel target [14]. They formulated that the performance of the SCL depends not only on the density, ductility, jet velocity but also the type of target material. Most of the tungsten heavy alloys have been processed with the tungsten composition containing more than 80 wt.% [4]. Since the Ni-Fe eutectic composition along with Co and Cu brings down the processing temperature of tungsten metal during powder-based liquid-phase sintering, it is indeed possible to produce similar matrix alloy composition (absence of tungsten as composite element) through conventional ingot meting route. The literature reported on production of matrix alloy through conventional ingot meting route and microstructure and mechanical property correlation is rather limited. Ekbom et al.[15] and Woodward et al.[16] have reported the mechanical properties (tensile and compressive) on Ni-Fe-W matrix compositions without the tungsten particles present in full composite formulations. Knipling et al. have also studied the effect of dissolved tungsten on the deformation behaviour of 70Ni-30Fe alloy in as-cast as well as heat treated conditions [17]. Thus, the present study is aimed to characterize matrix alloy without the presence of tungsten particle as composite through typical vacuum induction furnace (VIM). As the solubility limit in Ni base alloy reported by several authors that it can dissolve into solid solution up to only 23%, the present study also aimed to examine the extent of tungsten solubility in Ni-Fe-Co base alloy during conventional melting. 2. Experimental details Two alloys with a nominal composition of 53Ni-29Fe-18W (Alloy-I) and 43Ni-11Fe-30W-16Co (Alloy-II) were prepared by blending elemental powders of Nickel, Iron, Tungsten and Cobalt followed by powder processing methodology in order to get uniform mixing and to reduce impurity interstitial elements such as oxygen etc. The blended powders were further cold compacted and pre-sintered at 1100oC in H2 controlled atmosphere furnace. Subsequently, these compacts were conventionally melted in vacuum induction furnace at a temperature of 1500oC and poured into mould in the form of ingot sizing around 70 mm diameter and 255 mm length. Typical flow sheet for processing of elemental powders for VIM melting is shown in Fig. 1. Fig. 1: Flow sheet for processing of elemental powders for melting. Selection of elemental powders and Hydrogen reduction at 700oC for 1 hrs Pre-mixing in Ball Mill (48 hrs) Cold Isostatic Pressing (Pressure â€“ 250 MPa) Green Compacts Pre-sintering at 1100oC with Hydrogen for 2 hrs Melt in Vacuum Induction Furnace (1500oC) A Sambasiva Rao et al./ Materials Today: Proceedings 5 (2018) 3587â€“3594 3589 The densities of as-cast ingots were evaluated by Archimedes principle and compared with the theoretical densities calculated by Rule-of-Mixture (ROM). The as-solidified ingots were subsequently sectioned from three different zones i.e from top, middle and bottom of the ingot to create various kinds of samples for characterization. Chemical compositions of as-solidified alloys were analyzed using Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) and Electron Probe Micro Analyzer (EPMA) / Energy Digressive Spectroscopy (EDS) for bulk and micro compositions, respectively. Samples were prepared as per standard metallographic procedure and etched with a solution of 5g FeC13 and 15 ml HC1 in 60 ml ethanol. The microstructures of the etched samples were examined by Optical and Scanning Electron Microscopes (OM and SEM). Microstructural characterization for both qualitative and quantitative was carried out using CAMECA make EPMA SX-100 model in un-etched condition. In order to retain second phase if any, as-cast alloys I and II were heat treated at 750ÂºC and then water quenched. The X-ray Diffractometer (make: Philips PW3020) equipped with a graphite monochrometer operated at 40 kV and 25 mA was used for recording the X-ray diffraction (XRD) patterns of both as-cast as and heat treated conditions for phase analysis. 3. Results and Discussion: 3.1 Green, sintered and VIM compacts: A typical photographs of powder compacts processed at three different stages are shown in Fig. 2 (a-c). The green compact exhibits gray in colour (Fig. 2a). On the other hand, pre-sintered compacts have shown a shiny appearance (Fig. 2b) while vacuum induction melted ingots has a dull cluster with a rough surface finish (Fig. 2c). The pre-sintering process mainly reduces surface oxidation and also makes it amenable to handle for further processing. As this process is conducted at 1100oC under reducing atmosphere, the atoms diffuse across the boundaries of the particles, and fused together and create a solid piece of mass [18]. As a result, the pre-sintered compact exhibits smooth and shiny compared to green compact (Fig. 2b). Fig. 2: Photographs of Alloys I and II processed at different stages: (a) Green Compact (b) Pre-Sintered Compact and (c) Vacuum induction melted ingot. The theoretical and experimental densities of both the experimental alloys are shown in Table 1. The vacuum induction melted ingots display density values nearly close to that of theoretical densities of the respective alloys. The minor differences can be attributed to the presence of micro porosity in as-cast materials. 