Datasets:

CambridgeMolecularEngineering

/

StressEngineeringLiterature

like 0

Follow

Molecular Engineering 10

ntAb and γ(t) =

Ab,t(t)/As(t).Finally, the welded area and fractured area during mechanical alloying was expressed as k and can be solved by combining Eqs. k=γ/τ(α(t)/(dα(t)/dt))+1γ/τ(α(t)/(dα(t)/dt))−1/2The results of theoretical analysis are provided in this section. The surface CNT length, length distribution, surface area, nominal area and embedded area were examined. In addition, experimentally measured parameters are presented. CNT dispersion was analyzed through optical image analysis from the fabricated composite.The CNTs collected from the particle surface at different mechanical alloying times are shown in . The measured CNT length information is summarized in . It was difficult to precisely measure the length of as-received CNTs due to the highly curved nature in 3D space. The measurements are accurate for CNTs mechanically alloyed for 3 min, 10 min, 30 min and 1 h, since they are laid on an Al foil. The 2D images reflect the correct lengths of the CNTs. As expected, the length of CNTs on the particle surface decreased as the mechanical alloying time increased. The average CNT length decreased from the original length of 4.24 μm to 1.69 μm in the first 10 min, and then slowly decreased to 0.85 μm after 1 h. As shown in , as-received CNTs form spherical agglomerates prior to the mechanical alloying process. These CNT spherical structures were crushed into dense CNT layers in the first 10 min of mechanical alloying, which damaged the CNTs. The sudden change of CNT length in the first 10 min indicated that the CNTs were severely damaged when the CNT spherical structures were crushed., a normal distribution was utilized to fit the histogram of the measured CNT lengths. The fitted mean (μ) and variance (σ2) at different mechanical alloying times are listed in . The surface CNT length distribution, ϕs(l), may be obtained as:where l is the length of a single CNT, g(l

;

μ, σ2) is the fitted normal distribution with mean of μ and variance of σ2; G(0 ;

μ, σ2) is the value of cumulative distribution function of normal distribution g(l

;

μ, σ2) at l

= 0 The fitted surface CNT length distributions at different mechanical alloying times are shown in (b). As the average length of the CNT length decreased, the CNT length variance also decreased during mechanical alloying.The SEM images of the fabricated Al6061–CNT samples are shown in . The CNT agglomerations were shown as black area in the SEM. The fraction of CNT agglomeration area over the total image area was measured by software ImageJ and is listed in as Aa. In the first 10 min, the CNT de-clustering was very slow due to rupturing of CNT spherical structure. After the CNT-metal powder was mechanically alloyed for 40 min, CNT agglomerated area was rarely observed. Since the agglomerated CNT weight fraction can be obtained from the images (Wa/Wt