10 5 53Ni-29Fe-18W (Alloy-I) 43Ni-11Fe-30W-16Co (Alloy-II) c a b c a b 3590 A Sambasiva Rao et al. / Materials Today: Proceedings 5 (2018) 3587â€“3594 Table 1: Theoretical and experimental densities of the alloys I and II. Description Analyzed composition (Wt. %) ROM density (g/cm3) Archimedes density (g/cm3) Alloy-I 53Ni-29Fe-18W 9.47 9.43 Alloy-II 43Ni-11Fe-30W-16Co 10.46 10.35 3.2. Chemical analysis: The chemical compositions of both the alloys obtained by ICP-OES and EPMA are given in Table 2. The tungsten volatile loss during conventional melting is observed to be minimal and the final composition of both the alloys has met the aimed composition. Impurity elements like carbon and oxygen have reduced to minimum level due to sintering under reducing atmosphere as well as vacuum induction melting. Table 2. Chemical compositions of both the alloys I and II in as-cast condition. Elements Bulk analysis (ICP-OES) Wt.% Micro analysis (EPMA) in Wt.% Alloy-I Alloy-II Alloy-I Alloy-II Ni 50.7 42.3 52.4 42.2 Fe 30.3 10.1 29.5 11.3 W 18.9 31.5 18.1 30.2 Co -- 15.9 -- 16.3 C <0.021 <0.024 -- -- O <0.015 <0.02 -- -- 3.3 Microstructural characterization: The optical microstructures of the as-cast alloys I and II are shown in Fig. 3 and 4. The alloy I exhibits the presence of typical dendritic structure with coarse columnar grains (Fig. 3 a and b). In contrast, the alloy II displays sub-structure within the grains (Fig. 4 a and b). It also depicts the cracks along the grain boundaries in alloy II. Presence of cracks in alloy II can probably be attributed to the formation of intermetallic consisting of cobalt [19-20]. The optical microstructures of the as-cast alloys both I and II do not show the presence of clusters of un-dissolved particles or second phase (Fig 3 and 4). However, micro-porosity is observed in high magnification images of both the as-cast alloys (Fig. 3 and 4). Fig. 3: Optical micrographs of Alloy I in as-cast condition at (a) low and (b) high magnification. b Micro-porosity a A Sambasiva Rao et al./ Materials Today: Proceedings 5 (2018) 3587â€“3594 3591 Fig. 4: Optical microstructure of Alloy II in as-cast condition at (a) low and (b) high magnification. 3.4 Electron Probe Micro Analyzer (EPMA) analysis: Back scattered electron (BSE) obtained for both the alloys are shown in Fig. 5 and 6. It is well known that the BSE image contrast depends on the average atomic number of the phases present in microstructure [21]. The higher atomic number element tungsten appears as brighter, while lower atomic number elements (such as iron, nickel and cobalt in our alloys) emerge as darker in the BSE microstructure. The BSE image obtained for alloy I displays single phase in absence of un-dissolved tungsten particles or any other second phase etc (Fig. 5). The BSE image of alloy II illustrates two phase structure with the distribution of fine particle with bright in contrast (Fig. 6). These bright particles are decorated along the grain boundaries (Fig. 6 a and b). The elemental analyses of both the alloys are displayed at Table 3.The analyses have revealed that the bright particles at the grain boundary regions in alloy II contain significantly high tungsten content compared to within the grain. The quantitative analysis result indicates that the bright contrast phase (intermetallic) is presumably Co7W6 type phase (Table 3). The chemical composition of the intermetallic phase in atom% (16.33W- 20.4Co) supports the above stoichiometry. It appears that the precipitation of intermetallic phase in alloy II occurs during solid state transformation. In addition, the grain boundaries also display the presence of cracks as observed in optical microstructure (Fig. 6 a and b). The EPMA analysis demonstrates that the alloy I show complete solubility of W in matrix. Interestingly, the alloy II also reflects high solubility of W in matrix. The presence of W in matrix of both the alloys supports the same (Table 3). This also reflects that the present alloys I and II can be prepared using conventional ingot metallurgy route with maximum solubility of W in matrix. Fig. 5: EPMA-BSE micrograph of Alloy I in as-cast condition. 100 Âµm BSE Micro-Porosity Cracks a Crack b Micro-porosity 3592 A Sambasiva Rao et al. / Materials Today: Proceedings 5 (2018) 3587â€“3594 Fig. 6: EPMA-BSE micrograph of Alloy II in as-cast condition at (a) low and (b) high magnification. Table -3: EPMA analysis of alloy I and II in as-cast condition. Description Location Composition (Wt.%) Ni Fe W Co Alloy I Within grain 52.7 29.6 17.5 -- At grain boundary 52.64 30.12 17.18 -- Alloy II Within grain 42.2 11.2 30 16.5 At grain boundary 25.4 10.9 49.4 13.5 3.5 X-Ray Diffraction: XRD patterns of the as-cast alloys are shown in Figs. 7 and 8. These patterns exhibit the presence of single fcc phase only. It indicates that the bcc W is completely dissolved in the fcc matrix and resulted in a single phase solid solution in alloy I. The alloy II also exhibits a similar trend. The intensities of X-ray peaks are different for alloys I and II (Figs. 7 a and b). This can be attributed to the presence of solidification texture due to sample orientation. The XRD patterns of the alloys I and II display single and two phases in heat treated condition respectively. The XRD pattern of the heat treated alloy II is shown in Fig. 8. It displays the two phases namely, Ni matrix and Co7W6. The formation of Co7W6 in alloy II is mainly because of the enrichment or micro-segregation of Co during solidification [19-20]. b Bright particle Crack BSE 2.5 Âµm BSE Crack Bright particles a Micro-Porosity 10 Âµm A Sambasiva Rao et al./ Materials Today: Proceedings 5 (2018) 3587â€“3594 3593 Fig. 7: XRD patterns of as-cast alloys (a) Alloy I and (b) Alloy II. Fig. 8: XRD pattern of Alloy II heat treated at 750oC for 20 min. Conclusions: 1. The alloys prepared by a combination of powder and ingot metallurgy route display close to theoretical density. 2. The Alloys I and II show the presence of single fcc phase in as-cast condition. While the alloys I and II exhibit single and two phase microstructure in heat treated condition, respectively. 3. The alloy II reveals the presence of the Co7W6 intermetallic phase in heat treated condition. This has been attributed to enrichment or micro-segregation of Co during solidification. 4. The present alloys can be prepared using conventional ingot metallurgy route with maximum solubility of W in matrix. 3594 A Sambasiva Rao et al. / Materials Today: Proceedings 5 (2018) 3587â€“3594 Acknowledgements Authors acknowledge Defence Research and Development Organisation for financial support and Dr Samir V Kamat, Director, DMRL for his kind encouragement. Authors gratefully acknowledged Dr. T.K. Nandy, division head Powder Metallurgy Division for his support and encouragements. Authors would also like to thanks to PPG, SMG and EMG groups of DMRL for their kind help. References: [1] F.V. Lenel, Powder Metallurgy: Principles and Application, Princeton: Metal Powder Industry Federation, 1980. [2] R.M. German, L.L.Bourguignon, B.H.Rabin, Powder Metall. 5 (1992), pp. 3â€“13. [3] R.Gero, D.Chaiat, High density tungsten alloys. In: Minkoff I, editor. Mater Eng Conf, (1981), pp. 46â€“50. [4] A.Upadhyaya, Processing Strategy for Consolidating Tungsten Heavy Alloys for Ordnance Applications, Materials Chemistry and Physics, 67 (2001), pp. 101-110. [5] H.J.Ryu, S.H.Hong, W.H.Baek, Mater Sci Eng A 291 (2000), pp.91-96. [6] W.D.Cai, Y.Li, R.J.Dowding, F.A.Mohamed, E.J.Lavernia, A Review of Tungsten-Based Alloys as Kinetic Energy Penetrator Materials. Reviews in Particulate Materials, 3 (1995), pp. 71-131. [7] C.C.Fu, L.J.Chang, Y.C.Huang, P.W.Wong, J.S.C.Jang, Advanced Materials Research, 15-17 (2007), pp. 575-580. [8] B.H.Rabin, A.Bose, R.M.German, International Journal of Powder Metallurgy, 25(1989), pp. 21-26. [9] R.M.German, L.L.Bourguignon, Powder Metallurgy in Defence Technology, 6 (1984), pp.117-131. [10] R.M.German, In â€˜Tungsten & Tungsten Alloys, edited by A.Bose and R.J.Dowding, Metal Powder Industries Federation, Princeton, New Jersey, (1992), p.3, [11] M.T.Stawovy, Single Phase Tungsten alloy, United sates patent, Patent No. US 7360488 B2, Date of patent Apr. 22, 2008. [12] B.Boume, K.G.Cowan, Shaped Charge Liner, United Sates Patent, Patent No. US 7261036 B2, Date of Patent 28 Aug 2007 [13] H.Hanwei, J.Shouya, J. Mater. Sci.Techol, 26(5) (2010), pp. 429-432. [14] Bai Xi, Liu Jinxu, Li Shukui, Lv Chicui, Guo Wenqi, Wu Tengteng, Materials Science and Engineering A553 (2012), pp.142-148. [15] L.B.Ekbom, U.Lindegran, J.E. Andersson, Int. J. Refractory Hard Met., 7(4) (1988), pp.210-14. [16] R.L.Woodward, I.G.McDonald, A.J.Gunner, Mater. Sci. Lett., 5 (1986), pp. 413-14. [17] K.E.Knipling, G.Zeman, J.S. Marte, S.M.Kelly, S.L.Kampe, Metallurgical