=

Aa/Aa,0), the dispersion can be written as d

= 1 −

Aa/Aa,0, where Aa,0 is the CNT agglomeration area when no CNT is dispersed. The dispersion, d, can be fitted with the equation shown in The SEM images of the particles mechanically alloyed for 30 min are shown in . Due to the complexity of the particle shapes, three simplified geometries as shown in (b)–(d) were used to approximate the particle shape for the analysis. Only a small amount of spherical particles ((d)) were found, and they were as-received particles without any deformation (or with slight deformation). The dimensions, D, H, L and W, can be directly measured from the SEM images. The particle layer thickness, h, was estimated from the optical images of the etched samples, which clearly showed the thickness of the merged layers within each particle (see (e)). Therefore, the surface area (As) and embedded area (Ae) can be quantified. During mechanical alloying, the deformed particles stack in layers. As shown in (a) and (e), the surface area will be exposed or welded in the layers. Therefore, the nominal area was measured as the surface area of the layers, indicated in (a). The α and γ are based on the measured data are listed in . In addition, the volume of each particle was estimated, and an equivalent particle diameter was calculated. The overall particle thickness was also measured and the volume average strain of the particles was calculated by Eq. where D is the initial particle diameter; r is integrating parameter.Finally, the overall CNT length distribution can be predicted from Eq. . The parameters used to calculate τ are listed in . ϕs(l, t), α(t) and d can be obtained with experimentally measured data. Since γ did not fluctuate much, a mean value of 0.334 was used. The curve-fitting equations and parameter values are listed in . The final results were computed by Matlab with an Euler explicit computational scheme. The flow chart is shown in . The k value decreased immediately as the mechanical alloying time passed. Initially, the agglomerated CNTs prohibited the welding of particles. The welding mechanism seemed to dominate once the dispersion of CNTs occurred.The average surface CNT length (μ), average overall CNT length (lall), overall CNT length distribution Φ(l,t), and weight fraction of the embedded CNTs (fe(t)) are shown in (a), the overall CNT length decreased significantly in the first 10 min, which was attributed to the crushing of the spherical CNT agglomerates. In (b), the average surface CNT length (μ) and overall CNT length (lall) coincided during the first 20 min of mechanical alloying. A smaller k value indicates a higher welding rate, providing protection for CNTs from further damage. Initially, the high agglomeration of surface CNTs prevented the embedding of CNTs inside the particles, since the welding rate was not much higher than the fracturing rate indicated by the larger k value shown in . In addition, the dispersion of CNTs was low in the initial stage. Consequently, less than 10% of the CNTs were embedded, and therefore, the surface and overall CNT lengths were similar. As the mechanical alloying time increased, more CNTs were dispersed and a low k value was obtained, enhancing the welding process. Therefore, the surface CNT length became shorter than the overall CNT length. The overall CNT length distribution and average CNT length does not change after 60 min of mechanical alloying because over 85% of the CNTs were embedded inside the particles protecting the CNTs from further damage. Although welding of the particles is regarded as a negative factor for the subsequent sintering process, it can provide protection of CNTs from further damage, especially when long mechanical alloying time is applied.The overall CNT length and length distribution during mechanical alloying were predicted for the first time, and the effects of welding and fracturing of the CNTs and aluminum particles were better understood. Experiments were conducted to assist the prediction of overall CNT length. The surface CNTs were successfully collected and analyzed, and the dispersion of CNTs was studied. The CNT length decreased significantly during mechanical alloying. Severe CNT length reduction occurred (from 4.24 μm to 1.69 μm) in the first several minutes due to the crushing of CNT agglomeration balls. After that, the length of CNTs decreased slowly to 1.16 μm, and the CNTs were dispersed in the following 1 h. In addition, the welding/fracturing of Al6061 particles and the dispersion of CNTs affected the overall CNT length. The welding of metal particles surrounded the CNT with metal layer and protected CNTs from further contact with the milling media. Therefore, limited CNT length reduction occurred after 1 h of mechanical alloying. Once the CNT dispersion took place, the welding mechanism dominated the CNT + Al6061 mechanical alloying process due to the ductile nature of Al6061. The model provided an insight into the breakage of CNTs during the harsh ball milling operation, which has been a challenge for experimental measurement. The work can provide useful information when evaluating the effects of CNTs on mechanical, thermal and electrical properties.Flexible electrically conductive films based on nanofibrillated cellulose and polythiophene prepared via oxidative polymerizationIndustrial ecology, sustainable manufacturing, and green chemistry have been considered platform‐based approaches to the reduction of the environmental footprint. Recently, nanofibrillated cellulose (NFC) has gained significant interest due to its mechanical properties, biodegradability, and availability. These outstanding properties of NFC have encouraged the development of a more sustainable substrate for electronics. In this context, the combination of NFC and conductive polymers may create a new class of biocomposites to be used in place of conventional electronics which are not optimally designed for use in flexible and mechanically robust devices. In this study, polythiophene was grafted onto nanocellulose surface at appropriate reaction times to obtain a strong, flexible, foldable films with capacity for electrical conductivity. Nanocomposites films were synthesized by a one-step reaction in which a 3-methyl thiophene monomer was oxidatively polymerized onto nanocellulose backbone. The nature of the fabricated NFC films changed from insulator to semiconductor material upon oxidative polymerization.The recent development of nanotechnology and their wide range of applications in various fields have shifted the current attention toward renewable raw materials and more environmentally friendly resources and processes. In this context, cellulose derivatives and polysaccharides have been gaining importance in the development and application of polymer materials (). Nanofibrillated cellulose (NFC) has gained substantial consideration due to its mechanical and optical properties, film-forming, biodegradability, recyclability, availability, renewability, and low thermal expansion, and has proved to play an important role in the area of green chemistry for several applications (). NFC is a promising green substrate for electronics when combined with conducting polymers (). The previously mentioned features of NFC in the presence of conducting polymers may provide electroconductivity and photoelectroactivity to the material (). Flexible organic conducting polymers have been gaining attention because of their potential applications in display devices, scaffolds for tissue engineering, biosensors, thin-film transistors manufacturing (), and as substitute for metallic conductors. Among the available conductive polymers, thiophene-based compounds have been employed in manufacturing devices such as thin film field-effect transistors and solar cells, to bioimaging due to the multiple functional and semiconducting properties and versatility of the thiophene (). The low cost, plastic-like flexibility and robustness of the organic semiconductors have resulted in their being considered as a potential alternative to conventional semiconductors (). The low solubility of thiophene monomer in organic solvents and subsequent self-aggregation behavior typically produce brittle materials (). In this sense, the development of new functionalities in the materials by combining conjugated polymers and biomaterials has opened opportunities to create a new class of biocomposites ( reported a novel technique for directly polyaniline grafting to chitin/chitosan by oxidative polymerization. Conducting and photoluminescent polymers were successfully grafted onto the surface of chitin powder (). However, the functionalized biopolymer in powder form may restrict its application in high performance electrically conductive materials. It is well known that mechanically robust and electrically conductive materials play a key role for many promising applications. Recently, polypyrrole-based films were obtained via in situ polymerization of pyrrole in a NFC suspension. prepared a conducting biomaterial by deposition of polypyrrole nanoparticles onto bacterial cellulose. A similar method was adopted by in which polyaniline was deposited on paper through oxidation process of aniline vapor using FeCl3. used Cellulose microfiber as a substrate to improve the mechanical properties of poly(3,4-ethylenedioxythiophene)/poly(styrene sulfonate). According to the authors, the employment of the reinforcing biomaterial with the conductive polymers produced an electrically conductive nanomaterial. increased the conductivity and thermal stability properties of the material by the incorporation of graphene into the conductive cellulose/polypyrrole composite. To the best of our knowledge, there are no studies on thiophene polymerization onto nanocellulose either by solvent casting method or by coating technique. In this study, polythiophene was grafted on a nanocellulose surface at appropriate times to obtain very flexible, robust, foldable and strong structures with capacity for electrical conductivity. Polythiophene-nanofibrillated cellulose (P3MT-g-NFC) films were synthesized by a one-step reaction in which the thiophene monomer was oxidatively copolymerized directly onto nanocellulose backbone.Fibres used for preparation of nanofibres were kraft pulp fibres from Domtar, Canada. Chloroform and isopropanol were acquired from Sigma-Aldrich and Caledon, respectively. 3-Methyl thiophene (3MT) was purchased from Oakwood Products, ferric chloride (FeCl3) from Ward’s Science company, and potassium bromide (KBr) from Alfa Aesar.The bleached kraft pulp fibres were transformed into nanofibers (with diameter ranging from 5 to 25 nm and degree of polymerization, 1200) using a commercial custom designed high shear grinder, Supermass Colloider (Masuko Corp., Japan). Thereafter, the defibrilllated cellulose was diluted with water and vacuum-filtered to produce a thin film. The films were then pressed to remove water under pressure for 15 min and then dried at 40 °C for 48 h (Polythiophene was grafted on NFC film (2.5 cm × 1 cm) through polymerization of thiophene monomer. FeCl3 was used as oxidant agent (). Chloroform was selected as optimum media for thiophene polymerization. The solution of 3MT (N3MT/NOH = 10) was introduced in chloroform solution (20 ml). In order to initiate the polymerization, FeCl3 (NFeCl3/N3MT = 4) was mixed with 5 ml of chloroform and added drop wise into the suspension. The mixture was stirred at 5 °C for 2, 8, and 24 h, in separated experiments, to obtain the different conductive nanofilms named P3MT-g-NFC -2, P3MT-g-NFC -8, and P3MT-g-NFC -24, respectively. A red to dark-brown color was found to appear on the NFC film, which was due to polymerization of thiophene (). The unreacted thiophene, P3MT and FeCl3 were leached out in isopropanol solvent. Thereafter, the wet nanofilms were wiped off by rubbing the film surface with soft tissue. The obtained films were dried for 20 min at 60 °C, and then weighed.The UV–vis spectra of the samples were acquired with a UV–vis spectrophotometer (Evolution 60S UV–vis spectrophotometer, Thermo Fisher Scientific Inc.). The nanofilms were cut and attached inside the wall of a styrene UV/VIS spectrophotometer cuvette. Fourier-transform infrared spectroscopy (FTIR) of P3MT sample was recorded on a spectrophotometer TENSOR 27 from Bruker by mixing 1 mg sample with 200 mg of KBr pellet. Attenuated Total Reflectance Fourier-Transform Infrared (ATR-FTIR) spectra of the NFC and P3MT-g-NFC films were recorded on the same equipment. Data were collected at room temperature from 4000 to 400 cm−1 with 50 scans. All films and granulated P3MT were analyzed with a Bruker Senterra Raman microscope using 785 nm laser excitation equipped with a camera helping with the selection of the analyzed spots. Bruker OPUS software program was used to process the Raman and FTIR data, find peak positions, baseline correction, and normalization. The washed, wiped and dried grafted NFC films were weighed, and the results were used to calculate the graft yield (GY) according with the following equation:Where mGNFC is the mass of the grafted biopolymer and mNFC is the mass of the NFC films before the polymerization. Four-point probe analysis (Everbeing International Corp) was used to determine the conductivity of P3MT pellet, native NFC and P3MT-g-NFC films. Conductivity measurement for P3MT was performed on pressed pellets. Resistivity measurements of the P3MT pellet and nanofilms were repeated at least five times in different regions and converted into conductivity using the thickness of the sample. The contact angles were measured by DataPhysics OCA-20 (Instruments GmbH, Germany). A drop of deionized water was added onto the nanocellulose-based films and digital images were taken at 2 s from at least five droplets. All measurements were conducted under standard atmospheric conditions at 23 °C and a minimum of three samples of each film were measured. The thermal stability of the samples was investigated using a TGA Q500 (TA Instruments) at a heating rate of 10 °C/min from 25 to 650 °C under nitrogen gas. The structure and crystallinity in the nanocellulose were evaluated by XRD (Phillips P.W. 1830 diffractrometer) with nickel-filtered CuKa radiation. The amount of crystalline phases, CIr, was determined based on the Segal method (where I200 and Iam are the peaks intensity associated to cellulose I and amorphous fraction, respectively. The tensile strength, Young’s modulus, and percentage of elongation of the film specimens were measured using an Instron machine (Model 3367) equipped with a 2 kN load cell, with a crosshead speed of 2.5 mm/min and a gauge length of 10 mm. Results are reported as mean values ± standard deviation.UV-vis spectra of the films based on thiophene grafting are consistent with previously reports (). The incorporation of the 3MT units onto NFC resulted in the appearance of absorption peaks in the UV–vis spectra. The addition of 3MT led to polymerization onto the NFC backbone and consequently an absorption band appeared around 430–440 nm (). This peak is related to a π- π transition, as is usually observed in many conducting polymer systems (). According to UV–vis spectra, the absorption band shifted with the increased time reaction indicating high aromaticity, and high molecular weight and the formation of π-conjugated structures (). Double absorption bands are presented for P3MT-g-NFC -24 and P3MT-g-NFC -8 films. Beside the typical absorption bands around 434 cm−1, a broad peak corresponded to (bi)polarons presented at 650–950 nm. This suggests the presense of a longer conjugation length, more coplanar thiophene rings (), and quinoid structure formation in the chain growth process. Therefore, the presented method succeeded for the first time in preparing P3MT-g-NFC films. shows the FTIR spectra of pristine NFC, P3MT and NFC-g-P3MT. The absorbances at 3319 cm−1, 2890 cm− 1,1641 cm−1, and 1033 cm−1 are associated with native cellulose (). The characteristic peaks of cellulose are observed at 2890 cm− 1 and range from 3250 to 3500 cm− 1 which are associated with C–H and OH stretching vibrations, respectively, while the band at 1641 cm−1 relates to the bending mode of the absorbed water (). A strong peak at 1033 cm−1 arises from C) which means that the structure and crystallinity of the NFC remained preserved upon chemical grafting. The characteristic peaks of P3MT chains at 2922 cm− 1 and 2857 cm−1 corresponding to asymmetric and symmetric stretching bands of the methylene groups, respectively (), were overlapped by the typical peak corresponding to the CH stretching vibration of cellulose. The slight absorption peak at 2962 cm–1, corresponding to the stretching vibration peak of the −CH2 bond, is presented more prominently in NFC-g-P3MT-24 and P3MT-g-NFC -8 films (). A peak is observed around 1320 cm−1, associated to CC aromatic ring stretching of the P3MT (). In summary, the graft density of polythiophene onto the nanofilm increased with the reaction time.The Raman spectra of native NFC, P3MT, and P3MT-g-NFC are shown in , the nanocellulose crystallinity can be estimated by the intensity of the 380 cm−1 band assigned to higher crystalline structure, and 1096 cm−1 band for amorphous conformation from the Raman spectra (). The Raman spectrum showed that the grafting reaction was successfully achieved. The colored marked spots from different regions from Raman microscopy of P3MT-g-NFC -24 spectra reveal that the NFC surface was homogenously grafted with polythiophene, since different regions of the film had similar spectra and consequently reacted equally (). The presence of strong vibrations of P3MT cancelled out the NFC peaks revealing a dense formation of thiophene chains onto the NFC backbone. The appearance of an intense band at 1355 and 1419 cm−1 is assigned to the stretching mode of the CC ring simple bond of the polythiophene (C stretching deformation of the radical cations, indicating the formation of a quinoid structure upon oxidation (The graft yield of the samples, as shown in , revealed a significant amount of conducting polymers grafted onto the NFC which is highly associated with polymerization time. The graft yield of 39.53% was achieved for the longer reaction time. The major resistance for graft polymerization is the linking of a free radical on the oxygen atom of the hydroxyl group with the oxidized 3MT. Once the thiophene monomer and the hydroxyl groups are coupled, the polymerization is triggered rapidly by another 3HT radical cation in chloroform solution (). In the other words, after 2 h, the system was basically engaged in the oxidation of the 3MT and reaction with the hydroxyl group of the cellulose. The incorporation of thiophene monomer favored formation of more radicals, which in turn generate more grafting sites for the 3MT. As a result of the 3MT polymerization onto the NFC, the change in color intensity at different polymerization time is attributed to the increasing chain length and grafting density.The conductivity of NFC and the P3MT-g-NFC samples was measured using a four-probe method. As shown in , the conductivity of NFC was determined to be 9.40 × 10−3 μS cm−1, while that of the P3MT-g-NFC samples prepared in chloroform for 2 h, 8 h, and 24 h were 5.32 × 10−2, 0.29, and 133 μS cm−1, respectively. Pressed pellets of the P3MT powder exhibited electrical conductivity of 0.27 S cm−1. Despite a substantial increase in the graft yields of the grafted NFC films, the amount of P3MT onto NFC did not necessarily result in the same magnitude in terms of increase in conductivity of P3MT-g-NFC films. NFC upon oxidative polymerization with 3MT for 24 h gave a sample with higher conductivity, which is attributed to the high grafting ratio and the molecular weight of the P3MT on the NFC surface. A similar study with chitin/chitosan () introduced the P3HT layer in the substrate surface which enhanced the conductivity of the material. From the results, the electrical conductivity of P3MT-g-NFC -24 h was 133 μS.cm−1, which is similar to that of silicon (15 μS cm−1) (). It is worth mentioning that the electrical conductivity and wettability of the samples remained unaltered after intense washing the grafted NFC films in isopropanol, as a result of the strong interactions between grafted P3MT chains and NFC backbone.In addition, the contact angle measurements were used to determine the effect of P3MT on the wettability property of NFC before and after grafting. The NFC has very low hydrophobicity with contact angle 54.3° which indicated the hydrophilic surface of NFC. In contrast, the presence of P3MT on the surface of NFC significantly increased hydrophobicity. The P3MT-g-NFC water contact angles varied with the reaction time, since the P3MT grafted to the surface of NFC resulted in the improvement of the hydrophobicity. The coating of thiophene on NFC surface can reduce water absorption from the environment, protect against degradation and increase the conducting properties of the NFC film.The degradation temperatures of NFC, P3MT and P3MT-g-NFC films were studied by thermogravimetric (TG) analysis (). The values of the maximum degradation temperatures can be seen from the derivative thermogravimetric (DTG) curves. The initial weight loss from 30 to 150 °C is ascribed to residual moisture present in the samples (). The nanocomposites showed lower onset degradation temperature than that of pristine NFC, due to the loss of intermolecular hydrogen bonds of nanocellulose by the presence of conducting polymer, as reported by . In native NFC film, the cellulose degradation started at 200 °C and continued until around 350 °C leading to depolymerization of solid cellulose to form various anhydro monosaccharide, carbon oxides, and char (). The weight loss for pristine NFC and P3MT-g-NFC was 53% and 50% at 350 °C, respectively, and 87% and 75% at 600 °C, respectively. For the P3MT-g-NFC, the loss was a result of the degradation process of the cellulose as well as the thermal degradation of the polymer backbone in polythiophene () that the acid medium of the reaction may affect the crystallinity of the NFC. However, the P3MT grafting onto the NFC had negligible effect on the thermal stability of NFC-based samples. This is especially important for organic thin-film transistors and sensors employed in biomedical apparatuses in which the operating temperature could be as high as 120 °C (). The presence of P3MT increased the percentage of left residue due to the to the rigidity of the P3MT backbone ( shows the XRD of NFC and P3MT-g-NFC composites. The percent crystallinity (% Cr) of NFC and the grafted cellulose products was calculated from the XRD patterns using the 2θ peak intensities between 14 and 18° and between 21 and 23° (). After graft polymerization with P3MT, all P3MT-g-NFC samples had similar diffraction patterns. Therefore, the original crystalline structure of NFC is still preserved after P3MT grafting. The crystallinity index of the NFC, P3MT-g-NFC -2, P3MT-g-NFC -8 and P3MT-g-NFC -24 was 65.4, 61.1, 64.7 and 67.7, respectively. The results showed that the P3MT grafting to NFC did not disorder the crystalline structure of the NFC. Interestingly, the nanomaterial with longer conjugation length showed higher crystallinity than native NFC. According to , the π-extended planar backbones enable self-assembly of regioregular sections to form crystalline regions. The well-ordered structures of the extended chains crucially contribute to the electrical conductivity and crystallinity of P3MT-g-NFC -24. The XRD results agreed with the TGA since the thermal stability of the polymer depends mainly on crystallinity.The stress-strain curves, tensile strength and Young’s modulus of pristine NFC and P3MT-g-NFC films are presented in . Although some works studied the electrical conductivity of conducting nanocomposites (), the mechanical behavior has not been characterized (). Native NFC film exhibited outstanding tensile strength of 253 MPa and Young’s modulus of 19.80 GPa. These mechanical properties are related to the strong interactions between nanofibrils and to the entanglement network (). The tensile strength of P3MT-g-NFC -2 sample remained almost the same as that of pristine NFC, and the tensile strength and young’s modulus decreased to 209 MPa and 14.20 GPa after the longer polymerization time of 24 h. As expected, P3MT-g-NFC nanofilms were slightly more brittle than pristine NFC. The elongation at break of P3MT-g-NFC films decreased with reaction time. The polythiophene grafted onto the NFC surface diminished the number of NFC inter-fibril OH interactions, since the sulfur group of thiophene interacted with the hydroxyl groups of NFC, leading to a decrease of the elongation of the P3MT-g-NFC films. P3MT-g-NFC film showed lower but still outstanding mechanical properties after the 24 h reaction. Even though the slight decrease in elongation at break (12%), the materials retained their flexibility as shown in . In summary, Chloroform and FeCl3 as a solvent medium and oxidative agent, respectively, preserved most of the crystallinity structure and, consequently, did not deteriorate the mechanical properties of the nanocomposite.Flexible and electrically conductive nanocellulose-based polythiophene materials were fabricated by oxidative polymerization of 3-methyl thiophene onto nanofibrillated cellulose film by using FeCl3 as oxidant. The conductive thin films showed good flexibility, high strength, and high electrical conductivity. The addition of 3MT to NFC has resulted in graft polymerization onto the NFC backbone and consequently absorption peaks corresponded to π-conjugated structures were observed. The oxidative polymerization of thiophene had negligible effect on the thermal stability since the crystalline structure of the NFC remained intact even after chemical grafting. The graft yield of nanocellulose film depended on the reaction time and the hydrophilic character of the nanofilm was found to be more hydrophobic with increase in P3MT chain length on the NFC. Although the mechanical properties of the films slightly decreased due to the polythiophene grafting, the electrical conductivity increased from 9.40 × 10−3 to 133 μS cm-1. This modification changed the nature of NFC film from insulator to semiconductor material after grafting with polythiophene. Interestingly, the conductivity of the P3MT-g-NFC thin films reached one order of magnitude above that of a typical semiconductor like silicon. These nanocomposite films may have potential for flexible electronic applications.Prediction of mechanical properties in friction stir welds of pure copperThis research was carried out to predict the mechanical properties of friction stir welded pure copper joints. Response surface methodology based on a central composite rotatable design with three parameters, five levels, and 20 runs, was used to conduct the experiments and to develop the mathematical regression model by using of Design-Expert software. The three welding parameters considered were rotational speed, welding speed, and axial force. Analysis of variance was applied to validate the predicted models. Microstructural characterization and fractography of joints were examined using optical and scanning electron microscopes. Also, the effects of the welding parameters on mechanical properties of friction stir welded joints were analyzed in detail. The results showed that the developed models were reasonably accurate. The increase in welding parameters resulted in increasing of tensile strength of the joints up to a maximum value. Elongation percent of the joints increased with increase of rotational speed and axial force, but decreased by increasing of welding speed, continuously. In addition, hardness of the joints decreased with increase of rotational speed and axial force, but increased by increasing of welding speed. The joints welded at higher heat input conditions revealed more ductility fracture mode.Friction stir welding (FSW) was invented at The Welding Institute (TWI) of UK in 1991 as a solid state joining technique, and it was initially applied to aluminum alloys FSW process parameters such as tool rotational speed, welding speed, tool pin profile and axial force influence the mechanical properties of the joints. In order to increase efficiency of FSW process, the mechanical properties of joints must be optimized. Therefore, it is important to determine the welding parameters at which the mechanical properties reach their optimum. One of the methods to modeling and optimizing the FSW process is Response Surface Methodology (RSM). RSM developed by Box and Wilson A series of investigations have been conducted on modeling the FSW process of aluminum alloys using RSM With the purpose of achieving the desired aim, the current investigation has been planned in the following sequence: (i) Recognizing the important FSW parameters that which are having influence on mechanical properties of joints, (ii) Finding the feasible limits of the recognized FSW parameters, (iii) Developing the experimental design matrix, (iv) Conducting the tests as indicated by the experimental design matrix, (v) Recording the responses, (vi) Developing the mathematical models, (vii) Checking the adequacy of the developed models and (viii) Analyzing the effects of the FSW parameters on mechanical properties of joints.a. Large numbers of trial experiments were conducted to find the range of each input parameters by varying one of the parameters and keeping the rest of them at constant values. Feasible limits of the parameters were chosen in such a way that the joints should be free from visible macro-defects as shown in b. The main parameters that affect the mechanical properties of FS welded joints and their feasible limits are summarized in CCRD initially invented by Box and Wilson . The measured response parameter was the normalized UTS, TE and hardness. The experimental design was created using Design-Expert Version 8.0 software as presented in . Random experiments were done so as to avoid any systematic error entering into the system.Pure copper plates of 2 mm thickness with UTS of 272 MPa, TE of 42% and hardness of 102 HV were used as BM. Plates were cut to 75 mm wide by 300 mm long using a power hacksaw with a metal cutting blade. In order to obtain a good primary joint configuration, the plate edges were smoothed by Supermill milling machine. Also the plates were secured in place using specially designed fixtures. Single pass FSW perpendicular to the rolling direction of plates was performed to produce the joints. The welded joints were sliced as shown in a, and then machined to the required dimensions as shown in b. Five tensile specimens were fabricated according to ASTM: E8 M standard to evaluate the tensile properties of the joints. Tensile tests were carried out using a universal tensile test machine at a cross-head speed of 2 mm/min. The Vickers hardness test was performed on the FS welded specimens using a 100 g load for 10 s. After conducting the test, the UTS, TE and hardness values of FS welded specimens were recorded. Microstructural changes were characterized by optical microscopy. The metallographic specimens were cross-sectioned from the FSW joints transverse to the welding direction, polished and then etched with a solution of 20 mL nitric acid and 10 mL acetic acid to reveal the microstructure. The fractured surfaces of the tensile specimens were characterized using scanning electron microscope (SEM) to understand the failure patterns.In the present investigation, to establish a mathematical relationship between the FSW process parameters and the UTS, TE and hardness of welds, a second order polynomial regression model that includes the main and interaction effects of all parameters was developed. The response properties of the FS welded joints are a function of rotational speed (A), welding speed (B) and axial force (C). The response surface can be expressed as follows:The second order polynomial regression equation used in this study is given by: where Y is the response, Xi and Xj are the coded independent variables, b0 is the mean values of responses and bi, bii and bij are linear, quadratic and interaction constant coefficients, correspondingly. For three FSW parameters, the selected polynomials could be expressed as:Y=b0+b1(A)+b2(B)+b3(C)+b11(A2)+b22(B2)+b33(C2)+b12(AB)+b13(AC)+b23(BC)The values of the coefficients could be calculated by means of some statistical terms . Also, in order to ensure an accurate model, ANOVA analysis was performed including tests for significance of the regression model and coefficients. The model was presented as two dimensional plots (contour plots) using the same software.The developed final mathematical model equations are given below:UTS=255.42-2.53A-1.48B+0.63C-5.75AB+10.5AC-4.4A2-6.9B2-2.2C2%TE=32.4+2.6A-3.5B+5.02C-0.31AB+0.11AC+1.06BC-1.87A2-0.44B2-1.3C2HV=79.59-4.7A+1.71B-3.04C-1.25AB+3.75AC-4.5BC+1.35A2-1.42B2-1.47C2The adequacy of the models so developed is then tested by using the ANOVA analysis. The results of the ANOVA are given in . Using this technique, it is found that calculated F ratios are larger than the tabulated values at a 95% confidence level; hence, the models are considered to be adequate. Another criterion that is commonly used to illustrate the adequacy of a fitted regression model is the coefficient of determination (R2). For the models developed for UTS, TE and hardness of joints, the calculated R2 values are 83%, 93% and 94% respectively. Also, the adjusted R2 values are 80%, 87% and 89% for the models developed for UTS, TE and hardness, respectively. These values indicate that the regression models are quite adequate. The normal probability plot of the residuals, the plot of the predicted response versus actual values, and the residuals versus the predicted response for the UTS, TE, and hardness of joints are illustrated in a–c, it is obvious that errors are spread normally because the residuals fall on a straight line. a–c reveals that the predicted response values are well in agreement with the actual ones within the limits of the FSW process parameters, because the observed values and predicted values of the responses are scattered close to the 45° line. A check on the plots in a–c reveals that the residuals scatter randomly, suggesting that the models proposed are adequate and there is no reason to suspect any violation of the independence or constant variance assumption The perturbation plot for the response UTS of joints is illustrated in . This type of plot shows the change of a response while each FSW parameters moves from the reference point, with all other parameters held constant at the reference value. Design Expert software sets the reference point default at the coded 0 level of each parameter. a–f illustrate the contour and surface plots, presenting the interaction effect of any two input parameters on the UTS where the other parameters are on their center level. As can be seen from , the increase in tool rotational speed, welding speed and tool axial force results in the increase in UTS of the FS welded joints up to a maximum value. The cross sectional macrostructures of the joints welded at low and high heat input conditions (experiments numbers 3 and 6, respectively) are illustrated in . The lower rotational speeds, higher welding speeds and lower axial forces (lower heat input condition) produce inadequate heat due to lower friction, which results in poor plastic flow and formation of defects in welded zone (WZ) and so, the UTS is lower (a). The higher rotational speeds, lower welding speeds and higher axial forces (higher heat input condition) produce sufficient heat for metallurgical phenomena such as grain coarsening a–c, it can be indicated that compared with BM, the WZ has much finer equiaxed grains due to dynamic recrystallization caused by simultaneously received the plastic shear deformation and frictional heat. Also, compared with joints welded at low heat input condition, the WZ of joints welded at high heat input condition has coarser grains due to appreciable grain growth and hence, the UTS is lower.The perturbation plot for the response TE of joints is illustrated in a–f illustrate the contour and surface plots presenting the interaction effect of any two input parameters on the TE. As can be seen from , the increase in tool rotational speed and tool axial force results in the increase in TE of the FS welded joints continuously where the decrease in welding speed results in the increase in TE. Increasing the tool rotational speed and axial force, and decreasing the welding speed lead to elimination of the defects in WZ of the joints and so higher TE (b). On the other hand, the higher rotational speeds, lower welding speeds and higher axial forces result in sufficient heat for metallurgical transformations such as grain coarsening, growth of participates and lowering of dislocation density at WZ , the samples welded at higher heat input condition show more dimples and fewer large voids in comparison with samples welded at lower heat input condition. reveal that despite smaller grain size of the WZ, a general softening and reduction of hardness occurs in the WZ contrary to that of the BM. Therefore, other metallurgical phenomena such as reduction of dislocation density a–f illustrate the contour and surface plots for the response hardness. As can be seen from , the decrease in tool rotational speed and tool axial force leads to the increase in hardness of the FS welded joints continuously where the increase in welding speed causes to the increase in hardness. On the other hand, the higher rotational speeds, lower welding speeds and higher axial forces result in grain coarsening (b and c) due to more heat generation in the WZ of the joints and hence, lower hardness. Also, higher heat input condition may result in reduction of dislocation density In present investigation, a numerical model predicting the mechanical properties of friction stir welded pure copper joints was developed. Based on the results obtained in this work, the following conclusions can be drawn:The operational range of process parameters for high quality FS welded joints of pure copper was achieved. The defect free welds were achieved under the condition of a rotation speed ranged from 700 to 1100 rpm, a welding speed ranged from 50 to 100 mm/min and an applied axial force ranged from 1.5 to 2.5 kN.RSM based on a central composite rotatable design was used successfully to develop a mathematical model for predicting UTS, TE and hardness of FS welded pure copper joints. The ANOVA analysis showed that the developed model can be effectively used to predict the UTS, TE and hardness of the joints at 95% confidence level.UTS of the pure copper FS welded joints increased with increasing of tool rotational speed, welding speed and tool axial force up to a maximum value, and then decreased.TE of the joints increased with increase of rotational speed and axial force, but decreased by increasing of welding speed, continuously. Also, the fracture mode of joints welded at higher heat input conditions revealed more ductility than that of joints welded at lower heat input conditions.Hardness of the joints decreased with increase of rotational speed and axial force, but increased by increasing of welding speed, continuously.Experimental and numerical analysis on the structural behaviour of cold-formed steel beamsA research study on the structural behaviour of cold formed steel beams with C-, I-, R- and 2R-shaped cross-sections at ambient temperature is presented, based on the results of a large programme of experimental tests and numerical simulations. Firstly, several four-point bending tests were carried out in order to assess mainly the failure loads and failure modes of the beams. Secondly, a suitable finite element model was developed to compare with the experimental results, and finally, a parametric study was undertaken in order to investigate the influence of the thickness, height and length of the beams on its structural behaviour.vertical displacement of the specimen at mid-span (section S1)design value of the resistant buckling momentcritical elastic moment for lateral-torsional bucklingresistant moment of the gross or effective cross-sectionmeasured bending moment about the xx′ axismeasured bending moment about the yy′ axiscalculated bending moment about the xx′ axiscalculated bending moment about the yy′ axismaximum load-carrying capacity of the beammaximum load-carrying capacity of the beam including its self-weightnominal thickness of the beam cross-sectionlateral rotation of the beam at mid-span (section S1)reduction factor for lateral-torsional bucklingmeasured strain in the beam at mid-span (section S1)partial factor for resistance of members to instabilitynon-dimensional slenderness for lateral-torsional bucklingStudies on the structural behaviour of cold-formed steel (CFS) beams are increasingly popular in the last decades. Instability phenomena, such as local, distortional, lateral-torsional buckling and their interactions, are the most interesting and complex subjects within this research field These buckling modes are mostly responsible for the ultimate strength of the compression members as they may occur even before parts of the cross-section yield. The low torsional stiffness, the high slenderness and the geometric imperfections that are characteristic of CFS members are some of the main causes for their high susceptibility to buckling The majority of studies in this field emphasise further the structural behaviour of these members by means of analytical approximations and purely numerical methods. The effective width method (EWM), which was included in the EN1993-1.3 Furthermore, the direct strength method (DSM) Most of the studies in the literature only take into account the structural behaviour of CFS members with just one profile and the majority of them are of numerical nature To conclude, in the near future, this work will be followed by an experimental and numerical study on the behaviour of such beams under fire conditions with the purpose of developing simplified calculation methods for fire design of cold-formed steel beams since there is nothing related to the fire design of these elements in EN1993, parts 1.2 The experimental tests on cold-formed steel beams were conducted in the Laboratory of Testing Materials and Structures of the University of Coimbra (UC), in Portugal. The experimental programme consisted of 12 quasi-static bending tests at ambient temperature, allowing the study of the flexural behaviour of 4 types of beams with different cross-sections. For each type 3 tests were carried out (B-C_i, B-I_i, B-R_i and B-2R_i, where i stands for the test number, i=1–3), in order to obtain a better correlation of the results.The specimens consisted of beams made of one or more cold-formed steel profiles, namely, C (lipped channel) and U (channel) profiles (The total beam length was 3.6 m for all specimens, but the span was only 3 m in such a way that the beams and their supports could be accommodated by the horizontal electric furnace available in the laboratory. As already stated, the following studies will address the fire behaviour of this kind of beams.In addition, the profiles were screwed together as indicated in by means of Hilti S-MD03Z 6.3×19 carbon steel self-drilling screws in S235 steel, at sections 0.05 m and 1.15 m away from the ends of the beams so that the spacing of the screws along the beam was about 1 m (). All the profiles were made of S280GD+Z structural steel.These profiles were manufactured by the company PERFISA S.A., which is specialized in the fabrication of CFS profiles in Portugal, and the choice of the cross-sections and the distance between the screws was based on the observation of CFS structures and design projects for this kind of buildings, representing commonly used details in several countries.Schematic and overall views of the experimental system used in the quasi-static bending tests at ambient temperature are shown in ) were loaded at two points 1.0 m (one-third of the beam span) from the supports of the beam in such a way that between the two loading points the beam was under pure bending state (four point bending test). The loading was applied by an ENERPAC hydraulic jack, model RR 3014 (no. 2 in ), which was hung from a two-dimensional reaction frame (no. 3 in ) that consisted of two HEB300 columns and a HEB300 beam of class S355 steel. This hydraulic jack had a maximum loading capacity of 295 kN and a maximum stroke length of 360 mm and was controlled by a servo hydraulic central unit W+B NSPA700/DIG2000. The tests were carried out in displacement control controlled by a TML SDP-200D linear variable displacement transducer (LVDT) (no. 4 in ). Additionally, beneath the hydraulic jack a Novatech F204 load cell of 250 kN capacity was mounted in order to monitor the applied load during the test (no. 5 in As it was intended to use the same test set-up for the fire resistance tests of CFS beams to undertake in the near future, a HEA160 steel column (no. 6 in A spherical plain bearing and a spherical hinge (respectively nos. 8 and 9 in ) were also assembled in the loading system in such a way that the load applied on the beams could easily follow the local and global deformations of the beams during the tests, especially, the lateral buckling. Although the spherical hinge had little degrees of freedom due to the threaded rods which allowed to make the connection between the HEA160 column and HEB140 beam, the spherical plain bearing could rotate 90° to both sides about an axis passing through its own centre and it was perpendicular to a plane formed by the longitudinal axes of the HEA160 column and the HEB140 beam. In addition, the spherical plain bearing could still rotate about 10° to both sides around an axis that passed through its own centre and it was perpendicular to a plane composed of the reaction frame.The tested beams were statically determinate over a roller and pinned support (respectively nos. 10 and 11 in . These supports were made of refractory stainless steel, typically used for elevated temperature applications. These supports prevented the vertical displacement, the lateral displacement and the lateral rotation of the beams. In addition the roller support allowed the horizontal displacement of the beams in contrast to the pinned support as it can clearly be seen in The instrumentation of the beams included LVDTs for displacement measurements (nos. 12 and 13 in ) and also TML FLA-6-11 strain gauges for strain measurements. Finally, the data acquisition was done by a TML data logger, model TDS-530.Four-point bending tests were used to assess the ultimate bending strength of the CFS beams at ambient temperature as well as to check the failure modes responsible for their failure, including local, distortional, global and their interactions. These experiments provided useful results for detailed numerical studies. The load was applied under displacement control at a rate of 0.01 mm/s until the specimen failed and reached its unloading stage, where the beam deformation or the lateral rotation of the beam was too large, or the maximum stroke of hydraulic jack was reached. Moreover and as already mentioned in this paper, the load applied on the beams, the displacements of the beams and supports, as well as, some strains in the beams were measured during the tests. Therefore, three LVDTs were used to measure the vertical displacements of the beams at three sections (S1, S2 and S3 – ) and two LVDTs to evaluate the lateral rotation of the beam at section S1 (mid-span), as shown in . A number of strains gauges were also placed around sections S1 and S2 () to measure the longitudinal strains and consequently to assess the bending moment in the beams. Lastly, two LVDTs were positioned in each beam support to allow the determination of their rotations (no. 13 in shows the load–displacement curves for the tested cold-formed steel beams as a function of the vertical displacement at section S1, dS1. It shows the results of the three tests carried out for each type of beam.The quasi-static structural behaviour of the beams (i.e., loading stage, failure load and unloading stage) was identical for all tests of each type of beam. The small differences detected between the load–displacement curves for the same type of beams were essentially due to the eccentricity of the load applied on the beams and, but slightly less significant, to the geometric and material imperfections in the specimens.An important conclusion to be drawn was that the 2R beams presented a mean ultimate load capacity of 132.32 kN (d) that is much higher than for the other types of beams tested. In contrast, the mean ultimate load capacity of the C beams was only 11.72 kN (a). Finally, the lipped I and R beams showed a mean ultimate load capacity of 41.68 and 60.14 kN (b and c), respectively. Hence, the maximum load capacity of the lipped I, R and 2R beams was over 3.5, 5 and 10 times higher than the one of the C beam, respectively. From these results it may also be concluded that the use of hollow sections (R beams) can increase by 1.45 times the load-carrying capacity of beams compared to the open sections (lipped I beams). On the other hand, at failure a sharp decay in the load was observed in all compound beams (there was no plastic plateau). One reason for that may be the local or distortional buckling in one profile close to the peak load. Beyond that, the resistance of the beams depended essentially on the remaining resistance of the other beams’ profiles.Furthermore but not so relevant in this case, during the unloading stage, some screws in the compressed part of the beams failed in shear, as it can be seen by the discontinuities in some curves in In what concerns the lateral buckling behaviour of the beams, it can be seen in that this one depended on the shape of the beam cross-sections as expected. The relative load (P/Pmax) applied on the beams is plotted in the vertical axis of the graph and the horizontal axis is plotted against different values of lateral rotation of the respective beam at mid-span. It can be observed that from the beginning of the tests, all the beams except the 2R beams showed immediately lateral rotation at mid-span of the beams (section S1), the C beams being the most affected. For instance, when the load on the beam B-C_2 reached its maximum capacity the lateral rotation at section S1 was already about 12°, whereas for beams B-I_2 and B-R_2 it was only 2.5 and 1° (), respectively. This improved behaviour resulted from the coincidence of the shear centre with the centroid, secondly, from the torsional stiffness of the compound cross-sections and lastly from the increased thickness of the beam cross-section. It is also important to emphasise that the 2R beams exhibited lateral-torsional buckling, but only after one of their U profiles failed by distortional buckling, as it will be seen later in this paper. presents, as an example, the rotations of the beam supports during the tests for the B-C_2 and B-R_2 beams (a and b, respectively). The rotations of the roller support for test B-C_2 coincided with the rotations of the pinned support, whereas for test B-R_2 the rotations of the two supports only coincided until its maximum load-carrying capacity. This was due to the fact that there has been neither local nor distortional buckling in Beam B-C_2 up to its maximum load-carrying capacity in contrast to the Beam B-R_2 that exhibited local and distortional buckling near the mid-span, closer to the roller support than the pinned support. So, the rotations of the roller support were higher than the rotations of the pinned support beyond its ultimate capacity (b). The same conclusions were observed for all lipped I, R and 2R beams since they all had a complex buckling behaviour, including local, distortional, global buckling and their interactions. Finally, it can also be seen in that the rotations of both beam supports were about 0.5° for the beam B-C_2 and 0.6° for the beam B-R_2 at the level of the maximum load.Another important parameter taken into account in this study was the strain evolution in the different cross-sections of the tested beams as a function of the loading applied on them () was similar up to the maximum load, in contrast to the open-section beams (C and lipped I beams, a). While the lateral rotation of the beam at mid-span increased, the compressive strains recorded by the stain gauges placed further apart from the vertical plane that passed through the geometric centre of the cross-section increased less than the ones recorded by the strain gauges nearer to that plane. Moreover, during the unloading stage some of the strain gauges located further apart from that plane inverted the sign of the strains. b show that the maximum measured value of tensile strain was 0.067 (ε_5), 0.106 (ε_11), 0.159 (ε_8) and 0.237% (ε_14) for, respectively, the C, lipped I, R and 2R beams at mid-span and at the maximum load level. On the other hand, the maximum measured value of compressive strain in the same conditions was respectively −0.113 (ε_1), −0.152 (ε_1), −0.179 (ε_1) and −0.323% (ε_2) (From these strain measurements (S.M.) and assuming that the cold-formed steel of the tested beams reached the yield plateau (), the bending moments about both the xx’ axis and the yy′ axis could be calculated.Similar moments were also calculated based on classical beam theory (C.B.T.) for comparison (). Good agreement is noted for both calculations (i.e. between M xx′ – S.M. and M xx′ – C.B.T. and also between M yy′ – S.M. and M yy′ – C.B.T.). The C beam was subject to biaxial bending around xx′ axis and bending around yy′ axis throughout the test while the other beams (I, R and 2R) were approximately under pure bending until their ultimate load-carrying capacity was reached. The reason was that the C beam was the only one in which there was no coincidence between the shear and geometric centres of the cross-section. It is still noticed that the signal change relative to strains (from compression to tension and vice-versa) recorded by some strain gauges () was due to the appearance of this bending moment around the yy′ axis (“weak” axis).The finite element program ABAQUS is a computational tool for modelling structures with material and geometric nonlinear behaviour [Schafer and Moen 2010]. ABAQUS version 6.10-1 All cold-formed steel beams were modelled by using shell elements (S4R) for the profiles and solid elements (C3D8R) for the screws. The S4R element was chosen because it is a general-purpose shell element from the ABAQUS program library, which also takes transverse shear deformation into account as well as the thick shell elements. Thick shell elements are based on Mindlin type theory, whereas the formulation of the thin shell elements is based on discrete Kirchhoff theory. However, the S4R element uses a mixed finite element formulation as it can be seen in detail in the ABAQUS Theory Manual The S4R element is doubly-curved, a four-node (4), quadrilateral and stress/displacement shell element (S) with reduced integration (R), a large-strain formulation, hourglass control and a first-order (linear) interpolation. Reduced integration elements converge non-monotonically and due to this reduced number of integration points hourglassing can occur in the S4R element, so an hourglass stabilisation control feature is built into the element to suppress spurious modes. The reduced integration reduces the amount of CPU time necessary for analysis of the model. Each node has three displacement and three rotational degrees of freedom. Lastly, each of the six degrees of freedom uses an independent bilinear interpolation function.The C3D8R element is defined as a three-dimensional (3D), continuum (C), hexahedral and an eight-node brick element with reduced integration (R), hourglass control and first-order (linear) interpolation. These finite elements have three degrees of freedom per node, corresponding to translations in the three directions X, Y and Z (global coordinates).Material non-linearity in the specimens was modelled with von Mises yield criterion and isotropic hardening. The stress–strain relationship of cold-formed steel profiles was described by a gradual yielding behaviour followed by a considerable period of strain hardening, whereas an elastic–perfectly plastic behaviour was assumed for the steel screws. shows the stress–strain curves used in the FEA for the CFS profiles based on tensile coupon test results and at the same time on other studies from the literature The influence of the finite element size on the behaviour of cold-formed steel beams was first studied. It was found that good simulations results could be obtained by using finite element meshes of 5×5 mm, 10×10 mm or 20×20 mm. To save computational time, finite element meshes of 10×10 mm for C, lipped I and R beams and of 15×15 mm for 2R beams () were generated automatically by the ABAQUS program and used in all simulations.A three-dimensional numerical model was used to simulate all buckling modes observed in the experimental tests. The cross-sections of the different beams, the screws, the beam support system and the beam loading system were reproduced with great accuracy in the numerical simulations. Such as observed in the real test set-up, the beam supports and the loading were applied on rigid plates attached to beams so as to distribute possible concentrated forces on them. Therefore, with regard to the loading on the beams, concentrated forces with the direction-Y were applied at the centre of those plates, each at a distance of 1 m from the nearest beam support, i.e., the forces were applied at one-third of the beam span (a). To simulate the pinned support, all degrees of freedom of the nodes located on the bottom surface and at the middle of the respective rigid plate were constrained, whereas for the roller support only the translations in the directions X and Y were constrained. Finally, the translations in the direction X of all nodes located at each end of both supports were constrained in order to prevent their lateral deformation (a). All simulated beams were modelled using the centre line dimensions, as it can be seen in Furthermore, two assumptions were introduced in these analyses for modelling the contact behaviour between the profiles and also between them and the screws: (i) a tangential friction coefficient of 0.2 was assumed and, (ii) a hard contact between the profile surfaces and a rough and hard contact was considered between the profiles and the screws.Each finite element analysis was carried out in two steps. Firstly, an eigenvalue elastic buckling analysis was performed to establish the buckling modes (eigenmodes) which were observed in the tests and, consequently, to determine the geometric imperfections to introduce in the model. After knowing their effects on structural response of this kind of beams, the following maximum values were chosen for the local, distortional and global geometric imperfections: h/300, 0.40t and L/750, respectively. Then, a general geometrical and material nonlinear static analysis with imperfections (GMNIA) was undertaken with the purpose of simulating the structural behaviour of cold-formed steel beams under bending at ambient temperature. The nonlinear geometric parameter (⁎NLGEOM=ON) was set to deal with the geometric nonlinear analysis, namely, with the large displacement analysis. shows a comparison of the load–vertical displacement curves of CFS beams obtained from the experimental tests and finite element analysis (FEA) used for the calibration of the model. All curves from FEA fit closely with the experimental curves, especially with the ones that presented the lowest maximum load. This good agreement and accuracy between the experimental and numerical results ensures a strong validity of the developed finite element model and also ensures reliable results obtained from the parametric study. From these graphs, it can be seen that the maximum numerical load of the C, lipped I, R and 2R beams was, respectively, 10.58, 39.86, 54.97 and 120.78 kN. So, the mean values of the FEA-to-experimental loading capacity ratios for these beams were 0.90, 0.96, 0.91 and 0.91, respectively. However, concerning the minimum value of the maximum load-carrying capacity of beam obtained from the three experimental tests for each type of beam, those ratios were already 0.92 for the C beam and 0.99 for the other beams. The developed numerical model reproduced both the loading stage and the failure load of all types of beams with great accuracy so that the numerical results were always on the safe side. The differences were higher in the failure load of the C beams than in the other beams because of the change of the action line of the force during the tests. The numerical post-collapse response of the R and 2R beams were less accurate with regard to the C and lipped I beams, but the same happened in the experimental tests, in other words, the unloading stage of the three R and 2R beams was not so identical in what concerns the C and lipped I beams. The reason for the differences between the numerical and experimental results and between the experimental results of identical test series (c and d) may result from differences in the residual stresses of the members, the straightness of the plates, the yield strength on the member cross-section due to cold-forming and the assembly process of these beams. The discontinuities in some curves corresponding to the failure of screws were not observed in the FEA due to the elastic–plastic behaviour modelled for the mechanical properties of these screws.a illustrate the numerical failure modes of the tested specimens under bending and they can be compared to the experimental failure modes as shown in b. The local, distortional and lateral-torsional buckling modes that were responsible for collapse of the beams are clearly identified. This confirms that the finite element model predicted the behaviour of cold-formed steel beams with an acceptable precision. The figures also present the finite element results in the form of von Mises or minimum principal stresses to help understand the behaviour of the beams.It was possible to observe that distortional buckling was the main failure mode responsible for the collapse of the compound beams. It was noticed that the 2R beams started to slightly rotate laterally in one direction, reversing its rotation as distortional buckling occurred on the most affected U profile (). In addition, failure of the web of the R beam only occurred after the distortional buckling of the U profile. Increase of the lateral rotation of the beam further increased the local buckling of the web (). It cannot be forgotten that the maximum load of the R beams was about half load of the 2R beams and if the local buckling was the main failure mode responsible for the collapse of the beam, that difference would be higher. The distortional buckling always occurred nearer to the roller support of the beams rather than in mid-length of the specimens since the other beam support (pinned support) could not move. Finally, the lateral-torsional buckling was the main failure mode responsible for the collapse of the C and lipped I beams (After validating the finite element model a parametric study has been performed considering several combinations of thickness, height and length of the beams so that the influence of these parameters on the flexural structural response of beams could be identified, as well as the evolution of strength-to-weight ratio (PW/SW) as a function of those parameters (). It is noticed that the first, the second, the third and last letter of the reference C–h–t–L corresponds respectively to the type of simulated beam (for this case corresponds to the C beam), the height (h), the thickness (t) and the length (L) of the beam. Therefore, five different thicknesses (1.5, 2.0, 2.5, 3.0 and 3.5 mm), heights (200, 225, 250, 275 and 300 mm) and lengths (3000, 3500, 4000, 4500 and 5000 mm) for each kind of beam (C, lipped I, R and 2R) were used in this study. summarises all numerical results showing that an increase of the number of profiles per compound cross-section leads to an increase in the PW/SW ratio. However, it is expected that this ratio stops increasing since the difference between the R and 2R beams was already small. The same tendency was found for this ratio in what concerns the increase of thickness and height of beams. Finally, the average PW/SW ratio of the lipped I, R and 2R beams was 1.80, 2.59 and 2.91 times higher than the one of the C beams, respectively. It should be pointed out that the PW/SW ratio had a strong reduction when the span of the beams changed from 3000 to 4000 mm, especially for the R and 2R beams.ifλ¯LT≤0.4χLT=1.0ifλ¯LT>0.4χLT=1.0/[ϕLT+(ϕLT2−λ¯LT2)0.5] are the appropriate section modulus of the cross-section depending on its class (elastic section modulus, Wel, for class 3 and effective section modulus, Weff, for class 4 cross-sections) and fy is the yield strength of steel. It is noticed that α in Eq. was equal to 0.76 (buckling curve d) since the beam profiles were connected to each other by screws. In addition, the effective section modulus was calculated considering the individual contribution of each profile and, consequently, the effective geometrical properties of class 4 cross-sections were still determined based on the Clause 5.5 of EN1993-1.3 in which EIy, EIw and GJ are the minor axis flexural rigidity, warping rigidity and torsional rigidity, respectively. ky represents the effective lateral buckling length factor and kw the factor which accounts for the beam end warping. Regarding the lateral deformed shape of the beams obtained from the FEA, the value of ky=0.8 has been used and the value of kw=1.0 representing the free end warping condition. On the other hand, Cb is a coefficient depending on the moment distribution along the length of the beams summarise the results obtained from all numerical simulations carried out respectively for C, lipped I, R and 2R beams and the corresponding results given by the currently available design rules. It should be pointed out that most of the numerical results were higher than the corresponding design results. The opposite was only valid for the I-250-2.5-5000, 2R-250-2.5-4500 and 2R-250-2.5-5000 beams, which means that the design methods, as presented here, may be on the safe side for CFS beams in the same conditions as the ones studied in this work and at least for spans lower than 4500 mm. In spite of this, from , it appears that different buckling curves could be adopted for each kind of beam in such a way that more accurate predictions can be made. So, further experimental tests on cold-formed steel beams should be performed, especially on compound beams. It is also noticed that, when the values of non-dimensional slenderness are low, they do not have to correspond exactly to safe design values.Another important conclusion to be drawn was that EN1993-1.1 An experimental and numerical investigation into the behaviour of cold-formed steel C-, lipped I-, R- and 2R-section beams under bending conditions at ambient temperature has been presented. A total of twelve four-point bending tests and fifty-two numerical simulations performed with the finite element program ABAQUS were made. Lastly, the suitability of design methods established by EN1993-1.1 for the buckling moment capacity was also investigated using the developed finite element model.As it was expected, cold-formed steel beams are very sensitive to local, distortional and global buckling and also their interactions. It was observed that the failure loads of the beams with C- and lipped I-shaped cross-sections corresponded to the lateral-torsional buckling modes, whereas the distortional buckling was the responsible buckling mode for the failure loads of the R and 2R beams. In order to improve the structural behaviour of these two types of beams, the authors suggested, for instance, that the U profiles of these beams are replaced by lipped U profiles like the C profiles, but with the lips towards the exterior side of the profile. In other words, the U profiles should be replaced by hat (omega) profiles The good agreement between the experimental and numerical results and between the respective failure buckling modes proves that the finite element analysis is a reliable tool to get quite accurate results. The finite element results showed that the strength-to-weight ratio of the simulated beams decreases a lot when their span increases, especially, from 3.0 to 4.0 m. It is also shown that EN1993-1.3 predictions may be conservative for beams comprised of two or more CFS profiles or even over-conservative as it was observed in some studied cases. However, these design guidelines may give unsafe results for these beams with spans longer than 4.5 m.Hence it is recommended that further experimental and numerical research is needed to developed new design guidelines for lateral-torsional buckling of cold-formed steel beams comprised of more than one profile and connected by screws.Crack growth behavior of 9Cr−1Mo (P91) steel under creep–fatigue conditionsSeveral components operated at high temperature are also subjected to cyclic loading making crack growth behavior under creep–fatigue conditions a significant concern during design and during service. This is especially the case for components designed for long term service. Creep–fatigue crack growth tests were conducted on a modified 9Cr–1Mo (P91) steel at 625 °C under constant load amplitude conditions with various hold times using compact type specimens. The crack growth rates per cycle increased significantly with increase in hold time when crack growth data were plotted with the cyclic stress intensity factor, ΔK. It is shown that the creep–fatigue interactions during crack growth for various hold times are represented better by the (Ct)avg parameter implying that the P91 steel behaves in a creep-ductile manner. The test results are also used for assessing the newly developed American Society for Testing and Materials (ASTM) test standard, E2760-10 for creep–fatigue testing.crack velocity at any given crack lengthsecondary creep (power law creep) coefficientnet thickness for side-grooved specimenstime-dependent fracture mechanics parametervalue of Ct in the small scale creep regimesteady state creep fracture mechanics parameterangular functions on which the creep zone size dependsrise time, hold time and decay time in loading waveformsscaling factor in the analytical expression for Ctstress intensity factor range under fatigue loadingload-line deflection change during hold due to creepHigher energy conversion efficiencies are achieved by an increase in the operating temperature of power-plant components such as steam headers, steam turbines, gas turbines, and nuclear reactors Creep–fatigue crack formation and crack growth rate data are necessary inputs for assessing the structural integrity of high temperature components in power generation and aircraft engine industries. In 2008, the American Society for Testing and Materials (ASTM) embarked on the task of developing separate standard test methods for creep–fatigue crack formation and creep–fatigue crack growth. The first standard entitled, “E-2714-09: Standard Test Method for Creep–fatigue Testing” was developed in 2009 The second standard entitled, “E-2760-10: Standard Test Method for Creep–fatigue Crack Growth Testing” was developed in 2010 Of particular interest to this work is the crack growth behavior of modified 9Cr–1Mo steel under creep–fatigue conditions. This material is designated by the American Society for Testing and Materials (ASTM) as grade T91/P91 steel. The prefixes in this designation correspond to tubing and piping applications, respectively. This material is commonly used in structural components such as steam headers, superheater and reheater tubes in ultra-super critical power plants. Such components typically operate at high steam pressures and temperatures under a combination of cyclic loading conditions with long hold periods under sustained stress. It is desirable to increase the maximum operating temperature of these steels up to 625–650 °C to increase the energy efficiency of ultra-super critical power plants Considerable work in the area of creep–fatigue characteristics of modified 9Cr–1Mo steel in the past have already been carried out The test material is ASTM grade P91 steel that has a creep strength of 94 MPa at 600 °C for a life of 100,000 h and was obtained from an ex-service pipe section with an outer diameter of 480 mm and a wall thickness of 45 mm from which specimens blanks were machined. The material was re-heat-treated to ensure consistency with original microstructure.Modified 9Cr–1Mo steel (P91/T91 as per ASTM A335/A213 respectively) was developed by Oak Ridge National Laboratory in the early 1980s. The grade 91 material, classified as martensitic steel is typically used in main steam pipes, superheaters & headers, boilers and turbines in supercritical and ultra-supercritical fossil power generation plants The material properties were obtained from an earlier study performed in support of creep–fatigue crack formation in 9Cr–1Mo steel shows the creep deformation behavior and summarizes the tensile and creep properties.The specimen geometry chosen for test program is the standard Compact Type, C(T) specimen with a width, W