and Materials Transactions A, 35A (2004), p. 2821. [18] ASM handbook Vo.7, â€˜Powder Metallurgyâ€™, 2015 [19] B.Katavic, M.Nikacevic, Z.Odanovic, Science of sintering, 40 (2008), pp. 319-331. [20] M.Seiji, O.Kenji, M.Tetsuo, Materials Transactions, 48 (2007), pp.2403-2408. [21] JI Goldstein et al., Scanning Electron Microscopy and X-ray Microanalysis, 3rd edition, Kluwer Academic Plenum Press, New York, (2003), p. 689. rix and Co7W6. The formation of Co7W6 in alloy II is mainly because of the enrichment or micro-segregation of Co during solidification [19-20]. b Bright particle Crack BSE 2.5 Âµm BSE Crack Bright particles a Micro-Porosity 10 Âµm A Sambasiva Rao et al./ Materials Today: Proceedings 5 (2018) 3587â€“3594 3593 Fig. 7: XRD patterns of as-cast alloys (a) Alloy I and (b) Alloy II. Fig. 8: XRD pattern of Alloy II heat treated at 750oC for 20 min. Conclusions: 1. The alloys prepared by a combination of powder and ingot metallurgy route display close to theoretical density. 2. The Alloys I and II show the presence of single fcc phase in as-cast condition. While the alloys I and II exhibit single and two phase microstructure in heat treated condition, respectively. 3. The alloy II reveals the presence of the Co7W6 intermetallic phase in heat treated condition. This has been attributed to enrichment or micro-segregation of Co duringCharacterization of Ni-Fe-W matrix alloys in as-cast and heat treated conditionsPresent work described the detail microstructural characterization of the two matrix alloys (Alloy I: 53Ni-29Fe-18W and alloy II: 43Ni-11Fe-30W-16Co). These alloys are prepared by a combination of powder and ingot metallurgy route display close to theoretical density. Both the alloys exhibit the presence of single fcc phase in as-cast condition. The Alloys I and II demonstrate the presence of single and two phases in heat treated condition, respectively. The present alloys can be prepared using conventional ingot metallurgy route with maximum solubility of W in matrix. The solubility of W in matrix of both the alloys is nearly same although the alloy II displays the presence of Co7W6 intermetallic phase. The intermetallic phase Co7W6 is observed only at the grain boundaries. This has been attributed to enrichment or micro-segregation of Co during solidification.Electronic and thermal properties of B2-type AlRE intermetallic compounds: A first principles studyThe ground state electronic structure and thermal properties of B2-type intermetallic compounds AlRE (RE: Pm, Sm, Eu, Tb, Gd and Dy) have been studied using a self-consistent tight-binding linear muffin-tin orbital (TB-LMTO) method at ambient as well as at high pressure. These compounds show metallic behavior under ambient condition. The band structure, total energy, density of states and ground state properties like lattice parameter, bulk modulus are calculated in the present work. The Debye–Grüneisen model is used to calculate the Debye temperature and the Grüneisen constant. The calculated results are in good agreement with the reported experimental and other theoretical results. The variation in the Debye temperature with pressure has also been reported. We present a detailed analysis of the role of f electrons of RE in the AlRE system.► The electronic and thermal properties of B2-type AlRE (RE: Pm, Sm, Eu, Gd, Tb and Dy) have been studied using the first principles TB-LMTO method. ► Thermal properties have been calculated using the DG model. ► The band structure indicates the metallic nature of the present intermetallics. ► The variation in the Debye temperature with pressure has also been reported. The possibility of structural phase transformation is predicted. ► Anomalous behavior in DOS is observed under compression, which may be due to the delocalization of f electrons under pressure.The rare earth (RE) lanthanide-based intermetallics are endowed with exotic physical, chemical and mechanical properties The energy dispersive powder X-ray diffraction measurements of some LnM (Ln=La, Ce, Nd and Gd; M=Cu, Ag and Zn) compounds have been performed by Degtyareva et al. the rare earths have different occupation numbers for 4f shell from 0 to 14 through the series from La to Lu. Due to this reason the AlRE compounds have a wide range of different magnetic as well as electronic properties. Some experimental information about the structure of AlRE equiatomic intermetallics can be found in literature In the present work we report the ground state electronic and thermal properties of AlRE (RE: Pm, Sm, Eu, Tb, Gd and Dy) intermetallics. These compounds crystallize in cubic cesium chloride structure (B2-type, Pm3m, Space Group 221). In our