= 50 mm, thickness, B

= 12.5 mm and initial notch, a0

= 13.5 mm. The dimensions chosen are in accordance with ASTM test standard The tests were conducted in both electric-actuator and servo-hydraulic test machines. The C(T) specimens were pre-cracked to an initial crack length to width ratio, a/W, of about 0.4, under cyclic loading at room temperature. The specimens were then side – grooved (10% of thickness on each side with 60 degree V-notch) to prevent tunneling at elevated temperature. The potential drop (PD) and the unloading compliance methods were used to monitor crack length during the tests. The waveforms for loading and unloading portions were triangular and the loading/unloading times were held constant (2 s rise and decay times). Hold times of predetermined duration (0, 60 and 600 s) were superimposed on the triangular waveforms at maximum load as shown in . All the tests were carried out at 625 °C and at a load ratio, R, of 0.1.The starting ΔK levels varied from 23.0 MPa√m to 29.1 MPa√m for the zero hold time or continuous cycling tests. The first set of 60 and 600 s hold time tests had starting ΔK levels of 23.6 MPa√m and 23.9 MPa√m respectively. In order to have overlapping crack growth data, the second set of 60 and 600 s hold time tests had a lower starting ΔK level of 19.6 MPa√m. These force levels ensured that each test yielded sufficient crack growth data. The minimum and maximum load, load-line displacements at minimum, maximum and hold time positions, unloading compliance, PD voltage, test temperature were continuously monitored and recorded during the tests. A summary of test conditions for all the tests is given in The tests were normally stopped prior to fracture and cooled to room temperature and subsequently subjected to cyclic loading at room temperature to break open the specimen. This practice helps in accurately determining the crack extension during the creep–fatigue loading. The crack size at five equally spaced points centered on the specimen mid-thickness line was measured at the end of the pre-crack and at the end creep–fatigue portion of the test. The initial crack size, a0, and the final crack size, af, were then calculated by averaging the five measurements along the crack front. Having measured the initial and the final crack size, the crack size at any instant was then calculated using the following equation where af, a0, a are the final, initial and instantaneous crack lengths, respectively and Vf, V0 and V are the corresponding final, initial and instantaneous value of the PD voltage.The description of the crack growth behavior under creep–fatigue conditions can be described in the terms of the stress-intensity factor, KI, or the average magnitude of the Ct parameter, (Ct)avg.The stress-intensity factor KI is strictly valid only for linear elastic behavior, but it can be used as an approximation if the plastic zone size and/or creep deformation zone near the crack tip is limited. For a side-grooved C(T) specimen subjected to mode I loading, the stress-intensity factor is given by F(a/W)=2+a/W(1-a/W3/2)(0.886+4.64(a/W)-13.32(a/W)2+14.72(a/W)3-5.6(a/W)4)(Ct)avg can be determined for test specimens in which both force and force-line deflection behavior with time are measured from the following equation:where ΔP is the applied force range, ΔVc is the difference in force-line displacement between the end and start of the hold time, th, during a cycle. F′/F is given by:F′F=12+a/W+32(1-a/W)+(4.64-26.64(a/W)+44.16(a/W)2)-22.4(a/W)30.886+4.64(a/W)-13.32(a/W)2+14.72(a/W)3-5.6(a/W)4 is appropriate for small scale creep regime.When hold times are too small for reliable measurement of difference in force-line displacement because of the resolution limitations of the extensometer, (Ct)avg can be estimated using the following equation. This equation has been derived for materials that exhibit power law creep behavior (Ct)ssc can be estimated numerically using the following equation (Ct)ssc=2αβ(1-ν2)EFcr(θ,n)ΔK4W(F′/F)(EA)2n-1th-n-3n-1For θ

= 90°, the value of β

≈ 0.33 and Fcr (90°, 8.24) = 0.387 where A – pre-exponent in power law-creep and η1 for C(T) specimen is given by :The first term on the right hand side of Eq. represents the small scale creep contribution and second term represents the extensive creep contribution to the value of (Ct)avg. h1(a/W,

n) for various a/W and n are available in Kumar et al. Combined creep and fatigue crack growth may take place at elevated temperatures. In most cases fatigue dominates at higher frequencies (f >

1 Hz) and creep dominates at lower frequencies (f

< 0.1 Hz) and hold times where (da/dN)time is related to (da/dt)avg by:The first term on the right hand side of Eq. accounts for cycle dependent crack growth rate and the second term represent the time-dependent part. In this approach, the cycle-dependent and the time-dependent crack growth rates during creep–fatigue conditions are assumed to be independent mechanisms. The cycle-dependent crack growth rate (da/dN)cycle was determined from fatigue tests at 625 °C without hold time. By re-arranging the equation, (da/dt)avg, can be calculated by:The alternate approach for predicting creep–fatigue crack growth is the dominant damage approach In this approach, the cycle-dependent and the time-dependent crack growth rates during creep–fatigue conditions are assumed to be competing mechanisms and the crack growth rate is determined by the greater of the two. In general Eq. is more conservative and is preferred for analyzing creep–fatigue data is more conservative in application when creep–fatigue crack growth rates are being predicted. In this paper, both approaches will be used to plot the data so that the differences between the two approaches can be assessed.Creep-ductile and creep-brittle are two types of creep behavior generally observed in materials during creep crack growth and creep–fatigue crack growth tests and by comparing it to a measured load-line displacement during the hold-time, ΔVc, a determination can be made about creep-ductile versus creep-brittle material. The material can be classified as creep-brittle if ΔVe

⩾ 0.5 ΔV and the crack growth behavior may be characterized by the stress-intensity factor. On the other hand, if ΔVe

⩽ 0.5 ΔV, creep-ductile conditions are said to prevail and the crack growth behavior should be characterized by (Ct)avg. The former condition is expected when there is large ȧ values and higher resistance to creep deformation, and the latter occurs with low ȧ values and higher creep deformation rates in the material. Here, ȧ is the crack velocity at any given crack length. shows a comparison of the change in displacement for the instantaneous elastic part and the measured change in load-line displacement during the hold-time. The open symbols are the results of 60 and 600 s hold time tests estimated from Eq. . The closed symbols are the results of 60 and 600 s hold time tests for the measured load-line displacement due to creep. It is evident that the change in displacement during the hold-time due to creep is two to three orders in magnitude higher when compared to their elastic counterparts. Thus, there is significant creep deformation at the crack-tip and the creep effects dominate the crack tip behavior. Hence, it is necessary to express the average time rates of crack growth during a loading cycle, (da/dt)avg, as a function of the average magnitude of the Ct parameter, (Ct)avg for creep-ductile materials such as 9Cr–1Mo steels. shows the crack growth rate behavior of 9Cr–1Mo steel at 625 °C as a function of stress-intensity factor range for the hold times of 0, 60 and 600 s. , except plotted as average time rate of crack growth rate, (da/dt)avg, as a function of ΔK for hold times of 60 and 600 s tests, where (da/dt)avg=1th(da/dN)time.In general, as expected, the crack growth rate increases with increase in hold time and stress-intensity factor range, ΔK. An overall reasonable correlation between crack growth rate and ΔK is an indication that dominantly linear elastic conditions were maintained in the various test specimens throughout the testing. However, there are other concerns about the use of ΔK at elevated temperature as discussed below.Under cyclic and static loading of metal specimens at elevated temperature, crack growth behavior is affected by creep deformation at the crack tip causing transients in the crack growth behavior in the data from the majority of the tests and have also been reported in several previous studies Initially, due to high elastic stresses in the crack tip region, creep-deformation occurs rapidly but slows down with accumulated time as the crack tip stresses relax due to redistribution. The rate of stress relaxation itself decreases with time. Concurrently, due to increase in crack size the applied ΔK level rises. These competing forces of stress relaxation at a decreasing rate and increase in ΔK result in a tendency for the crack growth rate to first decrease, and then subsequently increase resulting in the “hook” in the da/dN or da/dtversus ΔK relationships. This is the motivation to seek other parameters that are able to establish better correlations such as the (Ct)avg parameter. are plotted with (Ct)avg, the hooks are expected to disappear because the value of (Ct)avg directly captures the stress relaxation trend and it also depends on the magnitude of ΔK which increases with crack size, as is evident from closer examination of Eqs. . If ΔVc is directly recorded during the tests, the measurement can be used via Eq. to determine the value of (Ct)avg. This measurement accounts for contributions to the creep deflection during the hold time from both the small-scale and the extensive creep terms in Eq. . When these measurements are not available because of resolution or other issues with extensometers, Eq. must be used to estimate the value of (Ct)avg. For some tests conducted in this study, the creep deflections during the hold time could be reliably measured. Thus, those results present an opportunity to verify the accuracy of Eq. using the measured values of (Ct)avg obtained from Eq. shows a comparison of the calculated values of C∗(t) and (Ct)avg and the measured (Ct)avg. The filled circle symbol and the continuous solid lines are the estimated values of (Ct)avg and C*(t) for the hold time of 60 s from Eqs. . The open circle symbols are the measured (Ct)avg values for the 60 s hold time tests. For the 60 s hold time tests, the (Ct)avg value is dominated by the small-scale creep term on the right hand side of Eq. . As expected, for short hold times the crack tip creep zone is expected to be small in comparison to the relevant specimen dimension and the creep zone growth constrained by the surrounding elastic stress fields characterized by K and time. In general, the contribution of the C* term is expected to be much less than the (Ct)ssc in short time hold time tests. It is also noted that the calculated values of (Ct)avg are consistently higher than the measured values by as much as a factor of 5. The reasons for this discrepancy are several. In the analytical estimates, we assume that the specimen is under pure plane strain conditions, we also neglect any contribution from the instantaneous plasticity at the crack tip, and we further neglect any contributions from primary creep The filled triangle symbol and the dashed lines are the numerically estimated values of (Ct)avg and C*(t) for the hold time of 600 s from Eqs. . The open triangle symbols are the measured (Ct)avg values for the 600 s hold time tests. For the 600 s hold time tests, the measured value of (Ct)avg was much closer to the estimated value compared to the case of 60 s hold time. Never-the-less, even in this case, the small-scale creep contributions to (Ct)avg seem to dominate the extensive creep contributions for the majority of the test indicating that dominantly elastic conditions were preserved for most of the test. clearly shows the differences between the measured and calculated values of (Ct)avg for both hold times and it underscores the importance of measuring force-line deflection during the hold time when conducting creep–fatigue crack growth testing. The current ASTM standard E-2760-10 does not require the measurement of force-line deflections and allows for estimated values of (Ct)avg to be used for correlating crack growth data. This should be examined more carefully and perhaps appropriate changes should be made to the standard.The results of the 60 and 600 s hold time tests for the dominant damage and the damage summation are plotted in and represented by filled and open symbols, respectively. The 60 and 600 s hold time with a max load of 9.0 kN load were completed within 62 and 128 h respectively, while the ones with 7.5 kN load required 143–321 h, respectively. In general, creep–fatigue crack growth data exhibit scatter that might be attributed to the measurement of force-line displacement during the hold time. There are a couple of outliers in the data trends in that are due to measurement issues. This is not surprising considering that the displacements during one cycle are small raising the probability of random errors in measurement. To reduce experimental scatter, the change in force-line displacement values during hold-time have been averaged over five successive cycles. We note that at the very end of the tests, the value of the minimum force-line displacement or the residual deflection starts to increase rapidly. This indicates rapid accumulation of inelastic deformation, which may be due to ratcheting or also due to rapid crack growth. Hence, the data collected after the minimum force-line displacement exceeds 0.05W were considered invalid in accordance with the ASTM Standard E2760-10 are noteworthy. First, the differences in the trends analyzed using the dominant-damage hypothesis and the damage-summation hypothesis are minimal. This is perhaps due to the domination of the time-dependent contribution to the crack growth rate compared to the cycle-dependent part for both 60 s and the 600 s hold times. Second, the hooks in the data trend observed in the da/dN or da/dt versus ΔK plots are no longer present strongly supporting the ability of the (Ct)avg parameter to correlate the data. Recall that the value of (Ct)avg depends both on the value of ΔK and the hold time. Third, it is observed from the plot that the difference in the crack growth rates for 60 s and 600 s hold times are much smaller in comparison with the plots with ΔK. All data appear to lie in a narrow band although there are some differences between the time-rate of crack growth between the conditions of 60 s and 600 s hold times. Notwithstanding these small differences, an almost linear correlation between (da/dt)avg and (Ct)avg is observed. This observation is well supported from the earlier studies of creep–fatigue crack growth behavior of several Cr–Mo steels using the (Ct)avg parameter We also note that the time rates of crack growth for the longer hold time tests of 600 s are lower than the crack growth rates from the 60 s hold time test; this difference is attributed to the time-dependent damage mechanisms at the crack tip. Saxena and co-workers The crack growth behavior of 9Cr–1Mo steel was investigated under creep–fatigue conditions at 625 °C. The creep–fatigue crack growth data was characterized using ΔK and the (Ct)avg parameters for the cycle-dependent crack growth and time-dependent crack growth rates, respectively. (Ct)avg was determined from experimentally measured force-line displacement rates during the hold time. It was found that for P91 Steels at 625 °C, the force-line displacement rate was dominated by creep deformation making (Ct)avg the more appropriate parameter for characterizing time rates of crack growth. Following other observations/conclusions can be drawn from the experimental data:When the crack growth rates per cycle were plotted with ΔK, the rates increased substantially with hold-time. However, when the time rates of crack growth were plotted with ΔK, the rates during the 60 s hold time tests were higher compared to the rates during 600 s hold time tests. Also, a “hook” was observed in the crack growth rates at the beginning of each hold time test.The correlation between crack growth rates and (Ct)avg was found to be significantly better and unique and the hooks disappeared from the data trends. The average time rate of crack growth during hold-time was lower for the 600 s hold time test than for the 60 s hold time test.There was minimal difference between data analyzed using the dominant- damage and the damage-summation hypotheses.Significant differences (factors of 2–5) were observed between the calculated values of (Ct)avg and those based on measured values of force-line deflection underscoring the importance of directly measuring the change in deflection during hold time for all creep–fatigue testing.Effect of shot peening on the residual stress and microstructure of duplex stainless steelThe effect of shot peening (SP) treatment on duplex stainless steel S32205 is studied in order to improve the material surface properties. Residual stress distributions in both ferrite and austenite are investigated by X-ray diffraction, and microstructure is explored using Rietveld method. The results reveal that different distributions of compressive residual stress between ferrite and austenite under the same SP condition are resulted from the diverse hardness for different phases in duplex stainless steel. After SP, domain sizes in both ferrite and austenite are refined, and microstrain, dislocation densities and compound fault probabilities are observed to increase sharply in the near surface layer. It is found that distribution trends of residual stresses along the variation of depths are similar to those of lattice parameters for both phases. It can be obtained that in the near-top surface layers, the SP influence on residual stresses and microstructure of austenite is stronger than those of ferrite under the same SP condition. These results reveal that SP treatment with proper processing is efficient for the improvement of the surface properties of duplex stainless S32205.Duplex stainless steel (DSS) consisting of approximately equal amounts of ferrite (α-phase) and austenite (γ-phase) often combines the best features of α-phase and γ-phase stainless steel. Generally, it has good mechanical properties, such as high strength and ductility, good corrosion resistance, and it has found a growing use in mechanically loaded constructions X-ray diffraction (XRD) line profile analysis evaluates microstructural parameters in a statistical manner, moreover, the analysis is easy, reliable, quick and non-destructive to specimen. Rietveld's XRD structure refinement based on simultaneous structure and microstructure refinement DSS S32205 was provided by Shanghai Baosteel Group Corporation. Continuous casting followed by a solution annealing treatment at 1050 °C and quenching in water was carried out on this material in order to avoid the precipitation of secondary phases. In this work, all samples were cut into 20 mm in diameter and 2 mm in thickness directly from ingots and then polished. The chemical composition is C (0.029), S (0.006), Si (0.42), Mn (1.27), Cr (22.10), Ni (5.17), Mo (3.10), N (0.18), P (0.021), and the rest Fe (all in wt. %).SP coverage was 100% on all samples. SP intensity is measured by the arc height of Almen specimen (A type), which is controlled by jet pressure of nozzle, SP time and the average ball diameter. The diameter of peening nozzle was 15 mm and the distance between the nozzle and samples was 100 mm. In this work, dual SP was carried out. The main aim of a second SP was not only to enhance the strength, but also to smooth the surface, hence smaller balls were used on the second treatment compared with the first one. Shot media were cast steel balls (hardness, 610 HV) in the first step and ceramic balls (hardness, 700 HV) in the second step. Two dual SP types in this work were set as 0.30 mmA + 0.15 mmA and 0.20 mmA + 0.15 mmA, respectively.XRD data were collected from Rigaku Ultima IV X-ray diffractometer (Rigaku, Japan) with D/tex 1D high-speed detector, which was operated at 40 kV/30 mA with Cu-Kα radiation (λ = 1.54056 Å). The system was set up with Bragg–Brentano optics for this study. Div H. L. Slit, Div Slit, Sct Slit and Receiving Slit were fixed as 10 mm, 1°, 1° and 0.15 mm respectively. Residual stresses were investigated on X-ray stress analysis (LXRD, Proto, Canada) with Mn-Kα radiation (2θ ≈ 152.8°, 30 kV, 25 mA) for γ-phase (311) samples and Cr-Kα radiation (2θ ≈ 156.4°, 20 kV, 4 mA) for α-phase (211) samples. The stress was determined by sin2Ψ method. The average penetration depth of Cr-Kα radiation in α-phase and Mn-Kα radiation in γ-phase was 4.7 and 16 μm, respectively Instrumental parameters of a Si standard sample The basic consideration of this method is the modeling of diffraction profiles by an analytical function, which is a combination of Cauchyian, Gaussian and asymmetry functions. It has been well established that the observed peak-broadenings of XRD line profiles are mainly due to the presence of domain size and r.m.s. strain. Cauchy and Gaussian type functions can well model the particle size and strain broadening, respectively. Being a linear combination of a Cauchyian and Gaussian functions, Pseudo-Voigt function is the most reliable peak-shape function and is widely used in the Rietveld structure refinement softwares Where L0