earlier attempts . The Debye temperature and the Grüneisen constants, by incorporating first principles theory in the DG model, are briefly described in . The results and discussion on electronic and thermal properties of all AlRE intermetallics are presented in , followed by discussion and conclusion.The total energy, band structure and density of states for AlRE are calculated in a manner similar to our previous work To calculate important thermal properties of a vibrating Debye lattice we have used the Debye–Grüneisen (DG) model where r is the Wiegner radius in a.u., B is bulk modulus in kbar and M is the average atomic weight, which is the weighted arithmetical average of the masses of the species for compounds The details about the prefactor used in Eq. The electronic band structure calculations are performed to estimate the total energy of AlRE intermetallics by using first principles TB-LMTO method. The total energy is plotted against different compressions for six AlRE compounds and shown in . The minimum of this curve defines the equilibrium volume V0 (or equilibrium separation r0), which is found to be 42.84 Å3 and corresponding lattice parameter is 3.45 Å, for AlPm, which is underestimated by 5.43% as compared to other theoretical data . The present calculated values of lattice parameters are in good agreement with the others calculated values We have presented band structure along the high symmetry directions for all the AlRE intermetallics in . As a matter of fact, the band profile is found to be almost same for all the AlRE compounds except small changes in the f like states. The lowest energy bands are due to Al-‘s’ states. It lies around −0.6 Ry relative to Fermi level and well separated from other states. The bands lying above this and just below the Fermi level (approximately −0.1 Ry) are mainly due to Al ‘p’-like states, which hybridize with the RE p-like states. The ‘d’ bands of RE generally lie above the Fermi level and hybridize with Al p-like states near Fermi level, while some d bands just touch the Fermi level. The cluster of bands, which are situated at the Fermi level, are mainly the itinerant ‘f’-like states of RE and hybridize with Al p states resulting in metallic behavior. We have also calculated total density of states (DOS) at Fermi level (EF) for all the AlRE intermetallics under ambient condition and depicted in , where the values of DOS are shown (for small values of DOS) to reveal the changes in s and p orbitals. At −0.2 Ry, the bands are predominantly due to Al p-like states but substantially hybridize with rare earth p states. At Fermi level the hybridization of RE f states with d states and Al p states can be seen. RE f-like state is represented by a sharp peak near EF in all the AlRE intermetallics. For AlPm, AlSm, AlGd and AlDy sharp peak (f-like states) corresponds to DOS values which lie between 700 and 800 states/Ry cell whereas for AlEu and AlTb there is an increase in DOS values and it corresponds to ∼1200 states/Ry cell. One can understand the reason for variation in the DOS values in these intermetallics as: from the periodic table if one moves from Pm to Dy, the number of f electrons increases. The sharp increase in DOS could be the reason for delocalization of f electrons in Eu and Tb even at ambient pressure. We have also calculated total density of states at Fermi level under compression for all the AlRE intermetallics. In we have plotted the total density of states at EF under compression for all the six AlRE compounds. Except for AlPm, AlEu and AlSm, a nearly linear decrease in DOS is noticed. In the case of AlEu and AlSm an increase in DOS at EF is noticed in between the compression value of V/V0=0.95–0.90 (). In the case of AlPm such increase in DOS is noticed twice as one can see in , first at compression V/V0=1.0 and second at V/V0=0.85. To understand the variation of DOS under compression in these three intermetallics, we have plotted the electronic DOS of RE-f states in AlEu for various compressions, as depicted in , which are manifestations of f electron delocalization. Similar study has been performed for the lighter AlRE intermetallics in our very recent paper We have analyzed thermal properties of six intermetallics using the DG model , as discussed earlier. The bulk modulus (B0), Wigner–Seitz radii (r0), Debye temperature (θD)0 and Grüneisen constants (γ0) at absolute temperature are calculated for all AlRE intermetallics and compared with the other theoretical calculations . Our results are in good agreement with other calculated values. We have calculated variation in θD with respect to pressure for all the AlRE intermetallics and presented them in , which depicts