=

h

+

k

+

l, h02

=

h2

+

k2

+

l2 (Miller indices h, k, l). Following this definition u is the number of broadened components and b the number of broadened ones.To account for the overall broadening, we define an effective size Deff, computed from the domain size D, the deformation and twin fault probabilities in the following way:Peak asymmetry is evaluated from the extrinsic deformation and twin faulting probabilities. By defining y1 as the peak intensity at the diffraction angle 2θ0

+

x2, where 2θ0 is the center of a fully symmetric profile, the peak asymmetry can be expressed as:The values of the compound fault probability parameters [1.5(α'

+

α''

+

β)] and the values of dislocation densities ρ are also calculated to estimate the overall effect of faulting the procedure as adopted in the earlier reference SP intensity of 0.30 mmA is usually regarded as industrial processing reference datum. So intensity of 30 + 0.15 mmA was chosen as research object in present work using XRD line profile analysis by Rietveld method. Profile refinement continues until convergence is reached in each case, with the value of the quality factor (GOF) approaching 1.2.Under SP intensity of 0.30 + 0.15 mmA, γ-phase weight fraction obtained by Maud software is 0.485 ± 0.008 at the depth of 15 μm, as shown in . And it ranges from 0.479 ± 0.007 to 0.511 ± 0.009 with the increasing depth to matrix from the top surface, indicating little decrease of γ-phase weight fraction. However, many researchers reported that γ-phase translates into martensite after SP Before SP, depth profile of residual stresses of α-phase and γ-phase are measured to be about - 75 and + 80 Mpa, respectively, in DSS S32205, as is shown in . Compared with the CRS in α-phase, the tensile residual stresses existing in γ-phase are due to the higher coefficient of thermal expansion in γ-phases during manufacturing and subsequent treatments reveals that with the increasing depth from the top surface, CRS in γ-phase increases to the peak value at 30 μm below the top surface and then decreases after SP, while, it keeps decreasing in α-phase. The maximum compressive stress (MCRS) is 940 and 967 MPa in γ-phase, and 748 and 835 MPa in α-phase when SP intensities are 0.20 + 0.15 mmA and 0.30 + 0.15 mmA, respectively. Under the intensity of SP is 0.20 + 0.15 mmA, the depth of surface deformation layers of γ-phase is about 150 μm, and that of α-phase is about 200 μm. The depth of surface deformation layers becomes bigger along with the increase of SP intensity when other parameters are fixed. As SP intensity has direct relation to the impact velocity of small balls, the faster the impact velocity, the higher the impact kinetic energy, therefore, surface deformation layer depth is bigger, while at the same depth, the higher SP intensity, the bigger the CRS.These results are due to concurrent processes of plastic deformation during SP. For materials with low hardness, at the surface, the plastic stretching of regions is dominating and CRS show its maximum at the surface. This is so since the maximum elongation occurs at the surface and decreases with increasing depth into the specimen. However, at the surface layer of materials with higher hardness, a distinct maximum of residual stress occurs below the surface, since the Hertzian pressure distribution existing under the shot at the moment of impact predicts a maximum shear stress at a point below the surface Furthermore, the less MCRS in α-phase (748 and 835 MPa) than that in γ-phase (940 and 967 MPa) is resulted from a peening-induced adiabatic heat production, which is caused by extremely short impact durations of concerning shot together with plastic deformation of various degrees according to material hardness In SP process, the influence of micro-indentation in surface layers on residual stress field cannot be ignored. Before SP, micro-indentation produced mainly in the manufacturing process will damage the fatigue fracture properties since it can accelerate the generation and growth of micro-crack, while it can be prevented by SP treatment with appropriate intensity. However, SP with a too high intensity will generate much more micro-indentation, and the effect of SP cannot be embodied obviously if the intensity is too low. Therefore, in this work, SP with intensities of 0.20 mmA, 0.30 mmA are chosen to reduce micro-indentation errors. A second SP (0.15 mmA) with smaller ball diameter compared with that in the first step is carried out to smooth the surface. In this way, micro-indentation errors are reduced to the minimums and the residual stress field is optimized.After SP with intensity of 0.30 + 0.15 mmA, lattice parameter variations of DSS S32205 obtained from Rietveld's analysis via depth from the top surface are shown in . It is evident that with increasing depth from the top surface, lattice parameter increases to the peak value of 3.6156 nm at 30 μm below the top surface and then decreases in γ-phase, while it continues decreasing in α-phase with a maximum value of 2.8869 nm at the top surface. Lattice parameters of both α-phase and γ-phase in the deformation layers differ from the substrate material lattice constants. It can be seen that these elastic strains are positive, relatively high, and inhomogeneous along the depth of both phases after SP. This may originate from lattice distortions of both phases in deformation layers during SP. The diversification trends of lattice parameters in both α-phase and γ-phase are as same as those of CRS, which is due to the relevance between the two factors The domain sizes and microstrain of the specimen under SP intensity of 0.30 + 0.15 mmA are measured along [111], [200] and [220] for γ-phase and along [110], [200] and [211] for α-phase, and the results are shown in , respectively. Although the domain sizes are obtained from three strong diffraction peaks, it is obvious that the variation trends are similar and the values are located in same level () due to the isotropy of polycrystalline DSS. The diversification trends of calculated domain size values are elevated rapidly with increasing depth from the surface to about 100 μm in γ-phase and about 150 μm in α-phase, and they then both keep nearly constant. The smallest domain sizes presenting at the top surface for DSS after SP are due to the most deformation on the surface. Opposite to the domain size diversification trend, microstrain change trend decreases from the top surface to the depth of 100 μm in γ-phase and 150 μm in α-phase (). In deformation layers, the microstrain in γ-phase decreases is faster than that in α-phase, and it is also higher at the same depth near the top surface under the same SP intensity.The lognormal distribution of domain sizes in both phases obtained from the Rietveld's analysis is shown in . It is clear from the plots that the most probable domain size values (peak maximum of the lognormal distribution) of two phases increase from the top surface to the depth of 100 μm. At the surface layer, domain become almost uniform in size, and the dispersion of domain size about the most probable increase rapidly at the depth of 100 μm. After SP, it is likely that there would be a wide range of domain size variation with the increasing of depth from the top surface. Under the same SP intensity, the most probable domain size value of γ-phase is less than that of α-phase at the top surface. However, it becomes larger at the depth of 100 μm. The former is characterized by a higher hardenability in γ-phase in the SP treatment, and the latter can be attributed to the less SP influence on γ-phase at the deeper layers.The domain sizes (D) and microstrain (ε) values estimated from the size–strain–shape analysis, the dislocation densities in the surface deformation layers can be determined via Williamson method Where ρ represents the dislocation density, <ε2> is the weighted average of ε2 after multiple measuring, and b→ represents the mold of Burgers vector in calculation. Burgers vector can be obtained according to the Ref. , the type of dislocation is mainly the in-plane misfit one. Combined with the analyses of , the depth distributions of dislocation densities under the SP intensity of 0.30 + 0.15mmA have been calculated and are shown in . As we know, SP can induce plastic deformation layer to specimen and the deformation degree decreases from surface to core region. As seen in , the variation trends of dislocation densities for all peaks are similar, and the values decline sharply from the top surface and then decrease gently, after that, they keep nearly constant and the values are located in the same level in the substrate. At the top surface, the dislocation densities reach 6.52 × 1014, 1.91 × 1015 and 8.76 × 1014/m2 for [110], [200] and [211] in α-phase, respectively. For γ-phase, they are 2.45 × 1015, 1.02 × 1016 and 3.32 × 1015/m2 for [111], [200] and [220], respectively. Before SP, the average dislocation level of DSS is about 1011–1012/m2. The much higher dislocation densities after SP is ascribed to the high kinetic energy of small shot balls during dislocation gliding.Considerably, the higher values of dislocation density and the larger decrease rate of γ-phase than those of α-phase in near surface (about 25 μm) are due to a higher hardenability of γ-phase. The higher work hardening rate in γ-phase can be attributed from two different mechanisms. On one hand, the low stacking fault energy presents in γ-phase, which is lowered even further with the increment of nitrogen. On the other hand, the affinity between N and Cr induces short-range ordering It can be noted that microstructure parameters such as domain sizes and microstrain have direct correlations with other microstructure parameters like the stacking faults. Deformation and twin faults induce a shift, broadening and asymmetry in the profile. Under the SP intensity of 0.30 + 0.15 mmA, compound fault probability values calculated by 1.5(α′ + α″) + β are shown in . It can be obtained that the maximum lies on the top surface in both phases, and γ-phase has higher values than α-phase due to the lower stacking fault energy in SP process The depth profiles of domain sizes, microstrain, dislocation densities and compound fault probabilities confirm that SP is a very efficient method to optimize the microstructure in the near surface region and to indentify the microstructure-changed layer, which can prevent internal dislocation out of specimen surface and constrain dislocation movement inside the grain and subgrain. In the microstructure-changed layer, the domain size increases and microstrain, dislocation density decrease with depth increasing, which leads to mechanical properties be weakened. Even so, the microstructure-changed layer can still reduce surface damage and improve the surface crack initiation resistance, which is the main reason for SP to improve the surface mechanical properties.With the method of XRD line profile analysis, the surface layer characteristics of shot-peened DSS are investigated. It is concluded that for in the near-top surface layers, SP has stronger influence on CRS and microstructure of γ-phase than on α-phase under the same SP condition. In α-phase MCRS locates at the material surface. However, for γ-phase with higher hardness, high residual stress is present at the surface and MCRS is found below the surface. Lattice parameters of both phases in deformation layers increase after SP. Weight fraction of γ-phase in DSS decreases hardly as γ-phase is strongly influenced by the increasing fractions of alloying elements, such as Ni, N. The variations of domain sizes, microstrain and dislocation densities along [1 1 0], [2 0 0], [2 1 1] diffraction directions in α-phase and [1 1 1], [2 0 0], [2 2 0] in γ-phase demonstrate that SP process can change microstructure in all plane diffraction directions. The lower domain sizes, higher microstrain, higher compound fault probabilities and higher dislocation densities of γ-phase than α-phase in the near-surface layers are due to its higher work hardening rate and stronger resistance against SP influence on microstructure. According to the different distributions of CRS and microstructural characterization in α-phase and γ-phase after SP, it is especially important to select proper processing parameters of SP to optimize the mechanical properties of surface material for DSS.Printed pressure sensor matrix with organic field-effect transistorsThe paper presents the construction and fabrication method of a pressure sensor matrix with organic field-effect transistors. The sensor structure consists of a matrix of air-gap transistors which is realized by roll-to-roll processing and laminating methods. High aspect ratio spacer structures are made by inkjet printing.The sensor cell transistor senses the applied force on the top substrate due to changes in the air-gap dimension. The sensor matrix has measurement range of 0.4 kPa−1–4.4 kPa−1, sensitivity 0.4 ± 0.1 kPa−1 and time response better than 300 ms. The structure is scalable and it has a sensitivity comparable to state of the art pressure sensor matrices that use organic field-effect transistors. Its fabrication process, however, includes standard, low cost mass production steps of printed electronics and it can be transferred to a roll-to-roll process.Pressure sensor matrices offer a unique solution to the measurement of real-time pressure and touch profiles on different surfaces, and can be used in many applications. For example robotic devices capable of adjusting the amount of force needed to hold and use different objects have been demonstrated where the pressure sensor matrix enables robotic systems with human-like sensing capabilities Different concepts of pressure sensor matrices have been demonstrated previously based on resistive A pressure sensor matrix based on pressure-sensitive rubber and organic transistors embedded on a plastic film is proposed in We believe that a fabrication method utilizing printed electronics processes is the optimal technology to bring pressure sensor matrix fabrication into production scale. Different printing technologies are utilized for realization of various mechanical and electrical structures. Gravure printing was used to make spacer structures in Printed electronics manufacturing methods offer a low cost alternative to current electronics manufacturing processes. Additionally, printed electronics processing can yield very large volumes in a short time, still offering the customization possibility for dedicated applications. Methods of printed electronics have been utilized previously for the fabrication of pressure sensor matrices. A pressure sensor matrix based on organic transistors was fabricated by inkjet printing in The structure of a pressure sensor cell is shown in Details of the deposited layers and manufacturing processes are presented in Section . The sensor cell consists of two plastic foils with patterned structures on both sides, forming a transistor structure. An air-gap is formed between the foils due to a printed spacer structure. The proposed cell can be considered as an air—gap field effect transistor (FET). The theory of air gap FET’s is presented elsewhere where μ is the electron mobility in the channel of the FET, W and L are width and length of the channel, VGS⁡ is gate voltage, VDS is source - drain voltage, VT is threshold voltageThe value of Cpress is the dielectric layer capacitor Cox and air layer capacitor Cairin series and it can be expressed bywhere ϵ0is the absolute dielectric constant and ϵrox is the relative dielectric constant of the dielectric layer. The relative dielectric constant of air is considered to be 1. dox and dairrepresent the thickness of the insulator and the air-gap, respectively, and A is the surface area of the gate.Pressure P applied to the top foil causes the foil bending. Assuming a zero initial mechanical stress of the foil the mechanical deflection of the foil membrane of circular shape at center iswhere P is applied pressure, E is the Young’s modulus of the foil, υ is the Poisson’s modulus of the foil, and r and h are the radius and thickness of the foil membrane, respectively.The distance dair between the gate electrode and transistor channel is changed. Thus Cpress is a function of the applied pressure in accordance with (2) consequently. Then the drain current is pressure dependent at constant gate potential in accordance with (1).The manufacturing process of the cell is shown in . As the bottom foil, a roll-to-roll fabricated transistor foil was used (transistors without the top gate). In this foil, the electrodes were formed by first roll-to-roll evaporating a thin 40 nm silver layer, and then etching the electrode patterns using rotary screen printed etchant A 50 μm thick polyethylene 2,6-naphthalate (PEN) plastic foil was used as the top foil (Teonex Q65FA, DuPont Teijin Films). The gate electrodes and spacers were inkjet printed using a PiXDRO LP50 advanced research printer capable of driving industrial multinozzle piezoelectric printheads. For the gate electrodes, a silver nanoparticle ink (DGP 40LT-15C, Advanced Nano Products) was printed using an SX3 printhead with 10 pL nominal drop volume by Fujifilm Dimatix. Prior to printing, the PEN foil was treated with O2 plasma (2 min at maximum power 0.3 W/cm2) in order to ensure optimal wetting and film formation of the silver nanoparticle ink. Printing process parameters, such as nozzle driving voltage waveform, substrate temperature (60 °C), print resolution (650 dpi) and multinozzle printing strategy, were optimized in order to obtain printed gate electrode patterns with high definition. Sintering of the printed nanoparticle ink was done in oven at 150 °C for 60 min.An inkjet printable low-viscosity UV-curable photopolymer with a peak absorption wavelength of 365 nm (Norland Optical Adhesive NOA 89, Norland Products Incorporated) was used as the spacer material. The printhead nozzle driving voltage waveform was optimized in order to obtain repeatable drop formation to ensure a uniform spacer matrix. Prior to printing, the surface of the PEN foil with printed gate electrodes was treated by dip-coating with a 20 wt-% dilution of Novec EGC-1720 (3 M), a solution of a fluorosilane polymer carried in a hydrofluoroether solvent (HFE-7100, 3 M). The purpose of the surface pre-treatment was to modify the wetting behavior of the photopolymer in order to control the aspect ratio of the printed spacers on both bare PEN and gate electrode surfaces. Printing was carried out using a KM512LHX printhead with 42 pL nominal drop volume by Konica Minolta. The spacer pattern was a matrix of single printed droplets at a varying pitch of 400, 500 and 800 μm over the whole printed gate electrode foil. In the spacing is 400 μm. Curing of the printed spacers was perfomed in a UV-curing oven for 2 min using a 120 W/cm lamp with a -bulb having a peak radiation intensity at 350–400 nm (F300S, Fusion UV Systems, Inc.).The inkjet deposited droplets formed very well defined dots having a width and height of 110–170 μm and 3–7 μm, respectively, depending on the surface material (PEN/silver gate electrode) (). In the final demonstration the spacers had a height of 6,5 μm. The inkjet process allows controlling of the height to width ratio of the spacers via controlling the droplet volume, surface wetting behavior and post deposition curing parameters. For a fixed droplet volume (42 pL) and fixed UV curing parameters, the contact angle of the deposited droplet was the main parameter that determined the height to width ratio of the spacers. The fluorosilane pretreatment resulted in a higher contact angle compared to the untreated surface, resulting in an increase in the height to width ratio.In addition to the spacers, a “gluing” frame was printed with the same spacer material around the structures in order to enhance adhesion in the lamination process. The frame was printed with different parameters than the spacers in order to get a proper dense supportive frame structure. Printing resolution was set such (360 dpi) that the printed droplets were as close to each other as possible but not quite touching, in order to maintain the droplet height to width ratio and resulting frame thickness (). UV curing was carried out using the same parameters as for the spacer matrix.a) was placed on top of the bottom foil face-to-face. The gate electrodes were aligned over the transistor channels (Figs. c). Heat and pressure was applied for 5 min on top of the hot plate. Temperature was varied between 100 °C and 110° in different lamination tests. A 500 g weight applied pressure on the 10 cm × 10 cm array area.The flexibility of the laminated demonstration matrix sheet is limited by the substrate thicknesses, but even more dominantly by the adhesion between the laminated substrates. In order to get a good “gluing” effect in lamination, a large contact area is needed. This is why the frame structures were added for extra adhesion (a,b). Also the spacer or frame material has to have a very good bonding force with the substrate or the active layers. The adhesion can be enhanced by increasing the spacer density or even using a different gluing material in the areas between the pixels.Seven randomly selected pressure sensitive cells were characterized individually. The sample matrix was placed under a probe manipulator. The probe was pressed and released using manipulator screws. A probe with a dull head (with 200 μm radius) was used for applying a point pressure. As the top foil was 50 μm thick, the area of the pressure application on the top could be considered point-like. From that point the pressure spread in the bending top foil over a larger area (b). In the pressure sensitivity measurement a larger probe area (5 mm2) was used to press the whole area of a single cell. The pressing force was measured using a standard laboratory balance.The transistors were biased on and the current from source to drain was measured continuously during the pressure application. At first point forces were applied and the effect could be seen in the transistor measurement results (). Larger pressing force increases the current as the gate air gap decreases. The transistor behavior changed according to the field effect change explained in Section . There was no change in dielectric leakage current to the gate even when a strong force was applied. In the cell current is plotted over time, with different pressing force applied. The cell demonstrates reversibility (it returns to the initial value) and good sensitivity. The small delay before reaching a stable current level can be explained by the physical recovery of the substrate after displacement. Sharp peaks in the plot are due to uneven pressure application (manual probe adjustment). The response time was faster than the chosen measuring time (300 ms sampling period). Also the probe manipulator system did not allow a fast pressure application. The response time is most probably limited to the mechanical delay in substrate recovery after displacement, and not limited by the transistor switching speed (which is in the range of milliseconds). shows similar response to applied pressures for two capacitive cells of the same matrix (same one shown in Figs. b shows multiple press and release actions on the cell, and a good recovery to the initial value. Still there was some drifting in the transistor current that caused some rising of the current levels over time. This threshold voltage shifting due to bias stress is typical in many organic and inorganic transistors Finally the sensitivity of the cell to the applied force was characterized. With the larger (5 mm2) probe pressing the total cell area the output current of the cell was measured. shows the relative change of current from the starting unstressed value (ΔI/I0) for different applied forces. The pressure was applied in increasing and decreasing steps. The values in forward and reverse measurement sweeps do not match perfectly, partly due to the drifting of the transistor current values. Hysteresis can also be of mechanical origin. The response to the applied force can roughly be estimated to be linear. The real response is obviously a complicated function of the bending of the substrate on a spacer matrix and at the same time the integration of the capacitance of the gate on such a bent substrate (like in Eqs. ). The mechanical saturation level of the current is reached at pressures over 4 kPa (see ). Variation in current response to the applied force in different cells is roughly 25%. This can be improved in the future by optimizing the structure and the process.The measurement range of the cell was from 0.4 kPa to 4.4 kPa. The sensitivity of the cell was 0.4 ± 0.1 kPa−1. The obtained measurement range and sensitivity is comparable with the work by Someya One observation regarding the dielectric in the air gap transistor was that the open dielectric surface is easily charged a. On the other hand the charging effect could be used for e.g. molecular sensing purposes In this experiment we have shown a novel fabrication method for 19 printed pressure sensors on a flexible substrate. The randomly selected cells showed similar characteristics. These sensors form a matrix array and can be enlarged to cover a large area. At the moment individual sensors are measured but in the future sensors are easy to connect together to form a sensor matrix.A pressure sensor matrix with organic field-effect transistors has been designed, fabricated and tested. The sensor matrix has a sensitivity comparable to the state of the art pressure sensor matrices that use organic field-effect transistors. However, its fabrication process includes standard, low cost mass production steps of printed electronics which can be transferred to a roll-to-roll process. The laminated air-gap transistor structure is simple, and can be scaled in all dimensions. Inkjet printing being a digital processing method can be used for tuning the spacer height and spacing of individual pixels, or for making arbitrary patterns for the pixels. By choosing thin substrates the flexibility and sensitivity can be enhanced, but at the same time the challenges increase in processing of the thin substrates. By choosing transparent conductors, the structure can be made almost transparent. In addition to the simple touch sensor application, the proposed air-gap structure opens up new possibilites for other more dedicated (e.g., gas) sensing purposes.Tomi Hassinen received M.Sc. in physics (major Industrial electronics) from University of Helsinki in 2003. He is working as a Senior Scientist in Printed sensors and electronic devices team. He started researching printed electronics at VTT in 2005, and is presently finalizing his Ph. D. work on printed transistors.Kim Eiroma (M.Sc. Tech) is a research scientist and expert in inkjet deposition for the fabrication of functional devices. He has worked at VTT since 2006 and has been involved in private and jointly funded projects covering a multitude of applications for printed functionality, such as printed antennas and metallization for e.g. optoelectronic devices, thin film transistor fabrication, microelectronic and hybrid integration, optical devices, diagnostics and product safety.Tapio Mäkelä Ph.D. is a senior research scientist in the VTT Printed and hybrid functionalities. He has 20 years of experience in printed functionalities and nanoelectronics. His research interests include nanoimprinting lithography, roll-to-roll nanoimprint lithography, roll embossing, nanogrids and organic electronics. He has published more than 100 journal and conference papers on these topics. He has participated several EU-project and proposals He has been e.g. as technical manager in POLARIC project (ICT 2009), word package leader in GreeNanoFilms (NMP 2013) and task manager in many other EU and national projects.Vladimir Ermolov graduated with honors in 1981 and received the Ph.D in 1986 from the Moscow Engineering Physics University (MEPhI). Since 1981, he had been as Senior Research Associate with the laboratory of Dielectric Devices (MEPhI). He worked many times as a visiting researcher in the Department of Physics, Helsinki University and Fraunhofer Institute of Nondestructive testing, Germany. He had been as a principal research scientist with Nokia research center from1998 till 2011, where he worked as project manager for many projects in areas of MEMS, nanotechnology, radiotechnology, mass memory technology and sensors. He was involved in commercialization of several technologies. Since 2011 he has been with VTT Technical Research Center of Finland at as a principal research scientist, where he had made project management and research in areas of radiotechnology, MEMS, nanotechnology, printed electronics and technology commercialization. He is the author and co-author of 52 in referred journals and the holder and co-holder of 45 patents and patents pending.Graphene/gelatin hydrogel composites with high storage modulus sensitivity for using as electroactive actuator: Effects of surface area and electric field strengthThe electromechanical properties of graphene/gelatin hydrogel composites were investigated under the effects of graphene surface area, electric field strength and temperature towards bio-actuator applications. The highest surface area of an embedded graphene (MG; grade M) in the gelatin hydrogel composites induced the highest dynamic modulus (G′) under applied electric field. The 0.1 vol% graphene (MG)/gelatin hydrogel composite possessed the highest ΔG′/G′o value of 352% in comparison with other materials in previous studies. Even the lowest ΔG′/G′o values obtained from the fabricated graphene/hydrogel composites were still greater than other dielectric elastomer materials investigated. The storage moduli of the pure gelatin and graphene (MG)/gelatin hydrogel composites, between 30 °C and 90 °C, exhibited three distinct regimes. In the deflection experiment, the bending distance and the dielectrophoresis force were found to increase monotonically with applied electric field strength with a deflection toward the anode side, indicating the attractive force between the anode and the polarized carboxyl group as the gelatin structure possessed negative charges under applied electric field.Electroactive polymers (EAPs) have been developed for many applications such as compliant electrode The objective of present work was to investigate the electromechanical properties of graphene/gelatin hydrogel composites containing an anionic surfactant (i.e., sodium dodecylsulfate) as candidate materials for bio–actuator applications. The electrical, thermal, and electromechanical properties were investigated and measured under the influences of graphene content and surface area, electric field strength, and temperature.Gelatin (Type B, bovine skin) and sodium dodecyl sulfate (SDS) were purchased from Sigma Aldrich (Singapore). Various graphene nanoplatelets (graphene), as purchased from XG Science Inc., China, have specified average thicknesses of 1–2, 6–8, and 15 nm and platelet diameters of 2, 15, and 15 μm, in which they are referred to as graphene grade C (CG), graphene grade M (MG), and graphene grade H (HG), respectively.Various concentrations of graphene; 0.01, 0.1, 0.5, and 1 vol%, were dispersed in water solutions filled with 1 vol% of SDS, sonicated via a transonicator (Elma, S 70H, D 78224) at room temperature, at 150 W, 50 Hz, for15 min. Next, 10 vol% of gelatin was dissolved in distilled water (pH = 6.40) at 40 °C overnight via magnetic stirring. The two solutions were well–mixed at 40 °C, and poured into a petri dish to obtain the graphene/gelatin hydrogel composites. The hydrogel composites were allowed to settle as a film at an ambient temperature (∼30 °C). Each hydrogel composite had a thickness of ∼1.39 mm.The true density of each graphene was measured by a gas pycnometer (Thermo Nicolet, Nexus 670) which was operated in He gas atmosphere (20 psi) at 25 °C with a purging gas time of 1 min. The true density of graphene was measured repeatedly 20 times to obtain the average value and the standard deviation.The Brunauer–Emmett–Teller (BET) surface area of graphene was measured through a Thermo Finnigan, Sorptomatic 1990 surface area analyzer (SAA). The samples were weighed and out gassed at 300 °C for 12 h before the measurements of the adsorption and desorption isotherms with He and N2 gas.Electrical conductivity of the graphene was measured at 25 °C. The fixture consisted of two probes, which made contact with the film surface. The fixture was connected to a power source (Keithley, Model 6517A) to supply a constant voltage source and to read the current. The applied voltage and the resultant current were used to calculate electrical conductivity of the graphene samples by the following Eq. where σ is the specific conductivity (S/cm), ρ is the specific resistivity (Ω cm), t is the specimen thickness (cm), I is the measured resultant current (A), Rs is the sheet resistivity (Ω), V is the applied voltage (V), and K is the geometric correction factor.The morphology and size of the graphene samples were observed using a H-7650 Transmission Electron Microscope (TEM; Hitachi High-Technology Corporation, Japan) at an operated voltage of 100 kV where an imaging software (SEMAFORE 5.21) was used to determine platelet diameter of graphene. Scanning electron micrographs of neat gelatin, and graphene/gelatin composites were obtained through a scanning electron microscope (SEM; S-4800, Hitachi, Japan) to determine the morphology at various graphene concentrations. The surface micrographs of neat gelatin and graphene/gelatin composites were taken using a voltage of 25 kV and a magnification of 10 000 times to observe the distribution of graphene in gelatin hydrogel composites.Atomic force microscopy (AFM; Park system, XE-100) was used to observe the topology and phase images of the composites. Images were taken in the non–contact mode with the cantilever (NSC-14-CrAu) tapping at a scan rate of 0.25 Hz. The electrostatic force microscope (EFM) was utilized at a scan size of 1.00 × 1.00 μm2 using a signal amplitude of 5 V. Each sample was scanned at two heights above the surface. In the first level, the AFM topology images were obtained via scanning tip in the non–contact mode, which responded to the Van der Waals forces. The second scan measured the tip-surface distance as a result of the electrostatic force which was obtained from the charge distribution and the degree of charge generated in the gelatin and graphene/gelatin hydrogel composites.A melt rheometer (Rheometric Scientific, ARES) was used to investigate the electromechanical properties of the gelatin and graphene/gelatin hydrogel composites. The samples were set with a parallel plate fixture at a diameter of 30 mm. DC voltage was applied at the electric field strength (800 V/mm) using a DC power supply (Instek, GFG8216A). First, a strain sweep test was operated to define the suitable strain for obtaining storage modulus (G′) in the linear viscoelastic regime. The appropriate strain was determined to be 0.10 %strain for both of the gelatin hydrogel and the graphene/gelatin hydrogel composites. Second, the temporal response and the frequency sweep test were pre–sheared at a low frequency of 0.039811 rad/s and low strain of 0.10% with the application of electric field (800 V/mm) for 15 min to assure with the equilibrium polarization in materials. In the frequency sweep test, the composite properties were measured as functions of electric field strength (0–800 V/mm) and temperature (30–80 °C). The deflection of the gelatin hydrogel and the graphene/gelatin hydrogel composites was determined under the influence of applied electric strengths in the range of 0–600 V/mm. For each hydrogel composite, the sample was fixed vertically in a transparent chamber containing polydimethylsiloxane (PDMS) with the viscosity of 100 cSt between the copper electrodes. In the experimental setup, the electric field was non-uniform due to the presence of the finite-sized relatively conductive sample, and non-symmetric because of the sample was suspended from the above but the lower end was free as shown in . The silicone oil and the 1% graphene/gelatin electrical conductivity values were 3.24 × 10−7 S/cm and 8.86 × 10−2 S/cm, respectively so there was a mismatch in the electrical conductivity. A high voltage power supply (Gamma High Voltage, UC5–30P) was connected to a DC power supply (Gold Sun 3000, GPS 3003D) for supplying DC electric field. The displacement of samples was recorded by using a digital video recorder (Sony, Handicam HR1). The composite deflection was measured with a Scion image (Beta 4.0.3) program. The dielectrophoresis force is the net distributed body force which induces the specimen deformation in a non-conductive medium and in a non-uniform electric field. The deflecting force (Fd) generated from the resultant dipole moments of the material was calculated fromEq. where Fe is the resisting elastic force (N), m is the mass of sample (kg), g is the gravity constant (9.8 m/s2), θ is the deflection angle, ρ is the density of fluid, and V is the volume of the displaced fluid. In our experiment, the elastic force can be calculated by the following Eq. where E is the young's modulus which is equal to 2G′ (1+ν) in which G′ is the shear modulus (taken to be G′ (ω = 1 rad/s)) and ν is the Poisson's ratio, which is equal to 1/2 for an incompressible sample, I is the moment of inertia t3w/12, t is the thickness of specimen, w is the width of specimen, d is the deflection distance, and l is the length of specimen.Characteristics of the different graphene samples are summarized in . The true densities of the three graphenes (grade C; CG, grade M; MG, and grade H; HG), as obtained from gas pycnometer, are 2.140 ± 0.10, 2.253 ± 0.12, and 2.202 ± 0.13 g/cm3, respectively. In agreement, Nieto et al. The surface area of MG exhibited the highest value of 389 m2/g because its morphology consisted of short stacks of graphene sheets. In general, the surface area of the graphene particles increased with decreasing particle size The morphologies and average diameters of the graphenes of various surface areas, as measured by TEM and shown in , are 1.098 ± 0.22, 12 ± 2.50, and 16 ± 2.13, consistent with the supplier material specifications.The electrical conductivity values of CG, MG, and HG with different surface areas are approximately 3065 ± 38, 15363 ± 393, and 8701 ± 80 S/cm as shown in . Thus, the highest electrical conductivity belongs to MG which also exhibits the highest surface area as shown in . The explanation for the electrical conductivity is that the greater surface area of the particles promotes electron transport well along the graphitic domain Surface morphologies, appearing in SEM, of the gelatin and graphene/gelatin hydrogel composites are shown in a–c for the 0.1 vol% and 1 vol% MG; this graphene possesses the greatest surface area, electrical conductivity, and hydrophobic attraction force. It can be seen that MG is well dispersed in the gelatin hydrogel at a low graphene concentration of 0.1 vol% with SDS (1 vol% of gelatin solution) as the dispersing agent because the attractive hydrophobic force between graphene sheets is screened by the SDS molecules surrounding the graphene surface c, since the large hydrophobic interaction between the graphene molecules becomes more dominant and hampers uniform and homogeneous dispersion of 1 vol% MG in gelatin solution.The topology and charge distribution on the surface of the MG/gelatin hydrogel composites can be observed by EFM at an external electric field of 5 V, as shown in a–c exhibit the topology of the gelatin hydrogel and the 0.1 vol% and 1 vol% MG/gelatin hydrogel composites without electric field. a shows the smooth surface of the pure gelatin hydrogel at nanoscale. A well-distributed and randomly-aligned of 0.1 vol% graphene in the gelatin hydrogel is confirmed through the topology image shown in c shows an agglomerated graphene (1 vol%) topology. a′–c' show the charge distribution of the gelatin hydrogel and the MG/gelatin hydrogel composites. The images