that as pressure increases, θD increases for AlGd, AlTb and AlDy intermetallics up to 400 kbar, which is quite natural. However, decrease in θD is noticed for rest of the three intermetallics AlPm, AlSm and AlEu up to very high pressure range of 400 kbar. θD starts decreasing at pressure values of 200, 150 and 120 kbar for AlEu, AlSm and AlPm, respectively. In the literature several relations have been derived, which correlates the Debye temperature, θD and bulk modulus by a square root law. An early attempt in this direction was made by Madelung From the important findings of the present paper and those reported earlier A comparison of variation in the Debye temperature with pressure, as shown in (present paper) and those reported in Figure 10 of Ref. of present paper). For further heavier AlRE compounds, the Debye temperature increases only, up to very high pressure. As a possible explanation of this behavior of AlRE group of compounds, the increase in f electrons might be due to the fact that the lighter AlRE are prone to structural phase transition as the pressure is increased while heavier AlRE compounds with mostly filled electronic states are not. Experimental work on such a problem might enhance our understanding on the role of f electrons of RE atom in AlRE compounds.The LDA functional used in the present calculation within the DFT has some limitations A systematic on electronic and structural properties of some AlRE (RE: Pm, Sm, Eu, Tb, Gd and Dy) intermetallic compounds using tight binding linear muffin tin orbital scheme, has been reported. Thermal properties have been calculated using the DG model. The aim of this study was to derive technologically important materials parameters, which can hardly be obtained from experimental measurements. It is found that all the AlRE intermetallics crystallize in B2-structure, which is in agreement with the others theoretical and experimental works. The studied AlRE intermetallics are metallic in nature. A linear decrease in DOS is noticed with compression for AlTb and AlGd and AlDy intermetallics, while increase in DOS is also found for rest of the three AlRE, i.e. AlPm and AlEu, and AlSm, which may be due to the delocalization of f electrons under pressure. We have used the Debye–Grüneisen model to calculate the Debye temperature and the Grüneisen constant using the bulk modulus and the sphere radius obtained from the TB-LMTO study. We have noted one interesting property in the variation of the Debye temperature with pressure. At around 120–200 kbar some AlRE (RE=Pm, Sm and Eu) intermetallics show decrease in θD with pressure, which may be an indication of structural phase transformation. While some AlRE (RE=Tb, Dy and Gd) show linear increase in θD with pressure even up to 400 kbar.Geometry and grain size effects on the fracture behavior of sheet metal in micro-scale plastic deformation► Material size effects in micro-forming process are studied. ► Ductility decreases with the decreasing ratio of specimen size to grain size. ► Number of micro-voids decreases with the decreasing ratio of specimen size to grain size. ► Non-uniform deformation takes place in micro-scaled specimen. ► Fracture behavior is modeled based on dislocation density.The demand on micro-parts is significantly increasing in the last decade due to the trend of product miniaturization. When the part size is scaled down to micro-scale, the billet material consists of only a few grains and the material properties and deformation behaviors are quite different from the conventional ones in macro-scale. The size effect phenomena occur in micro-scale plastic deformation or micro-forming and there are still many unknown phenomena related to size effect, including geometry and grain size effects. It is thus critical to investigate the size effect on deformation behavior, especially for the fracture behavior in micro-scale plastic deformation. In this research, tensile test was conducted with annealed pure copper foils with different thicknesses and grain sizes to study the size effects on fracture behavior. It is found that flow stress, fracture stress and strain, and the number of micro-voids on the fracture surface decrease with the decreasing ratio of specimen size to grain size. Based on the experimental results, dislocation density based models which consider the interactive effect of specimen and grain sizes on fracture stress and strain are developed and their accuracies are further verified and validated with the experimental results obtained from this research and prior arts.The demand on micro-parts and micro-products is increased significantly due to the trend of product miniaturization. To efficiently