appear as a bright contrast indicating the presence of the generated attractive force between the probe and the sample surface. The degree of generated attractive force on the gelatin hydrogel and the MG/gelatin hydrogel composites are shown in . Both 0.1 vol% and 1 vol% MG/gelatin hydrogel composites possess the degree of generated attractive force of 108 and 76%, respectively, values which are higher than the pure gelatin hydrogel.First, the temporal responses of the pure gelatin and the graphene/gelatin hydrogel composites by alternately switched on and off were investigated under the applied electric field strength of E = 800 V/mm. The temporal characteristics of each material were determined under the linear viscoelastic regime under strain of 0.10%, and at the frequency of 100 rad/s, where the time required for G′ to respond is important in the actuator application. Induction time (τind) is the time required for G′ to reach the steady state when E is switched on. Recovery time (τrec) is the time required for G′ to decay toward its steady state, E is switched off.From the previous works, Kunchornsup et al. shows the comparison of G′ of the pure gelatin and the graphene/gelatin hydrogel composites (0.1 vol% and 1 vol%) during the time sweep test under the influence of an electric field. For the pure gelatin hydrogel, G′ rapidly reaches a steady-state value as the electric field is applied. This is due to the induced dipole moment generated within the gelatin molecules The graphene hydrogel composite, 0.1 vol%, was investigated further for the electromechanical properties under the effect of graphene surface areas of41, 115, and 388 m2/g for the CG, HG, and MG graphenes, respectively, at an electric field range of 0–800 V/mm. The storage modulus response (ΔG′) and the storage modulus sensitivity (ΔG′/G′o) of the composites are shown in at a frequency of 100 rad/s, a strain of 0.10%, and at a temperature of 30 °C. The ΔG′ and ΔG′/G′o of 0.1 vol% graphene/gelatin hydrogel composites increase with increasing electric field strength and with increased graphene surface area due to the generated polarization on carboxyl groups within the gelatin molecule leading to intermolecular interactions The effect of graphene concentration on the electromechanical properties of the graphene/gelatin hydrogel composites was investigated under an applied electric field strength of 0–800 V/mm. The ΔG′ of the composites vs electric field strength are shown in . The ΔG′ increases monotonically with increasing electric field strength (0–800 V/mm). The ΔG′ at an applied electric field strength of 800 V/mm reaches values as high as 78 000, 456 000, 1 254000, 283 000, and 128 000 at graphene concentrations of 0, 0.01, 0.1, 0.5, and 1 vol%, respectively. The ΔG′/G′o values of the graphene/gelatin hydrogel composites are also tabulated in . The increase of graphene concentration leads to the increase of G′o since the nanoplatelets act as a reinforcement filler shows the storage modulus sensitivity characteristics of several electroactive polymers and dielectric elastomers. The ΔG′/G′o comparison of these materials can be made between The polyesterurethane (LPR) exhibits the highest sensitivity under the dielectric elastomer type, in which the ΔG′/G′o is 2.08 at 2000 V/mm. In our work, the 0.1 vol% graphene/gelatin hydrogel composite storage modulus sensitivity is 3.52 of E = 800 V/mm, clearly a superior response relative other materials. Furthermore, both ΔG′ and ΔG′/G′o decreased with graphene concentration greater than 0.1 vol%. The poorly dispersed graphene leads to the phase separation between the gelatin hydrogel and the graphene agglomeration, as previously observed in the SEM and topology surface images in c. Although ΔG′/G′o values of 0.5 and 1 vol% graphene composites were reduced relative to the 0.01 and 0.1 vol% graphene, they still were greater than that of the pure gelatin hydrogel, dielectric elastomers, and other electroactive materials.The effect of temperature on the pure gelatin and the graphene/gelatin hydrogel composites are shown in , at the frequency of 100 rad/s and 800 V/mm. compares G′800v/mm and ΔG′ vs. temperature of the pure gelatin hydrogel and 0.1 vol% graphene/gelatin hydrogel composite consisting of three regimes. In the first regime, G′800v/mm and ΔG′ decrease with increasing temperature from 30 °C to 40 °C due to the conformational change from the denatured helix gelatin to random coil molecules The deflection response (d) and dielectrophoresis forces (Fd) of the pure gelatin and hydrogel composites were investigated under an electric field strength of 600 V/mm. The samples were attached between two copper electrodes (one anode and another neutral) in a PDMS chamber as shown in . Under the influence of electric field strength, the samples deflected toward the anode side as shown in a–c, indicating the attractive force that was generated from the polarized carbonyl groups in the gelatin molecule to the anode side; the polarized carboxyl groups produced the net negative charges in the gelatin structure. The pure gelatin, 0.1 vol%, and 1 vol% graphene/gelatin hydrogel started to deflect at the critical electric field strengths of 100 V/mm, 50 V/mm, and 150 V/mm, respectively. The 0.1 vol% graphene/gelatin hydrogel composite also exhibited the largest deflection distance than pure gelatin and 1 vol% graphene/gelatin hydrogel composite at 600 V/mm because the greater polarization was generated through the graphene. Conversely, the 1 vol% graphene/gelatin hydrogel composite exibited the lowest deflection distance among others as excessively high amount of graphene nanosheet obstructed the polarization The d and Fd of the pure gelatin and the graphene/gelatin hydrogel composites with applied electric field strength are exhibited in a–b. Under higher applied electric field, larger dipole moments are created, inducing greater d and Fd from these materials. The d of the pure gelatin, 0.1 vol%, and 1.0 vol% graphene/gelatin hydrogel composites are 13.5, 14.7, and 13.1 mm, and Fd of the pure gelatin, 0.1 vol%, and 1.0 vol% graphene/gelatin hydrogel composites are 0.032, 0.082, and 0.029 N, respectively. The 0.1 vol% MWNT/gelatin hydrogel composite show the highest d and Fd values due to the highest amount of polarized carboxyl groups through the suitable graphene content, consistent with the result of the degree of generated attractive force in The 0.1 vol% graphene/gelatin hydrogel composite in the current study provides the largest d and Fd at 14.7 mm and 0.082 N, the latter is much higher than materials in other studies.In our study, the electromechanical properties of the pure gelatin and graphene/gelatin hydrogel composites were investigated under applied electric field strength under the effects of surface area, graphene concentration, and temperature. The highest surface area of graphene blended in gelatin induced the highest storage modulus response (ΔG′) and storage modulus sensitivity (ΔG′/Go) due to the strongest interfacial force between the nano-particles and the matrix, leading to the enhanced polarization on the carboxyl groups in the gelatin molecules with the presence of graphenes. The storage modulus response ΔG′ increased significantly with increasing graphene concentration from 0 to 0.1 vol% under applied electric field strengths of 0–800 V/mm. The maximum ΔG′ and ΔG′/Go were 1.25 × 106 Pa and 3.52, respectively, for the 0.1 vol% graphene/gelatin hydrogel composite. For the influence of temperature, both G′ and ΔG′ showed three behavior regimes in the temperature range of 30–90 °C. Lastly, the deflection distance (d) and the dielectrophoresis force (Fd) of the pure gelatin, 0.1 vol%, and 1 vol% graphene/gelatin hydrogel composites increased monotonically with increasing electric field strength. The 0.1 vol% graphene/gelatin hydrogel composite delivered the greatest d and Fd suggesting that it is the most suitable candidate for actuator applications.Characterization Of Non-Metallic Waste Material Reinforced Polymer CompositesNon-metallic waste has been a source of pollution everywhere. In this paper Neem wood particles and waste tyre rubber particles is taken as non-metallic waste. These particles (size 200 micron) were used as reinforcements for fabricating composites with thermosetting and thermoplastic polymer matrix. Epoxy resin was thermoset matrix and Polypropylene was thermoplastic matrix. Tensile and flexure strengths were evaluated and compared with both type of matrices. Neem wood particles reinforced epoxy composites were observed better than tyre particles reinforced epoxy composites in tensile modulus. Tensile strengths were reduced in both Neem and Tyre epoxy composites. Modulus of elasticity of Polypropylene reinforced with Neem and tyre particles composites were improved 400 times and tensile strength were improved 230 times more than Propylene. Water absorption was increasing with the filler content in both PP and resin based composites. But it was 0.5% by weight.138–121 Ma asthenospheric magmatism prior to continental break-up in the North Atlantic and geodynamic implicationsAlong the Galicia and Gorringe banks and in the Iberia Abyssal Plain of the North Atlantic, unroofed sub-continental mantle fills the gap between ‘true’ oceanic crust and the continental crust margin. These lithospheric peridotites are intruded by gabbros and dolerites, and locally covered by basalts. Primary magmatic zircons extracted from gabbros and meta-gabbros of the two banks were dated by the U–Pb chronometer, and initial hafnium isotope signatures (ϵHfi) were determined on the same grains. For Mt. Gettysburg at Gorringe, gabbro emplacement ages of 137.5±0.5 (2σ) Ma and 135.7±0.8 Ma are obtained, and corresponding ϵHfi lie at +20.5±0.3 (2σ) and +19.5±0.4, substantiating magma formation from severely LILE-depleted mantle domains. Gabbro zircons from Mt. Ormonde at Gorringe yield a much younger age of 77.1±0.4 Ma and the Hf isotopes document an intermediately LILE-depleted mantle source having a ϵHfi of +7.6±0.4. Given its age and Hf signature, emplacement of this rock can be ascribed to the alkaline magmatic event that also affected the Iberian Continent in Upper Cretaceous time. Concerning the Galicia section, zircons from a meta-gabbro yield an emplacement age of 121.7±0.4 Ma and a ϵHfi of +14.0±0.2, and a ϵHfi of +14.6±0.2 is obtained for zircons from a previously dated meta-gabbro of identical age. These results indicate magma extraction from mantle reservoirs that are slightly less LILE-depleted than those sampled by the about 20 Myr older Gorringe gabbros. The data demonstrate that magmatism occurring prior to complete separation of Europe from America was essentially of asthenospheric origin. Both the 138–135 Ma ages for the Gorringe gabbros and 122 Ma ages for the Galicia gabbros are at least 5 Myr older than the oldest sediments on Gorringe, and the break-up unconformity at the Galicia Bank, respectively. Magma source signatures of the syn-rift gabbros are in agreement with values expected for differently depleted Cretaceous MORB-type mantle reservoirs, and the age-difference for magmatism between the Gorringe and Galicia banks suggests a rate of 4.4±0.3 cm/yr for northward progression of continental rifting. Based on the new results, a structural model for Iberia–America rifting is discussed putting forward the idea that magma emplacement produces a level of weakness and decollement between the rifting crust and its underlying lithospheric mantle.In contrast to the formation of oceanic lithosphere along active ridges, basaltic magmatism affecting the continental lithosphere during rifting processes is much less documented, in particular for cases such as the Iberia margin, where rift-related volcanism is absent on the Continent. Sampling by the Nautile and Cyana submersibles, ODP-drilling, and dredging has allowed to recover a large variety of rocks along the Iberian passive margin (), revealing that the continental crust lies adjacent to a belt of largely serpentinized peridotites, locally intruded by gabbroic rocks or covered by basalts Geochemical results and Nd isotope signatures for a variety of intrusives in the peridotites of the Galicia margin and Iberian Abyssal plain suggest the involvement of differently LILE-depleted magma sources Peridotite ridges at the Ocean floor occur along about 700 km off the Iberia margin () reaching from the Galicia margin to the Gorringe Bank in the south (e.g., . The Mt. Gettysburg peridotites of the Gorringe Bank are intruded by an about 0.5 km thick and 50 km long gabbro body. Peridotites are cross-cut by tholeiitic basalts that also cap the peridotites, including lava flows and pillows (At Mt. Ormonde, which is also part of the Gorringe Bank (In addition to these gabbros from Mt. Gettysburg, we analyzed a ferrogabbro to ferrodiorite sample from Mt. Ormonde (CY15-03, ), collected at about 350 m water depth, among blocks lying immediately above the gabbroic basement sequence (e.g., The Iberia Abyssal Plain section was investigated during the ODP Legs 149 and 173 ) is documented by the N–S trending Anomaly J The Galicia Bank peridotites form a ridge at the toe of the Continent margin (), cropping out along an about 1 km thick section. The ultramafic rocks are intruded by gabbros and dolerites, and in some places they are covered by an upper tectonic unit, which consists of rocks metamorphosed during low-temperature shearing, related to syn-rift detachment of the continental crust from the lithospheric mantle (see cross-sections of ). In other places, peridotites and gabbros are covered by breccias, and/or post-rift sediments and basalts. The metamorphic unit on top of peridotite–gabbro complex is composed of chlorite schists, derived from a meta-gabbro, for which a zircon U–Pb age of 122.1±0.3 Ma was obtained for protolith emplacement into the host peridotites (sample Gal-10-09, ). An additional sample from this metamorphic layer, collected at a water depth of 3612 m (GAL-32-07, Two of the Gorringe samples (GOR-07-01 and -05) are coarse cumulate olivine–plagioclase–clinopyroxene gabbros carrying minor secondary minerals such as tremolite, chlorite and talc. Sample GOR-07-02 is a leucogabbro containing Fe-oxide, brown amphibole and minor biotite that developed exclusively around the oxides. The fourth sample (GAL-07-04) is a poikilitic troctolite with cumulus plagioclase and olivine. Secondary phases are brown amphibole, chlorite, talc and minor biotite. Crystallization at 0.6 GPa is inferred from low Na and Al contents of clinopyroxenes Gabbros of the Gorringe Bank show a wide range of compositions (0.2–4% TiO2, 11–5% MgO, Mg# of 86–49), and they have slightly LREE-enriched patterns at 2–30 times chondritic abundance () and moderate europium anomalies range from positive to negative. These patterns are interpreted to reflect increasing differentiation (decreasing Mg#) produced by crystal fractionation in a closed system, i.e., within the gabbro layer ) and the younger, strongly silica under-saturated alkaline lavas cross-cutting Mt. Ormonde Gabbros recovered at ODP Leg 149 sites 899 and 900 () are strongly sheared and metamorphosed showing a predominant fine-grained granoblastic texture. Locally preserved primary mineralogy includes coarse clinopyroxene, plagioclase and rare ilmenite. Al-bearing clinopyroxenes and metamorphic spinel crystals inside plagioclase crystallized at pressures close to 0.8 GPa Gabbros are coarse-grained, mainly composed of clinopyroxene and interstitial plagioclase with rare orthopyroxene and olivine. A few gabbros contain Al-rich diopside, comparable to those formed under pressures reaching 0.8 GPa (24 km depth) in the Iberia Abyssal Plain The meta-ferrogabbro or meta-diorite sample (chlorite schist) was taken at about 1 km from the earlier dated sample (Gal-10–9 According to micro-paleontology, the oldest sediments on the gabbros and peridotites are of Barremian age (124 and 119 Ma; Leg ODP 103; K–Ar dates for gabbros of the Gorringe Bank yield a mean age of 135±6 (2σ) Ma for kaersutitic hornblendes, 105±6 Ma for undeformed plagioclase, and 82±6 Ma for deformed plagioclase Late alkaline magmatism in Mt. Ormonde of the Gorringe Bank () produced lithologies including olivine-nephelinites, alkaline lamprophyres and phonolites Our own attempts to date minerals from chlorite schists, i.e., metamorphosed ferrogabbros or diorites drilled at site 899 (ODP leg 149) have failed due to the very high degree of alteration and metamorphic overprint affecting even the commonly very robust zircons and titanites. A single 40Ar–39Ar biotite date of about 136 Ma is interpreted as the time of shearing Zircon was extracted from 2 to 5 kg gabbro samples by classical methods including the Frantz isodynamic separator and heavy liquids. Prior to grain-by-grain hand-picking under the binocular microscope, all zircon grains were mechanically abraded Hf was separated during the same chemical procedure as U and Pb, being present in the 3 N HCl elution volume preceding elution of Pb and U. Additional purification was performed after Zircons of both gabbros from Mt. Gettysburg are perfectly euhedral, yellow, transparent grains of relatively large size (100–300 μm) such as illustrated in the photomicrographs of . Six fractions from the GOR-07-02 gabbro yield concordant dates defining a mean age of 137.5±0.5 (2σ) Ma for high-temperature crystallization of the basaltic magma within the peridotites (). In the same way, six zircon fractions from the other gabbro sample (GOR-07-05) gave a mean age of 135.7±0.8 for magma solidification in the peridotites (). Although both zircon populations are of excellent crystallographic quality, they contain surprisingly large amounts of initial common Pb (low 206Pb/204Pb, ), for which corrections were performed following the model for Pb evolution of asthenospheric mantle (). The analytical errors are dominated by uncertainties on the composition of initial Pb in the zircons. For each error calculation, variations of mantle Pb over 100 Myr were propagated. Such high common Pb was already observed for the earlier dated gabbro zircons from the Galicia margin ). Note that Hf isotope ratios measured today directly reflect initial values because correction for in situ decay of 176Lu is negligible (very low Lu/Hf in zircon) and the differences between today and Cretaceous signatures are exclusively due to the increasingly divergent evolution of the MORB vs. the CHUR reservoir.Zircons from the Mt. Ormonde ferrodiorite (CY15-03) are large euhedral and transparent crystals of equal good quality as those from the Mt. Gettysburg gabbros (). Seven size-fractions yield concordant and slightly discordant data showing a trend to slightly higher 207Pb/235U ages (). Initial common Pb is on average lower than in the other two gabbro zircon populations (). If a mean value is calculated from all fractions, an age of 78.0±1.0 Ma is obtained, and if the concordant fractions alone are used, an age of 77.1±0.4 is defined. The slightly discordant dates can be explained either by a change of initial Pb composition in the magma during zircon crystallization or by the incorporation of very small amounts of radiogenic Pb. Although we cannot distinguish between these two possibilities (no old cores visible in the zircons), the incorporation of old relic zircon components from the magma during ascent through the ridge cannot be ruled out. One hafnium isotope analysis on the dated CY15-03 zircon grains yields a value of +7.6±0.4 for ϵHf77 Ma with a duplicate analysis giving an identical number of +7.4±0.4 (Zircons from the chlorite schist (GAL-32-07) are euhedral, transparent, and colorless grains, carrying opaque inclusions () as also observed in the earlier dated meta-gabbro ). Pre-metamorphically, these rocks were probably ferrogabbros or diorites, the most likely lithology to produce abundant zircons of large size, and LREE-enriched whole-rock patterns. Transformation to a chlorite–albite rock occurred during late low-temperature deformation (e.g., The zircon ages of 137.5±0.5 and 135.7±0.4 Ma determined for the Gorringe gabbros date high-temperature crystallization of the magma. They therefore answer the question on the exact emplacement age and geodynamic significance of the earlier low-temperature K–Ar and 40Ar–39Ar amphibole ages ranging between 143 and 135 Ma compares ϵHfi and U–Pb ages of the gabbro zircons with the evolution of both a pristine (CHUR) and increasingly LILE-depleted (DM) mantle, with the latter reflecting the model curve for average N-MORB sources. For Mt. Gettysburg gabbro zircons, ϵHfi of +20.5±0.3 and +19.5±0.4 lie significantly above the DM reference curve indicating magma extraction from mantle domains that are significantly more depleted than N-MORB sources. The small difference of initial isotope signatures among the two gabbros most likely reflects original variations in degree of mantle source depletion. Our Hf data corroborate the view that depletion of the upper mantle is substantially more complex than suggested by the smoothness of the DM model curve.The new U–Pb zircon age of 77.1±0.4 for the CY-15-03 gabbro sample of Mt. Ormonde shows that this rock belongs to the series of younger intrusions, however, it is more than 10 Myr older than suggested by earlier 40Ar–39Ar dating on biotite, obtained from other rocks of the alkaline intrusions ), which agrees with similarly depleted mantle sources traced for other members of the alkaline suite by Sm–Nd systematics (ϵNdi between +6.9 and +4.3 For the Galicia margin meta-gabbros the new age of 121.7±0.4 Ma corroborates together with the earlier U–Pb zircon age of 121.4±0.3 Ma that emplacement of mantle-derived melts into the continental lithosphere of the rift occurred before both continental break-up and tectonic unroofing of gabbros. Their ϵHfi of +14.6±0.2 and +14.0±0.2 lie on or very slightly below the model curve (DM) for LILE-depleted mantle (Initial Hf isotope signatures of the Gorringe and Galicia gabbro zircons indicate that magmas were generated from severely LILE-depleted mantle domains, i.e., the convecting asthenospheric mantle at that time. No melt contribution from other mantle reservoirs or crust can be identified. It therefore seems that magmatism during continental rifting reflects melting of the same type of mantle sources as subsequently melted to generate the North Atlantic oceanic lithosphere. Asthenospheric mantle sources are also observed for magmas drilled in the Iberia Abyssal Plain at Leg 149 () yielding ϵNdis up to +10.3 for gabbros Both 138–121 Ma magmatism in the Galicia–Gorringe banks, and contemporaneous basaltic volcanism in the Newfoundland and Tore–Madeira ridges ), and assuming that crystallization of the syn-rift gabbros represents the same stage in rift evolution, an average rate of 4.4±0.4 cm/yr can be deduced for migration of magmatism and hence, northward propagation of continental rifting in Early Cretaceous time.The asthenospheric origin of syn-rift basaltic magmatism can help to constrain models for non-volcanic rifting and passive margin formation (). According to regional plate kinematics, extensional tectonics would have occurred in E–W direction along the W-Iberian margin (e.g., ). Under these conditions the stretched crustal segment may be located either above the stretched mantle zone (). Moreover, differential motion between crust and mantle can help to explain both peridotite–gabbro deformation under decreasing P–T conditions, and their final tectonic exhumation at the Ocean–Continent boundary. In other words, the difference in rheological behavior of crust devoid of magma, and the lithospheric mantle considerably weakened by the presence of magmas, is probably a key to understand rifting processes. We therefore consider that the shear zone, responsible for final unroofing at the toe of the passive margin probably lies near the crust–mantle transition, where magmas are frozen, rather than within the uppermost mantle such as proposed earlier A study of mechanical alloying processes using reactive milling and discrete element modelingThe milling progress of mechanical alloying in SPEX shaker mills was investigated using different ball sizes and ball to powder mass ratios (charge ratios). Reactive materials were used, for which an exothermic reaction is mechanically triggered after a certain period of milling. The milling progress was determined experimentally from the temperature trace of the milling vial exhibiting a peak at the time of such a reaction. An expression for the milling dose was introduced to describe the effect of different milling parameters on the milling progress. In the first approximation, the milling dose leading to the mechanically triggered reaction remained constant over a range of charge ratios and could, therefore, be used to gauge the milling progress. The milling progress was described theoretically using the discrete element method. The theoretical milling dose that correlates well with its experimental analog was found to depend on the head-on impact energy dissipation rate. The presented approach is suitable for scale-up and optimization of mechanical alloying of various materials.Mechanical alloying is a rapidly developing technology capable of producing a wide range of dispersion strengthened, energetic, nanocrystalline, and other advanced alloys Because of the large number of process parameters, it is reasonable to expect that a successful process description can be obtained using a numerical technique. A number of mathematical descriptions of mechanical alloying have been proposed in the literature An alternative approach to assess the milling progress has been initially suggested by Schaffer and McCormick It has been suggested that the mechanically activated reaction proceeds spontaneously if the adiabatic reaction temperature of the components exceeds 1800 K Parallel to the experimental determination of milling progress, a numerical model will be developed and the computational results will be analyzed to establish a correlation with the experimental data. The main objective of this study is to develop a methodology enabling direct and efficient comparisons of the experimental and computational descriptions of mechanical alloying progress. In the future, such a methodology can be used to optimize and scale up production of advanced mechanical alloys for a wide range of practical applications.The high-energy ball mill used in the experimental study was a SPEX 8000 series shaker mill. The SPEX mill is a vibratory mill; its vial is agitated at high frequency in a complex cycle that involves motion in three orthogonal directions The reciprocating velocity of the vial in the SPEX mill is directly proportional to the motor rotational speed. Under various loading conditions, the rotational speed of the actuator input shaft was measured with a stroboscope. The nominal rotational speed was 1054 rpm, yielding an oscillation frequency of 17.6 Hz.A hardened steel vial was used with hardened steel balls. No process control agent was used in this work and the materials were milled under argon. The measured diameters of the balls used were 2.36, 3.16, 4.76, and 9.52 mm (nominally 3/32, 1/8, 3/16, and 3/8 in., respectively). The ball-to-powder mass ratio (charge ratio, CR) was set to vary between 2.5, 5, and 10.Thermite mixtures known to have extremely high adiabatic reaction temperatures were used in these experiments. Specifically, Al–Fe2O3 and Al–MoO3 thermites with adiabatic reaction temperatures of 3135 and 3253 K, respectively, were used A negative temperature coefficient thermistor was mounted on the milling vial and connected to a personal computer-based data logger to monitor the temperature. The temperature acquisition rate varied depending on the milling time scale, typically the temperature was logged every 10th of a second to half a minute. The thermistor circuit was calibrated between two temperatures corresponding to 0 and 100 °C. However, the exact temperature is not significant; rather the time of initiation is more important and was always accurate within 1% for any sampling rate.Examples of the measured milling temperatures are shown in . The process consists of the activation period with a gradual temperature increase and stabilized temperature region. During this period, fine mixing and particle size reduction occurs. Ignition is mechanically triggered at a critical state by a ball–ball or ball–vial collision. The reaction occurs with a large heat release where heat is transferred to the vial and balls, producing an abrupt increase in the vial temperature. After the reaction, the vial temperature slowly decreases as a function of the ambient conditions. In , each plot represents a different charge ratio, which changes as a function of the number of balls because the powder mass and ball diameter are constant. As the charge ratio increases between 2.5, 5, and 10, the initiation time decreases to 38.6, 24.1, and 9.3 min, respectively. Hence, a shorter milling time is required to obtain the same degree of refinement at which the reaction is triggered.The processes of mechanical alloying are greatly influenced by the impact characteristics of the grinding media such as friction and restitution coefficient. The impact velocity, thickness and strength of the powder layer coating the balls, and the ball size contribute to the variation in restitution coefficient and yield an average restitution coefficient of 0.7 for coated balls. The relative error among the trials varied between 1% and 8% except for the 3.16 mm coated balls where the error was 20%. This poor reproducibility is likely due to a less reproducible coating thickness, which reflects the condition in the milling vial. The collisions involving the coated balls were consistently less elastic compared to the uncoated balls. Furthermore, the restitution coefficient was less influenced by the ball diameter for the coated trials.In similar investigations with larger balls and lower velocities, the restitution coefficient was found to vary in the range of 0.38–0.8 depending on the powder thickness and demonstrate a smaller average coefficient of restitution of 0.385 for larger ball diameters. The lines in show the trends used to describe the restitution coefficient in the numerical simulations, as discussed in more detail below.Discrete element method (DEM) modeling was employed to study the milling progress of high-energy ball milling. In this numerical scheme, the motions of individual balls are traced and the interactions of the balls are monitored contact by contact. The term “discrete element”, in an approach originally proposed by Cundall In this work, a partially latching spring model developed by Walton and Braun where E is Young’s modulus and ri is the ball radius. To ensure a sufficiently large normal stiffness K1, the maximum ball deformation is limited to 1%. A stiffer linear spring with spring constant, K2, is used during the unloading (restoration) stage to account for a finite plastic deformation. K2 can be obtained from the coefficient of restitution, e. It is assumed to be independent of the impact velocity for the elastic–plastic case considered here, and is defined byThe coefficient of restitution is assumed to vary between 0.5 and 0.8 as a function of the thickness of the powder layer expected to coat the ball surfaces. This thickness is proportional to the ratio of total surface area of the balls to the powder mass. The coefficient of restitution variation used in the model is illustrated in for the charge ratios of 2.5, 5, and 10. The appropriate choice of the restitution coefficient accounts for the presence of the milled powder, thus bypassing the problem of computationally expensive modeling of individual powder particles (see The numerical integration scheme employed in this model requires a sufficiently small time-step for contact force modeling, which is related to the normal stiffness, K1, by the equation where mi is the mass of one ball and n is the desired number of time steps for one contact. Typically, the value of n is selected from 40 to 50 to ensure the accuracy of trajectories and energy losses At the beginning of the simulation, balls are randomly positioned inside the milling vial and assigned small random velocities; however, the net momentum of the system is initially zero. For each time step, forces between balls are calculated for all contacting balls using the interaction force model. The new translational and rotational accelerations of the balls are calculated by Newton’s equation of motion. The new velocity and position of the balls are obtained by explicit integration of Newton’s equation via the time-centered, finite-difference method In order to theoretically study the milling progress, the energy transferred to the powder must be numerically predicted. This energy lost in all collisions during the time interval ΔtE due to the powder being deformed is described in terms of energy dissipation rate, Ed, by the following equation:where E1, and E2 describe the energies of a binary impacting system before and after collision, respectively; k is the collision index, and Nc is the total number of collisions for the time interval ΔtE. A time interval of 0.2 s was selected to compute the energy dissipation rate. In a computational experiment, the energy dissipation rate was continuously calculated every 0.2 s until its temporal changes became insignificant. Thus, the simulation time is judged by the convergence of the energy dissipation rate and is typically between 4 and 8 s. shows the energy dissipation rate versus time for ball diameters of 2.36 and 9.52 mm. For both diameters, Ed spikes at the beginning of the calculation and after approximately 0.5–1 s it begins to stabilize; it fluctuates around its average value for the remainder of the simulation. The fluctuation in Ed increases when the number of balls is reduced. To analyze the results, the Ed parameter assigned to each run is computed to be the average of all points in the stable region. In addition to quantifying the total rate of energy dissipation, the rates of energy dissipation due to different types of collisions were tracked. Specifically, collisions were classified as a function of the impact angle.The complete set of input parameters listed in corresponds to empirical measurables including: vial size, mill rotational speed, vibration frequency and amplitude, ball diameter, total mass of milling balls, Young’s modulus for steel, friction coefficient, and restitution coefficient. The DEM output results include the energy dissipation rate, impact frequency, impact velocity, and impact angle. The model was run for the same parametric variations used in the experimental study. Specifically, the ball size and charge ratio (ball load) were systematically varied and the restitution coefficient was adjusted accordingly as discussed above. Because the simulation results are described in terms of energy, the following assumption was used to compare the computational and experimental results. The milling time is proportional to the inverse of the energy dissipation rate – the greater the energy dissipation rate, the shorter the milling time for the same degree of structural refinement of the milled powder.Experimentally observed times of spontaneous initiation during milling of Al–MoO3 and Al–Fe2O3 are shown in The DEM model produced several descriptive characteristics of the ball milling process and the collision statistics. The collision frequency was determined as a function of the number of balls and is shown in . It is shown for the varied total ball mass and ball diameter, and a fixed vibration frequency. The number of collisions ncoll is proportional to the number of balls nb: is generally maintained for different ball diameters. The total energy dissipation rate Ed was computed as a function of the ball mass and is shown in . As noted above, this energy dissipation rate is the average of the values for each 0.2 s iteration after the simulation results are stable. The trend in illustrates that Ed is independent of ball diameter and is proportional to ball mass mb: can be qualitatively understood for the milling process, in which the general pattern of the ball motion does not change significantly as a function of the ball size.In addition to the energy dissipation rate computed for each ball mass, the Ed was examined as a function of charge ratio. The inverse energy dissipation rate 1/Ed is considered as the numerical analog to the experimental milling time t. The DEM results for a 2 g sample mass corresponding to the experiments presented in . It is apparent that t is justifiably proportional to 1/Ed, since the empirical and numerical curves demonstrate lower milling times as the charge ratio increases. At the same time, the specific shapes of the calculated curves showing change of inverse of the total energy dissipation rate as a function of ball diameter cannot be unambiguously correlated with the experimental curves of milling time as a function of the ball diameter, as shown in . Therefore, further analysis is needed, e.g., considering whether the collisions with different impact angles have different influence on the achieved milling progress.By tracking the impact angle during the simulation, the collision energies have been categorized as either head-on: impact angles less than 30°, or glancing: impact angles greater than 30°. The energy dissipation rate was then accordingly computed for both head-on and glancing impacts. The sum of the head-on and glancing energy dissipation rates is the total energy dissipation rate. illustrates the inverse Ed versus the ball diameter for the total Ed, head-on Ed, and glancing Ed for both 2 and 5 g sample masses. It appears that the calculated curves for the inverse Ed for the head-on collisions approach the experimental curves of milling time as a function of the ball diameter much better than similar curves for the 1/Ed for the glancing collisions. The head-on collisions account for approximately 46% and 34% of the total collisions for the 2 and 5 g sample, respectively. This 12% difference indicates that a greater number of balls in a fixed volume result in a system with fewer head-on collisions. represent experimental milling times and their computational analog. The trends observed in experiment and numerical simulations are qualitatively similar. However, direct comparisons are difficult. The significance of changes in the milling times as a function of ball size for a given charge ratio needs to be assessed. Also, it is unclear which collision types and their respective rates of energy dissipation are critical in achieving structural refinement in the mechanically alloyed powder. The following discussion is aimed to address the above questions.Recently, it has been suggested that the progress of mechanical alloying or reactive milling can be described using the specific milling dose, defined as the work performed on the powder where mp is the powder mass. It was assumed that the value of Dm determines the state of the milled material achieved as a result of specific progress of mechanical alloying. Eq. does not consider the effect of the milling intensity on the state of milled material or degree of structural refinement achieved. This requires, as discussed above, that the milling intensity remains within the range necessary to achieve the desired refinement or structure. It is also assumed that ignition is triggered at a specific state of the milled material, that is, a specific degree of grain refinement. Therefore, the effect of milling intensity on the ignition triggering is also neglected. Based on the above assumptions, the critical milling dose Dm∗ can be introduced that characterizes the milling progress when the achieved degree of grain refinement is adequate for triggering the ignition mechanically. Eq. can be analyzed considering the trends observed in the DEM results relating the number of collisions to the number of balls, Eq. , and the energy per collision to ball mass, Eq. . Thus, the critical milling dose can be expressed aswhere the definition for the charge ratio CR