fabricate micro- parts and products, micro-forming is one of the promising approaches due to the advantages of high productivity, low production cost and the good mechanical properties of micro-formed parts. In design and development of micro-parts via micro-forming, understanding of material deformation behaviors in the process is critical to produce quality parts and products. For macro-scaled metal forming process, the analyses have been extensively conducted To explore micro deformation behavior and mechanics, a lot of prior researches have been conducted. Geißdörfer et al. In micro-forming process, the material undergoes large deformation. Fracture is one of the defects commonly occurring in sheet metal-formed parts caused by the tensile stress exceeding the strength limit of material. Controlling the amount and uniformity of deformation in each forming step are critical to avoid fracture. Among the prior studies, there is a lack of in-depth research on the interactive effect of specimen and grain sizes on the deformation and fracture behaviors in micro-forming process. In order to avoid the fracture in micro-forming process, it is essential to study and model the change of material properties when the material size is reduced from macro- to micro-scale. In this research, the tensile tests of pure copper foils were conducted to study the effect of changing specimen and grain sizes on the deformation and fracture behaviors in micro-scale plastic deformation. Material models describing the size effect on fracture stress and strain are established based on the experimental results and the conventional models of dislocation density evolution.Pure copper is selected as the testing material due to its wide applications and good formability. The as-received copper foils have the thicknesses ranging from 100 to 600 μm. The samples were annealed at the temperatures ranging from 500 to 800 °C at the vacuum condition for 2–4 h to obtain different grain sizes. The heat-treated samples were then etched with a solution of 5 g of FeCl3, 15 ml of HCl and 85 ml of H2O for 20–30 s. The microstructures of the testing samples with different thicknesses (t) and grain sizes (d) are shown in . The samples were cut to dog bone-shape by electrical discharge machining for tensile test.The tensile test was conducted at room temperature in an MTS testing machine with the load cell capacities of 1 and 5 kN. The elongation of the testing specimens was measured by an extensometer with the gauge length of 25 mm. Since the deformation behavior of pure material is sensitive to strain rate, a low strain rate of 0.002 s−1 for all the specimens was performed in this research. It is thus assumed that the testing samples are deformed under a quasi-static condition and the strain rate effect could be neglected . The interactive effect of the specimen and grain sizes is quantified with the ratio of specimen size to grain size:The tensile test for each condition (t/d) was performed on a number of samples. The mean stress–strain curves are shown in . The variations of fracture stress and strain with N are shown in . It can be seen that the flow stress, and fracture stress and strain decrease with the decreasing N.Heat treatment process causes grain recrystallization. The grain size, grain shape and material texture could be different with different annealing temperatures and holding times, which could further lead to the different mechanical properties of the testing samples. The decrease of N could be caused by the increase of grain size. The relationship between the strength of material and grain size could be modeled with the well-known Hall–Patch relation in the following:where σy and d are yield stress and grain size respectively. σhp and k are material constants. The Hall–Petch relation was developed based on the pile-up of slip bands at grain boundaries in plastic deformation. The Hall–Petch relation was further developed with considering the strain hardening effect.where σhp(ε) and k(ε) are constants for a given strain. Based on the Hall–Petch relation, the decrease of flow stress with the decreasing N could be explained with the fact that grain boundary strengthening effect decreases with the increase of grain size. In addition to the above explanation, the decrease of flow stress could also be attributed to the contribution change of different deformation mechanisms among dislocation motion, grain boundary sliding and grain rotation. Miyazaki et al. The relationship between fracture toughness and grain size has been investigated in prior studies. It is found that there is a linear relationship between the fracture toughness and the inverse of grain size