=

nb

·

mb/mp is used. For a certain specific degree of refinement, it is expected thatwhere tinit is the time when the reaction is initiated.This reasoning suggests that the milling time required to trigger initiation depends on the diameter of the milling balls exclusively via the charge ratio. A similar relation was suggested by Delogu et al. The product of the measured milling times leading to initiation and the charge ratios, CRtinit, is plotted as a function of the ball diameter in . The values of CRtinit for a series of experiments with different CR superimpose and do not change significantly. Thus, to first approximation, the present observations appear to support the tentative trend as expected from Eq. . Significant deviations from constant behavior predicted by Eq. , or even linearity exist, however, especially for smaller ball diameters where milling times are greater than expected. The observed relative deviations from linearity are different for Al–Fe2O3 powder with different sample mass and therefore a different total number of balls. These deviations are however identical for Al–Fe2O3 and Al–MoO3 with the same mass and therefore the same total number of balls. This indicates that variations in collision statistics are observed depending on the total number of balls.It is interesting to note that especially for small balls, a resonance condition appears to exist as the number of balls is varied. shows the milling dose for Al–Fe2O3 powder at a constant ball diameter, but varying number of balls. It is observed that at 10 g, all balls follow a collective motion with only small relative velocities, resulting in drastically weaker impacts and therefore longer milling times.The comparison of CRtinit between the 2 and 5 g sample mass for the Al–Fe2O3 proves that the CR in Eq. accurately scales the sample mass, however, the observed dependence on the ball diameter is not intuitive. The values of CRtinit are different for Al–MoO3 and Al–Fe2O3. It is reasonable to expect that different materials or different stoichiometry require mixing of the components on different length scales for initiation to occur. The proportionality among material systems could be further quantified in future work as a function of the activation energy of the exothermic reaction.The DEM results characterize the energy dissipated in the milling process, while the experimental results characterize the time or energy input per unit mass of powder. A theoretical milling dose function can be introduced aswhere mp is the mass of the powder load and Ed is the average rate of energy dissipated. Different types of collisions can be more or less significant regarding the energy dissipation rate as demonstrated in . The theoretical milling dose for head-on and total Ed as a function of the ball diameter is shown in . The milling dose is shown for the number of balls that correspond to the three charge ratios and the two powder loads of 2 and 5 g, as in the experiments illustrated in . The calculations based on the total Ed reveal a relatively constant milling dose for all ball diameters. The milling dose plot with the head-on energy dissipation rate, Eh, shows a different trend that correlates better with the experimental milling dose as shown in . Although not shown, the trend for the glancing Ed is the difference of the total Ed and head-on Eh, thus a maximum for Eh is a minimum for the glancing Ed, resulting in the constant total Ed trend. Based on the better correlation of the experimental milling dose and its computed analog derived from 1/Eh, the head-on collisions are suggested to be more significant in defining the milling progress. This finding agrees with reports stating that the sliding or glancing impacts do not contribute significantly to the deformation, coalescence, and fragmentation can now be directly compared. The theoretical milling dose has a divergence similar to the experimental milling dose with small diameter balls, but demonstrates less efficient milling for CR

= 10 rather than CR

= 2.5 as the experimental results. For CR

= 5 and 2 g milling sample for both systems, the trends are in good agreement with the DEM prediction. The validity of Eqs. is also well represented in the DEM results with a near constant milling dose for 4.76 mm balls among all charge ratios. This intersection point represents the most efficient milling condition for the examined charge ratios. In a scaled up operation, the convergence, similar to that observed in this work for 4.76 mm diameter balls, may occur at a different ball diameter, but numerical modeling is now expected to identify the convergent ball diameter and generate the additional parameters required for successful production. The theoretical milling dose, although expressed in terms of energy, behaves similarly to the experimental milling dose and demonstrates the model’s ability to capture the physical interactions during milling.This research established that the sharp temperature increase occurring in reactive milling of powders capable of highly exothermic reactions is a useful indicator of the milling progress. The milling progress for a range of parameters can be expressed by a relationship called the milling dose, a function that is proportional to the product of the milling time and the charge ratio. Experimentally, the milling dose was found to be constant for a specific material system over a range of charge ratios. The concept of the milling dose validated the experimental approach as a practical technique to determine the milling progress. The mechanical alloying process in a SPEX shaker mill was successfully simulated using a DEM numerical scheme with a soft sphere interaction model. The DEM model produces numerical values for the energy dissipation rate that are assumed to be inversely proportional to milling time. The head-on collision energy dissipation rate was selected for use in the theoretical milling dose because it demonstrated a better correlation to the experimental milling dose. As the model qualitatively predicts the trends observed in the experiments, it is suggested that the model accurately describes the progress of mechanical alloying. Although this model does not consider local phenomena and its implementations are restricted for the cases when the milling intensity is within the range required for synthesis of an alloy with specific structure, it confirms that an energy transfer approach is adequate to model the progress of mechanical alloying.Understanding mechanical property anisotropy in high strength niobium-microalloyed linepipe steelsThermo-mechanical processing of linepipe steels may result in anisotropy in mechanical properties, notably, yield strength and toughness, depending on the chemical composition and microstructure. These relationships are exceptionally important in spiral-welded pipe. Given the current interest in the development of high strength linepipe steels, we have examined in detail the mechanical property anisotropy phenomena using a combination of electron microscopy and crystallographic texture analysis in API L485 (X70) and API L555 (X80) steels. In this presentation, we describe the results of a study that has enhanced our understanding of the relationship between the microstructure and texture with anisotropy in mechanical properties.The microstructure of both X70 and X80 microalloyed linepipe steels as imaged via electron microscopy was similar and did not exhibit any significant anisotropy in the plane of the sheet. The microstructural constituents, polygonal ferrite and acicular ferrite (bainitic ferrite: ∼5–10% in X70 and ∼15–20% in X80) were also distributed uniformly throughout the volume of the specimens (0°, 45°, and 90° with respect to the rolling direction).The anisotropy in yield strength and Charpy impact toughness of X70-Nb and X80-Nb–Mo microalloyed linepipe steels was examined by using orientation distribution function analysis. The texture fibers of X70 and X80 microalloyed steels were similar but with significant differences in the intensity. Deformation textures mainly consisted of α-fiber (〈110〉//RD), γ-fiber (〈111〉//RD), and ε-fiber (〈110〉//TD). The major components of texture observed were {112}〈110〉, {332}〈113〉, {110}〈001〉, and {001}〈110〉 orientations. The observations suggested that the RD fiber centered at {112}〈110〉, {113}〈110〉, and {223}〈110〉 was responsible for the anisotropy in yield strength. The intensity of these texture components was higher in both X70 and X80 microalloyed steels in the rolling directions (RD) as compared to the 45° to the RD.Currently there is a strong demand to transport crude oil and gas by linepipe at higher operating pressures to increase the capacity. This requires steels that are characterized by high strength–high toughness combination. Increasing the strength of linepipe steels enables a significant reduction in wall thickness with consequent reduction in weight. Thus, a major goal within the steel industry is to develop high strength microalloyed linepipe steels. It is, however, important that the increase in the yield strength is not accompanied by a decrease in fracture toughness and formability because a decrease in toughness will encourage stress-induced cracking, and reduced formability will cause difficulties in forming (e.g. pipe-bowing). Thus, high strength in conjunction with high toughness and formability are the primary needs of the linepipe steel industry Alloy design and thermo-mechanical processing plays an important role in the evolution of the final microstructure and associated mechanical properties. Alloying additions such as Mn, Nb, V, Ti, Mo, Ni, Cr, and Cu are commonly employed in linepipe steels to obtain the desired microstructure and mechanical properties Controlled thermo-mechanical processing is considered as the primary route for the development of API grade linepipe steels because it provides the desirable and fine-grained microstructure. Furthermore, it allows high strength–toughness combination to be achieved via alloy design and/or accelerated cooling Thermo-mechanical processing of linepipe steels may result in anisotropy in mechanical properties, notably, yield strength and toughness, depending on the chemical composition, microstructure, and crystallographic texture. Steels tend to develop strong fiber textures during the controlled rolling, which involves processes such as deformation, recrystallization, and transformation. The relationship between microstructure, texture, and strength–toughness combination are exceptionally important in spiral-welded pipe and constitutes the objective of the study described here. Given the current interest in the development of high strength linepipe steels, we have examined in detail the mechanical property anisotropy phenomena using a combination of electron microscopy and crystallographic texture analysis in API L485 (X70) and API L555 (X80) steels. In this study, we underscore the importance of relationship between anisotropy in mechanical properties and texture, which at present, is far from complete. However, from the view point of complete analysis, microstructural characteristics are also briefly described given that similar microstructures have been previously presented on a number of occasions [The materials used in the study described here are two microalloyed linepipe steels that were processed to obtain yield strength of 490 MPa (70 ksi) (X70) and 560 MPa (80 ksi) (X80), respectively, at ArcelorMittal, East Chicago, USA. The nominal chemical composition of X70 and X80 linepipe steels are listed in . Both the steels are low in carbon content and primarily contain Nb in X70 and Nb–Mo in X80 as microalloying elements. The role of small amounts of titanium was to tie-up nitrogen and limit grain growth, while niobium facilitates grain refinement and provides strengthening via precipitation as NbC in the ferrite matrix and on dislocations. Other elements such as Cr and Cu were present as residuals. The X70 and X80 steels were continuously cast as slabs and thermo-mechanically processed to thickness of 12.7 mm and 11.7 mm, respectively. The processing details are not described due to proprietary reasons.Flat tensile specimens of 25 mm gage length were machined according to ASTM E8M specification. In order to investigate yield and tensile strength anisotropy, specimens were machined from the plates at inclinations of 0°, 30°, 45°, and 90° with respect to the plate rolling direction (RD). The tensile tests were performed using a servohydraulic MTS system. The tensile tests were performed at room temperature at a low strain rate of 5×10−4

s−1.The impact toughness was measured using Charpy v-notch specimens that were prepared according to ASTM standard E23. These were machined from plates at inclinations of 0°, 45°, and 90° with respect to the rolling direction. The Charpy tests were performed at RT (20 °C), 0 °C, −20 °C, −40 °C, −55 °C, and −70 °C. For statistical purpose and to determine the range of data, three samples were tested for each condition.To examine the microstructure, small coupons were cut from the microalloyed steels and mounted in Bakelite. Standard grinding and polishing techniques were employed to obtain mirror-finish surface. Next, the polished surface was chemically etched with a solution of 2% nital to reveal the microstructure for examination via light and scanning electron microscopy (SEM). Grain size distribution was measured using Image J analysis software.Transmission electron microscopy (TEM) was carried out to identify the constituent phases in the steels and examine the dislocation structure and strain-induced precipitation. Electron transparent foils were prepared by cutting thin wafers from the steel samples, and grinding them to ∼50 μm thickness. Three millimeter disks were punched from the wafers and twin-jet electropolished with a solution of 10% perchloric acid in ethanol as electrolyte. Carbon extraction replica approach was also used to study size, morphology, and distribution of precipitates. The surface of the polished specimens was etched with 2% nital and carbon was evaporated onto the etched surface. Finally, the surface was scored to ∼3 mm squares and the sample was first etched with 10% nital and then with 2% nital. Subsequently, the extracted replicas were rinsed with distilled water and placed on the copper grid and dried. Foils and carbon extraction replicas were examined with a Hitachi 7600 TEM operated at 120 kV.For the texture measurements, 20×20 mm2 samples are cut in a manner similar to the tensile test specimens and mechanically polished to mirror finish. The Mo Kα radiation was used in the X-ray diffraction, and pole figures were measured in the back reflection mode. Pole figures corresponding to (110), (200), (211), and (310) were obtained. The orientation distribution functions (ODFs) were calculated using a series expansion method (lmax=22) from the pole figure data and plotted in contour lines in the Euler space (Bunge’s notation).Representative engineering stress–strain plots for X70 Nb-microalloyed and X80 Nb–Mo microalloyed linepipe steels are presented in . These correspond to selected inclinations of 0° and 45° with respect to the rolling direction (RD).The yield (YS) and tensile strength (TS) of X80 Nb–Mo microalloyed linepipe steels derived from the tensile tests are summarized in , which also includes data for test directions other than 0° and 45° with respect to the rolling direction. Both X70 and X80 microalloyed steels met the defined yield strength (σy>485 MPa for X70 and σy>555 MPa for X80 steels) in different directions. However, in general, higher yield strength and ultimate tensile strength were obtained for transverse direction (90° to the RD) than along the longitudinal direction (0° to the RD). The yield strength varied from 594 MPa to 626 MPa, with a minimum value of 589 MPa at 45° to the RD. in X80. In X70 steel, 0° to the RD direction was the low strength direction.Charpy impact toughness data is presented in as a function of temperature and sample orientation. As expected, Charpy impact toughness decreases with decrease in test temperature. The impact toughness was greater along the longitudinal direction (0° to the RD) than along the transverse direction (90° to the RD). The impact toughness at 45° to the RD was intermediate between longitudinal (0° to the RD) and transverse directions (90° to the RD) at the test temperatures greater than −20 °C, whereas at temperatures less than −20 °C it was lower than both the longitudinal (0° to the RD) and transverse directions (90° to the RD). Similar behavior was observed for the low strength X70 Nb-microalloyed steel. Thus, there was anisotropy in impact energy in a manner similar to the yield strength, showing significant variation in toughness along different test directions and is discussed in Here, we will briefly describe the microstructural characteristics because similar microstructures have been presented and previously discussed by Misra’s group []. However, from the view point of complete analysis the salient features have been outlined.Light micrographs for X70 and X80 microalloyed steels corresponding to 0° and 45° to the RD are presented in . In both the X70 and X80 steels, there were regions where microstructure was nearly uniform but there were regions that consisted of combination of fine and coarse grains. Similar behavior and variability in the grain size range were observed in other directions. It is clear from the grain size distribution analysis of both the microalloyed steels that the majority of the grains were grains in the size range of 1–5 μm.Scanning electron micrographs illustrating the microstructure at a relatively higher magnification are presented in . At the magnifications available in SEM, it was possible to identify pearlite constituent in X70 and bainitic ferrite in X80 microalloyed linepipe steels, even though the volume fraction was small.In addition to light and scanning electron microscopy, transmission electron microscopy studies were conducted to analyze the differences in the microstructure, grain size, and precipitation. Representative micrographs illustrating polygonal ferrite, degenerated pearlite (pearlite with broken or small-sized cementite particles), bainitic ferrite (acicular ferrite), and strain-induced precipitation (precipitation on dislocations) are presented in . From extensive TEM analysis, it was apparent that the high strength X80 Nb–Mo microalloyed has a significantly higher volume fraction of bainitic ferrite (greater by ∼20%) as compared to the relatively lower strength X70 Nb-microalloyed steel, irrespective of the orientation of the sample with respect to the RD.A comment on degenerated pearlite merits attention since it has not been adequately emphasized previously. Degenerated pearlite is formed by the nucleation of cementite at ferrite/austenite interface followed by carbide-free ferrite layers enclosing the cementite particles in the transformation temperature range between conventional pearlite and upper bainite []. However, the cementite here is thin and discontinuous. Conventional pearlite deforms inhomogenously with strain localized in narrow slip bands, whereas the fine degenerated pearlite is expected to experience uniform strain distribution during deformation [The size and morphology of the precipitates in both X70 and X80 microalloyed linepipe steels were studied using carbon extraction replica and compared with the foil analysis data. Representative analysis of precipitate distribution in X70-Nb and X80-Nb–Mo microalloyed steels along 0° and 45° to the rolling direction (RD) is illustrated in . The particle size-distribution was analyzed using a number of micrographs of the type presented in . The coarse cuboidal-shaped precipitates (not presented in the histogram) were (Ti,Nb)C precipitates of size range ∼20–150 nm, while the near-uniform size precipitates were NbC of size range ∼2–20 nm. In a manner similar to the transmission electron microscopy study of electron transparent thin foils, rod-shaped molybdenum carbide precipitates could not be located in the extraction replica. This again suggests that Mo is present in solid solution in X80 steel or substitutes for Nb in the NbC precipitates.The five poles pertinent to the discussion of textures in steels are (200), (110), (211), (310), and (222). We have considered here (200) and (110) poles because they yield the highest X-ray intensity. Experimental data is also presented for (200) and (110) pole figures. From the examination of the pole figure data, we can describe the developed texture by relating the positions and intensities of specific orientations with those of the specimen geometry. Textures in hot rolled steels are generally represented by {hkl} 〈uvw〉, where {hkl} refers to the orientation of the grains such that the {hkl} planes are parallel to the rolling plane of the hot-rolled steel and the 〈uvw〉 directions are parallel to the rolling directions (RD).Steels tend to develop strong fiber textures and it is convenient to represent the textures by iso-intensity diagrams in ϕ1 sections and by fiber diagrams. Deformation textures consist of (i) α-fiber (ϕ1=0°, ϕ=0–90°), 〈110〉 directions parallel to the rolling direction (RD), stretching from {001}〈110〉 to {110}〈110〉; (ii) γ-fiber (ϕ1=0–90°, ϕ=55°) with {111} plane parallel to the rolling plane of the sheet steel, running from {111}〈110〉 to {111}〈112〉; and (iii) ε-fiber (ϕ1=90°, ϕ=0−90°), 〈110〉 directions parallel to the transverse direction (TD) of the steel. The ε-fiber runs from {001}〈110〉 to {110}〈001〉 with 〈110〉//TD The (200) poles of the main components of bcc transformation textures in X70 and X80 linepipe steels are illustrated in together with the ideal orientations. Ideal orientations are identified by symbols, while experimentally observed orientations are presented as iso-intensity contours. Among them, the {332}〈113〉 component of ε-fiber forms by transformation from the {110}〈112〉 orientation present in the deformed austenite and the {113}〈110〉 component of α-fiber is derived in a similar way from the fcc {112}〈111〉 orientation Other important ideal and experimentally observed orientations, which constitute part of the transformation texture of X70 and X80 linepipe steels are plotted in . They include {111}〈112〉, {554}〈225〉, {111}〈110〉, and {112}〈110〉.Similarly, the deformation texture can be represented in a very compact manner by presenting them in the (110) pole figure. In a manner similar to (200) pole figure, illustrates the ideal positions of the α, β, and γ fibers in the (110) pole figure. The α-fiber texture is common in hot rolled steels and is characterized by the 〈110〉 direction parallel to the rolling direction (RD) with the plane parallel to the sheet surface ranging from {100} to {311}. The γ-fiber texture refers to the preference of grains having {111} parallel to the sheet surface with no preferential 〈uvw〉 direction parallel to RD. The (211) and (310) pole figures are not presented here because they were considered less significant.To obtain a less ambiguous and more quantitative description of textures, orientation distribution function (ODF) was calculated from four different pole figures (200, 110, 211, 310) () by the series expansion method and is represented in the sections (ϕ=0°, 5°, …, 90°) through the Eulerian space. These four pole figures were used to obtain ODF (see below). illustrate the ϕ1 section of ODF in the X70 Nb-microalloyed steel and X80 Nb–Mo microalloyed steel, respectively. The different textures are denoted by different color symbols. The components of α-fiber (RD-fiber) include: {001}〈110〉, {113}〈110〉, {112}〈110〉, {223}〈110〉, {111}〈110〉, and {110}〈110〉. In the X70 Nb-microalloyed steel, the α-fiber exhibits a high intensity at 0° to the RD (a). The components of α-fiber of high intensity are {112}〈110〉 and {113}〈110〉, whereas at 45° to the RD, the {111}〈110〉 component have the highest intensity in the α-fiber. The relative intensity of each components of the fiber texture with regard to the angle to the rolling direction is discussed below. a also shows the presence of other high intensity ε- and γ-fibers. If we now compare the texture of 0° to the RD with 45° to the RD (b), we note that α-fiber has a weaker intensity in 45° to the RD. The differences in the intensity of γ-fiber in the two directions are not significant.The components of γ-fiber include: {111}〈110〉, {111}〈123〉, {111}〈112〉. All the components of the γ-fiber are a little strong in 45° to the RD in comparison to that in the rolling direction. However, the differences in the intensity are not large. Similarly, the ε-fiber components are {001}〈110〉, {111}〈112〉, {554}〈225〉, {332}〈113〉, and {110}〈001〉. The {001}〈110〉 component of the ε-fiber is similarly intense in both 45° to RD and 0° to RD. The {110}〈001〉 is absent in the RD direction but continues to exist in 45° to RD.In X80 Nb–Mo microalloyed steel, the texture fibers are similar to those observed in X70 (). But the intensity of different components of α-, γ-, and ε-fibers are higher in the X80 steel, in both 0° and 45° to the RD.Major ideal orientations of α, γ, ε fiber textures are illustrated in to help in identification and analysis of the texture results observed in hot-rolled X70 and X80 Nb-microalloyed steels. The specified texture fibers as well as the relevant Miller indices of main components of each texture fibers in the standard notation are illustrated. The ϕ2=45° Euler-space cross section is selected to display the experimental ODFs. Each texture is mapped in three-dimensional Euler space as defined by three orthogonal axes (ϕ1, ϕ, ϕ2). The two-dimensional ϕ2= 45° cross section ODF is chosen for simplicity and it is also technologically the most important section of the Euler space. The orientations along the α-fiber (RD-fiber) are developed during the hot rolling of steels, whereas the ε-fiber (TD-fiber) components are mostly observed in hot-rolled as well as in recrystallization.The hot-rolled textures of X70 Nb-microalloyed steel with 0° and 45° to the RD are shown in a and b, respectively, while for X80 are presented in . The maximum intensity for both the X70 with 0° to RD sample and 45° to the RD sample is 4.5 times random, and the texture is relatively weak. In comparison to X70, in X80 steel, the maximum intensity is 7.5 and 6 times random in 0° to the RD and 45° to the RD, respectively, implying the presence of stronger texture (). The {001}〈110〉 and {112}〈110〉 individual orientations are present along the α-fiber (RD-fiber). Similarly, the {001}〈110〉, {110}〈001〉, and {111}〈112〉 orientations are the main components located along the ε-fiber (TD-fiber).The fiber properties of these samples are displayed in more detail in a–c. The RD fiber of X70 steel corresponding to 0° to RD in the orientation space between the {113}〈110〉 and {223}〈110〉 components is stronger compared to 45° to RD (a). The {112}〈110〉 component of α-fiber is particularly important from the viewpoint of yield strength anisotropy. Similar findings apply to the RD fiber in the orientation space between the {331}〈110〉 and {110}〈110〉 components. Other components of the RD fibers, namely {111}〈110〉 and {001}〈110〉 have relatively higher intensity in 45° to RD.For the ε-fiber (TD) texture, {001}〈110〉, {111}〈112〉, {554}〈225〉, and {332}〈113〉 components have similar intensity in both 0° and 45° to the RD except that the {110}〈001〉 component is stronger in 45° to RD than that in 0° to the RD sample (The γ-fiber (ND) texture also exhibits a similar behavior in 0° and 45° to the RD (c). The different components of the γ-fiber are {111}〈110〉, {111}〈011〉, {111}〈123〉, and {111}〈112〉.Similarly, the details of the fiber properties of X80 steel with two rolling orientations are displayed in a–c. In general, the different components identified in X70 steel were also present in X80 steel. But the intensity of different major components of α-, γ-, and ε-fibers are stronger in X80 steel including {113}〈110〉 which is relevant from the viewpoint of yield strength.It may, however, be noted that {110}〈001〉 component of ε-fiber which has previously been suggested to be also responsible for yield strength anisotropy shows a behavior that is different from {112}〈110〉 with regard to the intensity, that is, {110}〈001〉 is stronger in 45° to the RD and weaker in 0° to the RD in both X70 and X80 steels. The trend is reverse to that of {112}〈110〉. There is a competition between {112}〈110〉 and {110}〈001〉 components. Given that the yield strength is higher in 0° to the RD than that in the 45° to the RD, implies that contribution of {112}〈110〉 is greater than the {110}〈001〉 component.In summary, the texture fibers of Nb and Nb–Mo microalloyed steels were similar but with significant differences in intensity. Deformation textures mainly consisted of α-fiber (〈110〉//RD), γ-fiber (〈111〉//RD), and ε-fiber (〈110〉//TD). The major components of texture observed were {112}〈110〉, {332}〈113〉, {110}〈001〉, and {001}〈110〉 orientations. The observations suggested that the RD fiber centered at {112}〈110〉, {113}〈110〉, {223}〈110〉 is responsible for the anisotropy in yield strength. The intensity of these texture components was higher in both 70 ksi and 80 ksi microalloyed steels in the rolling directions (RD) as compared to 45° to the RD (The grain size and microstructural differences for a particular steel along different directions to the plate rolling directions were insignificant, but there is a good agreement between the yield strength anisotropy and texture results such that the orientations responsible for the observed anisotropy are predominantly located along the α-fiber and include, {112}〈110〉, {113}〈110〉, {223}〈110〉, in particular. Moreover, the observed behavior was similar and consistent in both the steels, which again point toward the relationship between mechanical anisotropy and texture. It is in this regard the present study advances our current understanding of planar anisotropy of the mechanical properties and underscores the determining role of texture in contributing to the planar anisotropy.Thermo-mechanical processing of linepipe steels results in anisotropy in mechanical properties, notably, yield strength and toughness.The microstructure of both X70 and X80 microalloyed linepipe steels was similar and did not exhibit any significant anisotropy in the plane of the sheet. The microstructural constituents were polygonal ferrite and acicular ferrite (bainitic ferrite) (∼5–10% in X70 and ∼15–20% in X80) and were distributed uniformly throughout the volume of the specimens (0°, 45°, and 90° with respect to the rolling direction).The coarse cuboidal-shaped precipitates of size range ∼20–150 nm were identified as (Ti,Nb)C, whereas the uniformly distributed precipitates were NbC of size range ∼2–20 nm.The texture fibers of X70-Nb and X80-Nb–Mo microalloyed steels were similar but with significant differences in intensity. Deformation textures mainly consisted of α-fiber (〈110〉//RD), γ-fiber (〈111〉//RD), and ε-fiber (〈110〉//TD). The major components of texture observed were {112}〈110〉, {332}〈113〉, {110}〈001〉, and {001}〈110〉 orientations.The analysis of texture fibers point to the suggestion that the RD fiber centered at {112}〈110〉, {113}〈110〉, {223}〈110〉 is responsible for the anisotropy in yield strength. The intensity of these texture components was higher in both X70 and X80 microalloyed steels in the rolling directions (RD) as compared to the 45° to the RD.Exceptional stability of food foams using class II hydrophobin HFBIIThe foam stability of aerated solutions containing the Class II hydrophobin protein HFBII from Trichoderma reesei has been investigated and compared with that of other typical food emulsifiers and aerating agents. In simple solutions, we have found that 0.1 wt% HFBII forms exceptionally stable foams across a wide range of solution pH conditions. In aerated solutions comprising xanthan thickener, in order to slow the rate of creaming, we demonstrate that the foams stabilised by HFBII show no significant change in bubble size or air phase volume over a period of at least 4 months. Such foam stability is far in excess of any food-aerating agent of which we are currently aware. HFBII stabilises foams purely by adsorption to the air–water surface, forming a highly elastic surface and providing resistance to both coalescence and disproportionation, without influencing the aqueous phase viscosity.Liquid foams are thermodynamically unstable and, given time, will eventually coarsen and dissipate (). Liquid food foams generally fall into two categories: those that are created and consumed within a short space of time, so that long-term stability of the foam is not an important consideration (examples include milk shakes, cappuccino, and beer); or those where the rheology of the continuous phase is increased to such an extent that the foam becomes kinetically trapped and effectively stabilised over a substantial period. Examples of this approach include products where the bulk phase is gelled, such as mousse or aerated soft cheese, or partially crystallised, for example ice cream or whipped butter. The ability to produce stable liquid foam, without needing to rely on a gelled or solidified continuous phase, has long been a desire of food manufacturers, but has never been realisable in practice. If this problem could be overcome, and the range of product types that the manufacturer is able to aerate in a stable fashion is broadened, then considerable opportunity would exist to improve product functionality, create new textures, or reduce the calorific density per volume through aeration.Aerated foods are subject to destabilisation processes such as coalescence and disproportionation. The latter is a coarsening process (analogous to Ostwald ripening in emulsions) due to diffusion of gas from small bubbles to larger ones, driven by difference in Laplace pressure. In many systems, disproportionation is the most difficult instability mechanism to control (). Aside from elevating the continuous phase viscosity, as mentioned above, the most common method of slowing destabilisation processes in food foams is to modify the gas–liquid interface by adsorption of surface-active molecules, such as proteins (). It has been shown that elasticity of the surface is the most important surface property for retarding coarsening by disproportionation. proposed a criterion for the prevention of disproportionation through consideration of the surface dilatational elastic modulus, which, if great enough, can eliminate disproportionation. For a purely elastic surface, this occurs when the following condition is met:where, γ is the surface tension, ED the surface dilatational elastic modulus, and A the surface area.When measured on an experimental time scale where relaxation can take place, e.g. via diffusional exchange, then ED is actually a visco-elastic modulus (), i.e. the surface dilatational modulus. Air–water (a/w) surfaces with adsorbed protein, for example, have a significant viscous response to deformations that are on time scales relevant to disproportionation, i.e. they are not purely elastic in their behaviour. As a result, the condition to prevent disproportionation according to Eq. is never practically met in food products, since a surface-active ingredient that imparts sufficiently high surface dilatational elastic modulus to prevent disproportionation has not yet been identified. provide a theoretical model relating the bulk and surface rheological properties to the process of disproportionation, considering both viscous and elastic contributions. According to their analysis, in order to significantly influence bubble stability over long time scales, a surface elastic modulus of 100 mN m−1 or (preferably) greater is required. One of the more elastic of surface-active proteins currently used in food systems is β-lactoglobulin, a globular milk protein that denatures at a surface or interface (). The surface dilatational modulus of this protein has been measured to be of the order of about 30–40 mN m−1 () and the surface shear elasticity to be less than 1 mN m−1 (). It can immediately be understood, therefore, that the elastic contribution of β-lactoglobulin, and in fact all other currently used food proteins, falls well short of the level required to inhibit disproportionation based on the criteria set by . Experimentally, this is well known and has been readily demonstrated on several occasions: see, for example, . In each of these reports, adsorbed proteins at the a/w surface in simple solutions could not prevent disproportionation over time scales required for long-term stability in foods products. have further examined the role of the interfacial conditions required to stabilise emulsions. They determined that for typically observed interfacial tensions and dilatational modulus in emulsions, a thick non-desorbing (insoluble) interfacial layer (of the order of the emulsion droplet radius) was required to prevent disproportionation. Similar requirements would be required for stabilisation of bubble dispersions and foams. However, such a surface structure is not produced using common food proteins and, therefore, long-term stability of such foams is not observed.There has been an increasing amount of activity relating to stabilisation of foams. In the context of foods, in particular, a review of recent developments of foam stabilisation has been published by ) on the remarkable surface activity of hydrophobin proteins derived from the filamentous fungus Trichoderma reesei, and the influence these have on the stability of some small-scale bubble dispersions. Hydrophobins are a family of small proteins (7–15 kg mol−1) first identified in Schizophyllan commune () and subsequently isolated from a number of filamentous fungi (). Two classes of hydrophobin have been distinguished based on hydropathy profiles (), a measure of the hydrophobicity profile of protein (): Class I hydrophobins (e.g. SC3 from S. commune) form highly insoluble aggregates which can only be dissolved with strong acids (). Class II hydrophobins (such as the HFBI and HFBII hydrophobins from T. reesei) are more readily solubilised, and can be readily dissolved in aqueous solution. In our previous paper () we reported measured a/w surface shear elastic moduli for HFBI and HFBII hydrophobins, which were in the range 500–700 mN m−1. These values represent more than an order of magnitude increase over moduli of other commonly used food proteins. While the condition for elimination of disproportionation may not be strictly met by this degree of elasticity, since our data was a measure of shear as opposed to dilatational elasticity, it is probable that it can be sufficiently retarded to allow control of foam over useful product shelf-lives. Indeed, we then showed how the high surface elasticity of HFBII could stabilise single bubbles to disproportionation with atmospheric air for significant periods of time, when compared to both β-casein and β-lactoglobulin, and also that HFBII could form a stable bubble dispersion for at least 4 days at room temperature.These data highlight the potential of hydrophobins to form stable bubbles and foams by surface adsorption alone. The ability to stabilise foam through surface adsorption as opposed to stabilisation via the bulk phase could provide the real potential to formulate aerated products, which could be designed with the appropriate continuous phase around a stable air phase.In this current study we apply the use of hydrophobin to foams, in both model systems and an example food product, comparing them with some other typical food emulsifiers/aerating agents. We examine the extent to which foam stabilisation can be achieved and discuss the potential we see for hydrophobins as novel foam-stabilising ingredients, particularly in the context of food products.Class II hydrophobin (HFBII) was obtained from VTT Biotechnology (Espoo, Finland), having been prepared as previously described (). Briefly, the hydrophobin protein was made by fermentation of a T. reesei culture, extracted, and subsequently purified. In this case, the hydrophobin was provided by VTT Biotechnology in an ammonium acetate buffer solution. In order to remove much of this, the aqueous solution was freeze dried to remove water and buffer and then stored at 40 °C in a vacuum oven (Gallenkamp) for 18 h. Removal of most of the buffer in this way aided preparation of solutions at different pH, most notably at pH greater than ca. 7. The hydrophobin protein was then reconstituted in pure water to a known concentration (ca. 0.5 wt%) and stored frozen. β-Lactoglobulin (from Bovine Milk, ca. 90%), Tween 80, and sodium azide were purchased from Sigma-Aldrich. Citric acid (99.5%+) and sodium hydroxide (97.5%) were obtained from BDH and Fisher Chemicals, respectively. Sodium caseinate (Na Cas >90% protein content) was purchased from DMV International. Xanthan (cold water dispersible, Keltrol RD) was purchased from CP Kelco. Sucrose was obtained from Tate and Lyle, UK, skim milk powder from Dairy Crest, UK (ca. 35% protein content), and Hygel 8293 (hydrolysed milk protein, produced by enzymatic solubilisation, 80% minimum protein content) from Kerry Bio-sciences, UK. Green and Black's organic hot chocolate powder contained 28.5 wt% cocoa powder, 16.3 wt% dark chocolate, total protein 9.1 wt%, carbohydrate 63.5 wt%, and fat 9.3 wt%, and was produced by Green and Blacks Ltd., UK. Aqueous solutions were prepared using distilled water (Elga Water purifier, surface tension 72 mN m−1 at 20 °C). Apart from the HFBII, as discussed above, all ingredients were used as received without further purification.Mix preparation: Aqueous solutions containing protein or surfactant were made at the appropriate concentration in water or in water containing 0.4 wt% xanthan gum, as a thickening agent (also referred to as continuous phase stabiliser). A summary of all the formulations used is shown in . For the solutions to be made up in water without xanthan gum (Formulations 1a–8a), Na Cas, Hygel, β-lactoglobulin, and Tween 80 were mixed for approximately 30 min in water to ensure complete dispersal. For the case of HFBII, this was added as an aliquot of concentrated solution into water. The concentrated stock solution was sonicated for 20 s immediately prior to dilution in order to dissolve any weak macroscopic aggregates that can form through shearing solutions of hydrophobin, as discussed previously (). For solutions prepared in water with 0.4 wt% xanthan gum (Formulations 1b–8b), Na Cas, Hygel, and β-lactoglobulin powder were mixed with xanthan powder before dispersing in water. For solutions prepared with either Tween 80 or HFBII, these ingredients were added to the aqueous phase after xanthan gum had been fully dispersed in water. All solutions containing xanthan were mixed at room temperature for at least 1 h to ensure good dispersal and hydration of this polysaccharide. Na Cas, β-lactoglobulin, and Tween 80 were all made up in water, and no change in pH was made. HFBII solutions were prepared across a range of pH conditions, and the pH was controlled by addition of either citric acid or sodium hydroxide. All solutions had 0.05% sodium azide added as a preservative, post-aeration.Aeration: 75 mL of aqueous solution, with dissolved protein or surfactant, was aerated to ca.150 mL using an aerolatte (Radlett, UK) hand held electric mixer at room temperature. The device consists of a whisk rotor, which is a wire coil shaped in a horizontal circle with an outer diameter of 22 mm rotated about a vertical axis through its centre at a rotational speed of approximately 12,000 rpm in air. Formulations 1a–8a (without stabiliser) were mixed and aerated for 2 min in order to ensure that both the appropriate air phase volume was incorporated and thorough bubble break-up were achieved. The measured air phase volume fraction at time t=0 was within the range 0.5–0.6. Formulations 1b–8b (containing stabiliser) were mixed and aerated for 4 min. This time scale was longer than for the formulations with no thickener, since the addition of xanthan led to slower incorporation of the required volume of air using this aeration device. This process resulted in a foam of measured air phase volume fraction ca. 0.5 at time t=0. Subsequently, portions of the prepared foam were portioned out for subsequent stability tests, as described below. All foams were stored at 5 °C.Analysis of foam stability through measurements of bubble size and foam volume was determined via the following experimental methods:(i) Total air phase volume as a function of time: 100 mL of foam was poured into a measuring cylinder. Changes in the foam height Fh were measured as a function of time. We calculate the total air phase volume fraction φair in the measuring cylinder using where Vw is the total amount of aqueous phase in the foam. Once the foam has collapsed, Fh=Vw and φair=0. The value for Vw was noted for each sample, typically being ca. 50 mL.Formulations 1a–8a did not contain any thickening agent and, as a result, the bubbles rapidly creamed to the surface. This leads, within several minutes, to an upper phase rich in air bubbles (a high air phase volume part) and a lower phase depleted of air bubbles (a low air phase volume part). The calculation of total air phase volume using Eq. does not take into account such system heterogeneity. Hence, by φair we mean total air phase volume within the 100 mL measuring volume of the cylinder. Therefore, this allows comparison between mixes where the foam creams quickly (Formulations 1a–8a) and mixes where creaming is slowed down due to the presence of a thickener (Formulations 1b–8b).(ii) Air bubble size as a function of time measured using light scattering: 20 mL of foam was analysed using a Turbiscan (TLAb Expert, Fullbrook Systems Ltd., UK). This instrument measures transmitted (180° from the incident) and backscattered (45° from the incident) light from a cylindrical sample vial containing the foam. In simple aerated formulations where air bubbles are the principal scattering species, bubble size changes can be monitored through variations in the backscattered light through the central area of the sample vial. The backscattered level BS is related to the photon transport mean free path λ* through the foam viaλ* is dependent on the gas phase volume fraction φair and the bubble mean diameter d throughwhere Q is the scattering efficiency factor and g is an asymmetry factor. For the purposes of these studies, the bubble size was determined between the heights of 20 and 30 mm above the base of the sample vial. This region of the foam was chosen such that measurement of bubble size could be made for the longest period of time without the complication of foam collapse and significant creaming in this area of the foam. Hence, data were only taken to the time point where foam collapse or the serum level reached this region of the vial, or to the point where the air phase volume fraction in this region deviated significantly from 0.5.(iii) Air bubble size as a function of time observed using optical light microscopy: This method was used to visually compare the stability of foams produced using Formulations 1b and 6b over a period of up to 1 week at 20 °C. Foam was carefully placed into the well of a Coverwell Press-Seal imaging chamber (size 20 mm diameter ×2.5 mm depth, Sigma-Aldrich) and then a microscope glass slide was pressed and fixed to this. This sealed set-up allowed visual observation of the foam over several days without evaporation of the aqueous phase. A depth of 2.5 mm was found most appropriate since no significant distortion of air bubbles was observed to result when attaching the chamber to the glass slide. Furthermore, significant air bubble growth could occur without subsequent distortion of the air bubbles. Foams were visualised using a LeicaDMR microscope, using a ×10 magnification objective. The microscope was attached to a JVC KY-F75U3CCD camera and connected to a computer through a FireWire connection. Images were digitally captured using KY-Link software (Optivision, Leeds, UK).Continuous phase moduli for elasticity (G′), viscosity (G″), and apparent yield stress were measured for a 0.4 wt% aqueous solution of xanthan gum at 5 °C, using an AR-G2 rheometer (TA Instruments Ltd., Crawley, UK) with a cone and plate geometry, where the stainless-steel cone was 6 cm diameter with a 2° angle. G′ and G″ were measured across a frequency range of 0.1–100 Hz, subjecting the solution to an oscillatory amplitude of 5×10−3