for 7075 series aluminum alloys where h, i, k and l are material constants. h and k can be used for the quantitative comparison of fracture stress and strain magnitude of different materials. i and l describe the change of fracture stress and strain with N, respectively. shows the normalized fracture stress and strain. It can be seen that the data points for the given values of N coincide with each other.where fgb is the volume fraction of grain boundary and a function of N. σgb and σi are the fracture stresses of the grain boundary and interior, respectively. When the grain size is large and the value of N is small, such as for the case of N with 1.2 in this study, there is about one grain over the specimen thickness and the volume fraction of grain boundary is small. It is thus assumed that the grain boundary effect could be neglected. The fracture stress in this case could be used to represent the fracture stress of grain interior. On the other hand, when the grain size is reduced to nano-scale and the value of N is large, the strength of material increases due to the increase of grain boundary strengthening effect. However, if the grain size is less than about 8–26 nm , the fraction of grain boundary can be written as and the experimental results in this research, it is found that the fraction of grain boundary increases with N, as shown in . Furthermore, the change rate of grain boundary fraction (dfgb/dN) decreases rapidly with the increasing N. The curve becomes gentle when the N is larger than 10. The rapid change of grain boundary fraction causes the occurrence of size effects which refer to the scatter of process variables shows the fractograph of the tested samples with the thicknesses of 600 and 100 μm, and the different values of N. It is revealed the ductile fracture mode of the samples. The grain boundary fraction in the material increases with N. The grain boundary acts as an obstacle to dislocation motion. The stress concentrates at the grain boundary zone and causes micro-void formation in the deformation process. By comparing the fractographs of the samples with the same thickness (600 μm), as shown in a and b, it is found that the number of micro-voids decreases with the decreasing N. In the extreme case with only about one grain (N
= 1.2) in the thickness direction, there is no micro-void found and the slip band and the typical knife edge rupture can be clearly observed on the fracture surface, as shown in c. The decrease of N leads to the localized deformation at the fracture region. Actually, the measured strain is not the fracture strain at the fracture region, but it is the averaged strain over the gauge length. The decrease of fracture strain with the decreasing N could be attributed to the inhomogeneous deformation and the non-uniform distribution of plastic strain along the gauge length. It causes a significantly large strain localized at the fracture region There is a close relationship between polycrystalline strengthening and dislocation. The density of statistically stored dislocation (ρs) is generated in grain interior and leads to work hardening like single crystal in deformation process. The strain continuity is accommodated by the geometrically necessary dislocation (ρg) in grain boundary. The density of the geometrically necessary dislocation in grain boundary is given by:The density of the statistically stored dislocation is given by:where C1 and C2 are constants. ε, b, d and Ls are the tensile strain, Burgers vector, grain size and slip length, respectively. The total dislocation density (ρt) is thus:Grain boundary is more strained than grain interior and thus has higher dislocation density. It is found that the hardness at grain boundary region is 30% higher than that at the grain interior where G is the shear modulus. α and σρ are constants. Eqs. are applicable up to the intermediate strain range for copper with σρ= 5 MPa and α
= 1, which has been validated by Hansen , the evolution of dislocation density in the testing specimen is examined and shown in . From the figure, it can be seen that the dislocation density is increased with N. The change of fracture dislocation density (ρc) with N is shown in . There is a linear relationship between the inverse of fracture dislocation density (ρc) and the inverse of N and can be expressed as:where e is the inverse of fracture dislocation density in the case out of the size effect occurrence rang (N is larger than 10–15), while f is the change rate of the inverse of the fracture dislocation density with the inverse of N. The equations in this paper are developed based on the range of N studied in the experiment of this research, viz., 1.2 ⩽
N