rad. The apparent yield stress was determined using a stepped flow approach to measure viscosity as a function of shear stress and shear rate. To calculate the apparent yield stress, the shear-thinning regime of the data was fitted to a Hershel–Bulkley model.An aerated chocolate milk shake, stabilised using hydrophobin was prepared to the following overall formulation: 10 wt% skim milk powder (ca. 35 wt% protein content), 8 wt% chocolate powder, 0.4 wt% xanthan gum, 1 wt% sucrose, 0.1 wt% HFBII, and 80.5 wt% water. Two separate mixes (A and B) were prepared, which when blended gave the overall formulation. Mix A was 35 g of an aqueous solution of HFBII, where the concentration of hydrophobin was 7.2 mg mL−1. Mix B consisted of the remaining ingredients, which were blended together and mixed with water, totalling 100 g. This mix was then heated to 80 °C for 30 s, before cooling to 5 °C. Mix A was then aerated using an aerolatte to a volume of 120 mL. The foam was then gently mixed with Mix B, and the air phase volume fraction measured to be ca. 0.4. 100 mL of aerated chocolate milk shake was then poured into plastic bottles, 0.05 g sodium azide was added, and then stored at 5 °C. Bubble stability was assessed visually over a period of 3 weeks.Aqueous solutions aerated without the addition of a thickening agent rapidly separate into two distinct layers consisting of an upper foam-rich phase and a lower aqueous-rich phase. This is due to drainage of the liquid and creaming of the bubbles. For the solutions aerated in this work, initially the air phase volume was ca. 0.5, i.e. below the close-packed limit for spheres of equal size. However, as the bubbles quickly rise to the surface, the air phase volume in the upper part of the foam phase increases rapidly. Ultimately, this leads to close packing of air bubbles and, subsequently, a polyhedral foam. Therefore, these experiments are a measure of the stability of bubbles in a “dry” foam environment.Total air phase volume as a function of time is plotted in , for Formulations 1a–8a. The milk protein stabilised foams collapse rapidly, with complete loss of air within less than 24 h. The foam stabilised by Tween 80 shows greater air phase stability than the milk proteins since this surfactant is able to stabilise a polyhedral foam structure more. Nevertheless, each of these typical food emulsifiers/aerating agents forms foams in water with far shorter lifetime than those stabilised by HFBII. At each of the four solution pHs studied, HFBII forms a foam that is stable to any significant air phase loss (>10%) over a period of at least 5 days. Subsequent collapse and air phase loss is then relatively gradual, and some foam is present for at least two or more weeks. Clearly, HFBII can form highly stable foams in such conditions where a polyhedral foam structure will be formed and, furthermore, such stability is observed across a wide range of pH conditions.Addition of xanthan gum has a significant effect on the rate of creaming, due to the apparent yield stress, which this polysaccharide provides to the continuous phase. Initially, this effectively traps the bubbles in position since the yield stress opposes the buoyancy force. However, as the foam starts to destabilise, through the mechanisms of coalescence and disproportionation, the bubbles start to grow. Ultimately, the size of the bubbles will lead to a buoyancy force, which exceeds that of the yield stress, and creaming will occur. Such conditions have been described by . We chose a concentration of xanthan such that creaming would be largely prevented until significant bubble growth had occurred; therefore, the results in this section provide a clear indication of bubble stability at around or below the close-packed limit. In this regime, one would expect that disproportionation would be the dominant destabilising mechanism since relatively fewer bubble would be in very close contact. As bubbles grow, however, some creaming occurs, the effective volume fraction in the upper part of the measuring cylinder increases, and coalescence would start to become a more significant factor. Another reason for adding xanthan to slow the rate of creaming was that the dispersed nature of the air phase in such a foam can be viewed as being more representative of that in many aerated foods such as whipped cream, ice cream, and mousse.Total air phase volume as a function of time for each of the Formulations 1b–8b is shown in . In terms of foam stability, addition of xanthan clearly leads to more stable, persistent foams. This is basically as one would expect, because xanthan provides a degree of stability via continuous phase gelation, restricting bubble movement and therefore slowing the creaming and coalescence rates. Bulk elasticity is also understood to retard the rate of disproportionation (), although it is unlikely to have a notable effect here. Our bulk rheological measurements of a 0.4 wt% solution of xanthan (containing no protein) are shown in a, where the influence of oscillation frequency on the elastic and viscous moduli is plotted. Since the rate of disproportionation (and therefore rate of bubble compression/expansion) is a variable dependent on bubble size, the elastic nature of the continuous phase needs to be significant across a range of deformation rates, which we measure via the frequency sweep. The values for G′ shown in a are at least an order of magnitude lower than those required to have any notable impact on disproportionation, based on theoretical work by . The value of G′ also decreases as the frequency of oscillation decreases, i.e. for smaller bubbles, where the rate of disproportionation is the greatest; there is a lesser influence of the continuous phase elasticity. Therefore, we can be confident that the principal stabiliser to disproportionation in each foam will be the surface adsorbed layer, i.e. the nature of the a/w surface due to the adsorption of protein or surfactant.Indeed, this is what we observe: β-Lactoglobulin, Na Cas, Hygel, and Tween 80, all stored at 5 °C produce foams, where the bubbles grow and the foam collapses completely within 5 days. In fact, >75% of the foam volume has been completely lost within about 24–48 h for these formulations, where over this time period each of the foams shows significant bubble growth and foam collapse.By some considerable margin, the most stable foams are those formed using hydrophobin HFBII, both in terms of retaining the foam volume and in maintaining bubble size. In fact, at all four pH conditions measured, HFBII shows similar foam volume stability (via surface adsorption), and this stability is far in excess of any food protein or surfactant that we are aware of. b further shows the effect of oscillation frequency on both the surface shear elastic and bulk moduli of the a/w surface stabilised by 0.01 wt% HFBII at pH 5.5. Although there is a general trend towards a lower G′(s) at low frequencies, it is quite apparent that the surface retains its highly elastic nature across the range of frequencies tested. One therefore concludes that the mechanical properties of the a/w surface formed by the adsorption of HFBII protein are directly responsible for foam stability.At the extremes of pH (4.0 and 8.6), the foams stabilised by HFBII do start to show some gradual creaming over a period of about 5 days, although this is a slow process and the interface between the serum phase and the foam phase was not well defined, i.e. although there was some depletion of bubbles in the lower serum phase, there was still a significant number of small bubbles located there. This process is likely to be due to some larger bubbles being formed during the aeration stage, which were too buoyant for the yield stress to prevent from creaming, as opposed to significant bubble instability and growth via disproportionation and coalescence. Nevertheless, a more detailed study of pH effects on bubble stability would be useful to determine any differences in the stabilisation capability of hydrophobin across a range of solution conditions. That said, HFBII clearly has considerable foam-stabilising capability from pH 4.0 to 8.6. This is consistent with previously measured surface shear rheology data (), which shows high values of elastic modulus (> ca. 0.3 N m−1) across a wide range of pH units (from pH 3 to 9).We demonstrate further the long-term foam stabilisation capability of HFBII in a solution containing thickening agent. shows two foams: one stabilised using 0.1 wt% HFBII and the other stabilised using 0.5 wt% Na Cas. In both examples, the aqueous solution contained 0.5 wt% xanthan. At time=0, the measuring cylinders were filled to 100 mL of foam, consisting of φair=0.5. Within 1 week, the foam stabilised by Na Cas had completely collapsed. However, in the case of the HFBII stabilised foam, over a period of 2 years and 5 months, less than 20% of the air phase volume had been lost. A proportion of this volume loss can probably be attributed to evaporation of water. Furthermore, although clearly some creaming has taken place over this considerable time period, visibly the air bubble size barely changed.The growth in bubble size over time was measured for each of the Formulations 1b–8b as a function of time, using the light scattering technique described. a and b show air bubble diameter dr relative to that at time t=0 for each of the foams; dr is calculated as a function of time in terms of d0, the diameter at t=0, and dt, the diameter at time t, asThe sizes of air bubbles at t=0 are also summarised in , where t=0 is the first measurement taken within 1 min of foam formation. In a it can be seen that each of the dairy based proteins and Tween 80 clearly show rapid bubble growth over a period of 1 day, growing to about three times their initial diameter; the measurement of size was then stopped. This increase in size leads to creaming of the air phase and foam collapse, as already discussed. Each of the foams stabilised by HFBII, however, shows very little change in air bubble size over a period of 4 months. Formulation 5b (HFBII at pH4.0) actually shows what appears to be a bubble size decrease over time. We believe that the overall size distribution is not actually changing to a great extent and, visually we noted no significant coarsening of the foam throughout the vial throughout the experiment. Furthermore, there is no collapse or air loss of the foam throughout this period, as is clear from . However, since the initial air bubbles formed in this formulation exhibited a larger size than the other hydrophobin foams (as indicated in ), one is probably measuring the effect of some creaming in the vial over the measuring area of 20–30 mm height. As a result, some of the larger bubbles cream beyond the measurement area, leaving a larger proportion of smaller bubbles. Almost all of this change occurs within about 5 days, and from then onwards the size is constant.Another interesting point to note from the initial bubble size data is that with the exception of the HFBII foam formed at low pH (4.0), the foams stabilised by HFBII have significantly smaller bubbles than the other foams measured. These data indicate that the surface activity of HFBII facilitates effective bubble break-up, and this is reinforced by the elastic nature of the bubble surface, preventing coalescence and disproportionation from an early stage.Stability of Formulations 1b (Na Cas) and 6b (HFBII at pH 5.5) were compared using optical microscopy to observe the evolution of bubble size over several days. shows images of these foams at three different time points. These image sequences were captured from a time-lapse video, which can be downloaded electronically from the “supplementary information” section.The foam stabilised by Na Cas shows rapid bubble growth over 12 h. In contrast, the foam stabilised using HFBII shows very little change in bubble size over a period of 6 days. We also draw attention to the presence of some non-spherical bubbles, which we have highlighted previously (), where we believe the high surface elasticity is great enough to prevent the bubble reverting to spherical geometry through surface tension forces. These images visually demonstrate the effectiveness of hydrophobin HFBII as a foam stabiliser, dramatically reducing both coalescence and disproportionation between air bubbles over time periods far in excess of other food proteins.A calculation of the Laplace pressure can be obtained from the bubble size and the surface tension. We have previously measured the equilibrium surface tension of HFBII to reach 30 mN m−1 (). For the case of a bubble of radius 50 μm stabilised by HFBII, the Laplace pressure is 1200 Pa. Although this value is significantly smaller than that calculated for a similar bubble stabilised by, for example, β-lactoglobulin (2000 Pa for a similar size bubble with surface tension 50 mN m−1), the magnitude still provides a driving force for bubble dissolution. This means that the protein must exhibit some resistance to compression and bending of the adsorbed layer.Foams stabilised by surface adsorption of HFBII clearly show stability well in excess of other food surfactants in simple aerated solutions. Here, we further highlight the effectiveness of hydrophobin as a foam stabiliser in a more complex formulation, i.e. a chocolate milk shake (). Although the formulation contains a number of further ingredients (cocoa powder, fat, protein, sugar), the foam phase shows good stability for a period of at least 5 weeks when stored at 5 °C, i.e. there has been no apparent loss of air phase volume and there has been no visible increase in air bubble size. HFBII can reduce the a/w surface tension to values below that of the other surface-active agents present. For example, the a/w equilibrium surface tension of skim milk protein has been measured to be 48 mN m−1 (), compared to a value of 30 mN m−1 obtained for HFBII (). Furthermore, HFBII also forms a highly elastic surface film. Consequently, once adsorbed at the bubble surface, the addition of other ingredients do not appear to greatly inhibit the surface-stabilising capacity of the hydrophobin protein in such a food product.Hydrophobin HFBII is known to be a highly surface-active protein: it reduces the a/w surface tension to about 30 mN m−1 () and, once adsorbed, forms a highly elastic surface. This provides mechanical resistance to both coalescence and disproportionation. In general, the ability of any adsorbed protein or surfactant to produce stable foams is related to both the structure of the molecule, the adsorption to the a/w surface, and the interactions between the molecules once adsorbed at the surface. However, there must be some underlying unique properties of HFBII that lead to such powerful foam-stabilising behaviour.HFBII is known to have an approximately spherical structure, exhibiting both a hydrophilic part of the surface and, a smaller, hydrophobic part (). The internal structure of the protein consists of eight cysteine residues, which are arranged in such a way as to stabilise the structure and retain the globular shape of the protein, thus preventing significant unfolding (). As a result, HFBII can be described as a small (ca. 2–3 nm diameter) molecule with a distinct amphiphilic nature, i.e. a protein Janus particle.There has been increasing interest in the use of particles (including Janus particles) to stabilise emulsions and foams (), partly because such dispersions are potentially far more stable than those produced by surfactants. This is due to the energy of desorption being much greater for a particle than for a smaller surfactant molecule. Although the general model of particle stabilisation may go some way in describing the behaviour of hydrophobin as a foam stabiliser, there is still much to be understood in terms of the adsorption behaviour of this protein to the a/w surface, the film elasticity, and the exceptional stabilising capability that ensues. For example, the nature of interactions between hydrophobin molecules once adsorbed at the a/w surface is currently not well understood. Such interactions may also play a significant role in the mechanical properties and, therefore, bubble and foam stabilisation.We have demonstrated the exceptional stabilisation of aqueous foams using hydrophobin HFBII, at a concentration of only 0.1 wt% protein and across a range of solution pH conditions. In the presence of a thickening agent to slow the rate of creaming, hydrophobin can stabilise foam to the extent where little, or no, air phase loss is observed, for over 4 months. In fact, we have an example where most of the air phase volume remains after 2.5 years storage at chill temperature. The stability of such foams is well in excess of those stabilised using other common food-aerating/emulsifying agents, such as milk proteins and Tween. We have also shown the potential of hydrophobin as a foam stabiliser in one example food product, a chocolate milk shake.The mechanism of foam stabilisation using HFBII is believed to originate through surface adsorption of this protein and the resulting high surface elasticity that results, i.e. there is no affect of this protein on the bulk phase rheology. Although more work is required to understand the surface behaviour, we propose that HFBII may act as a nature-designed Janus-like particle, adsorbing strongly to the a/w surface, and effectively resisting surface changes due to processes such as disproportionation. This is in contrast to milk proteins, which exhibit a relatively low elasticity and have relatively little effect on slowing the rate of disproportionation. A more detailed model of the physical properties of hydrophobin at surfaces and interfaces is required, however, in order to fully understand its mechanistic behaviour and further exploit the potential of this class of proteins in a variety of technical applications.The ability to create foams that exhibit exceptional bubble stability at low concentrations over a period of several weeks or even months could lead to a number of new applications. In foods, the ability to produce foam of greater stability may lead to improved storage stability as well as improvements in physical and sensory properties of products such as ice cream, sorbets, and low-fat whipping cream. Moreover, use of hydrophobins could further lead to the possibility of aerating food products that currently do not contain air because of instability problems: for example, mayonnaise, shelf-stable milk shakes, smoothies and other beverages, yoghurt, and gelatine-free mousse. As a result, benefits such as fat/calorie reduction or improved/new product textures are possible.Finally, hydrophobins are a class of fungal proteins some of which are presently consumed: for example, hydrophobins are present in mushrooms. Therefore, there is signficant potential for hydrophobins, in an isolated form, to be used in food products.Supplementary data associated with this article can be found in the online version at Analytical and numerical studies on reducing lateral restraints in conventional & all steel Buckling Restrained BracesA typical Buckling Restrained Brace (BRB) consists of a steel core and a mortar-filled tube to prevent buckling of the core. In BRBs, the mortar used in a casing considerably increases their weight. In another type of such braces, to reduce the weight, a steel casing is used to avoid buckling of the steel core. In this paper, discontinuous restraint is investigated analytically and numerically to manage buckling behavior of the core along the steel tube.In the analytical section, equations are proposed to determine a suitable distance between the restraints in rectangular and cruciform sections using inelastic buckling, tangent and double modulus theories and their combination with the Romberg-Osgood behavioral model. In the numerical section, first the cyclic behavior of 9 Conventional BRB models with continuous and discontinuous mortar casing is evaluated using the Abaqus software. Then, the appropriate distance between restraints is determined for the numerical model and compared to those from analytical equations. Results show that the tangent modulus theory is more compatible with the finite element model. Moreover, in cruciform cores, it is possible to reduce the amount of mortar up to 64% without any changes in the cyclic behavior of bracing. Finally, two all-steel BRB models are exposed to cyclic loading where steel plates prevent core bucking. Those results demonstrate that the cumulative ductility exceeds the minimum value defined by AISC.Steel braces demonstrate an ideal behavior under tension and dissipate a major part of energy by yielding, while they are prone to buckling and instability under compressive loads. The buckling of these braces under compression interrupts the function of structure and significantly reduces energy dissipation. On the other hand, an increased cross-sectional area of braces to prevent buckling under compression totally changes the structural behavior and increases the strength and stiffness of the braces under tension imposing a severe force on other members []. Various approaches to prevent buckling of the braces or self-centering braces reducing the residual deformation have been studied []. Buckling Restrained Brace, BRB, has been introduced to prevent buckling of the braces under compression and reduce the level of tension. Generally, this type of bracing systems consists of a steel core (like rectangular, cruciform, tubular sections) which bears tensile and compressive forces and a set to control the buckling of the steel core. The restraining set, which can consist of a concrete casing or a set of various steel plates and profiles, does not play a role in bearing the tensile and compressive forces and only prevents the instability of the steel core [BRBs with concrete- or mortar-filled tubes consist of three components: steel core, outer steel tube and mortar or concrete casing. It is difficult to manufacture BRBs in steel factories due to the use of the mortar which leads to more cost and time of production, increased weight and size of lateral cross sections in comparison with conventional steel bracing. Also, the high dead weight and large size of lateral sections restrict the application of the BRBs in lightweight steel structures, compared to conventional steel braces []. Their use in bridges is controlled by stricter criteria due to highly variable environmental conditions and large dimensions of the bridges increasing the weight of the BRBs leading to higher initial deformations in addition to more difficult construction. Therefore, the weight reduction for the BRBs can have a good impact in design and implementation processes [These disadvantages have attracted the attention of researchers to the introduction and investigation of all-steel BRBs [] where a set of steel members is used to maintain core stability instead of concrete casing. The geometry of these restraining members is also of great importance in the stability of the whole system, resulting in extensive research on the shape of the core and restraining members []. Naghavi et al. investigated cyclic behavior of four types of BRB frames with ABAQUS []. Li et al. studied the experimental and analytical performance of composite frames with BRBs [Bolted connections used to assemble the encasing members of all-steel BRBs not only simplify the construction process, but also allow for inspection of the core and its replacement after earthquake due to the disassemble conditions []. An idea proposed to decrease the weight of all-steel BRBs is to reduce their length. The main consequence of this approach is the creation of higher strains in comparison with conventional models, which may exacerbate the failure in the core []. Another idea proposed to reduce the weight of the BRBs is the application of lightweight materials for their components. Dusicka et al. studied the bracing performance of a glass fiber reinforced polymer (GFRP) tube to restrain an aluminum core [The global buckling of the BRBs before core yielding is a great concern, as confirmed by the results of many previous studies. Watanabe et al. experimentally studied the cyclic performance of the BRBs with mortar casing []. They found that as the dimensions (the moment of inertia) of casing fall from a certain amount, the global buckling occurs in the casing and the core. In all-steel BRBs, there are short distances between the restraining members and the center of the core due to their interface for prevention of core buckling. In such systems, reducing moment of inertia of the steel casing may raise this concern [Another important concern about the behavior of the BRBs is the boundary conditions between the core and concrete or steel restraining member or the boundary conditions between the core and the frame. In recent years, factors such as the type of debonding material between the core and concrete casing, details of core-gusset plate connections, design process have been studied experimentally and numerically for the BRBs. A small gap (less than 2 mm) between the core and the concrete or steel encasing allows the core to move freely inside the casing and to experience longitudinal strain along directions perpendicular to axial loads (due to the effect of Poisson's ratio). As the dimensions of the gap rises, the forces caused by collisions between the core and the restraining encasing increases due to higher buckling modes, which is not favorable []. Hoveidae and Rafezy studied the effect of details of all-steel BRBs on local buckling by parametric study and numerical modeling []. They assessed parameters such as coefficient of friction (COF), empty space and thickness of debonding material between the core and the restraining member. Wang et al. examined the experimental and numerical performance of the BRBs in different connection conditions [In previous studies, a combination of inelastic buckling theories and performance of the BRBs has been less considered. Wu et al. examined the effect of higher modes on the performance of a new type of all-steel BRBs []. Lin et al. studied the force applied to restraining member due to local buckling of the core []. A fundamental question raised for the BRBs is that whether it is necessary to fill the whole tube with mortar to deactivate buckling modes of the steel core and whether it is also necessary to place restraining members throughout the entire length of the core for all-steel BRBs. If not, some advantages both in term of cost efficiency and construction can be concerned:The total weight of a BRB decreases due to the less use of mortar (a) or steel restraints results in ease of transport and installation of braces and less initial deformation leading to better compressive strength. On the other hand, the decreased interface of mortar and steel core reduces the cost of debonding materials.Reducing the amount of mortar can encourage designers to employ more expensive materials with higher strength, lower weight and weaker tangent behavior. The increased strength prevents the restrainer material from damage in severe earthquakes and creates stable cycles in the behavior of bracing system.In all-steel BRBs, the distance between restraining tube and the core is short due to prevention of core buckling. In such a case, the tube should have a larger cross-section leading to required moment of inertia to prevent global buckling of the bracing system. In case of discontinuous restraints, it is possible to place the tube further away from the core to increase its moment of inertia. For example, steel plates may be used to provide lateral support for the core. (The modified BRB model with mortar casing is created by placing the mortar in specific lengths and filling the gaps by Expanded Poly Styrene (EPS). The mortar can be placed step by step to construct this model. For example, the mortar is injected into the steel tube by 10 cm in length, a specific distance is then filled with EPS and this process continues until the brace is accomplished (a). To prevent slippage of concrete segments, a shear key should be used for each segment to manage the application of the modified conventional BRB in construction. This process is simpler for all-steel BRB; the details shown in b can be implemented inside two channels and then those channels are bolted or welded to each other.In this paper, it is attempted to determine an appropriate distance for restraints by developing inelastic buckling theories, so that higher buckling modes can be achieved. In this study, tangent and double modulus theories [] are discussed based on the Romberg-Osgood behavioral model []. Then numerical models prepared by Abaqus software [] are used to compare the results with analytical ones. In this modeling, the cyclic behavior of the BRBs with square and cruciform cores is evaluated. The reliability of modeling and extraction of numerical results is investigated by comparing the results of reference experimental model [] and those of numerical model prepared via Abaqus software. It must be noted that the results of hardening models proposed by Prager, Chaboche and Romberg-Osgood are compared to experimental results to enhance the accuracy of numerical models in the validation section to select the best model. In the next step, a conventional BRB with discontinuous casing is evaluated. To eliminate some concerns and simplify the construction process, the proposed all-steel BRB model is then introduced and its cyclic behavior is analyzed. The most important feature of all-steel BRBs is the increased moment of inertia of restraining member to prevent global buckling, in addition to the reduction of weight. The location of restrainers is determined based on the elimination of initial buckling modes and the achievement of higher wave-shaped modes.To determine the appropriate distance between restraining members, it is necessary to derive equations based on inelastic buckling, considering the nonlinear behavior of the core. Solutions for inelastic buckling problems entirely depend on material behavior curve in the plastic range and geometric form of the section. The tangent and double modulus theories [] are employed to solve the problem based on the Romberg-Osgood behavioral model. In addition to the good fit of Romberg-Osgood mathematical model with the behavior of steel core [], the slope of its behavior curve also changes continuously. The optimum shape of the core is also an effective factor in the results due to the increased potential of core buckling, so that it is essential to provide maximum moment of inertia for the core with a constant cross-section in order to achieve more appropriate conditions. Cruciform sections provide more moment of inertia for the core than rectangular sections and retard the buckling. In the following, related equations are obtained to determine the restrained length for preventing inelastic buckling.The tangent modulus of behavior curve for steel is an effective parameter in determining the restrained length based on the tangent and double modulus theories. In the Romberg-Osgood behavior model, the strain of steel is defined in terms of stress as follows [where H and n are constant parameters obtained according to the steel type and its behavioral characteristics. The range of plastic strain is used to determine these parameters. To solve the problem numerically, it is assumed that the steel SS400 is used, for which the elastic modulus, yielding stress, ultimate stress and ultimate strain are 200 GPa, 288 MPa, 400 MPa and 0.22, respectively. The plastic strain and its equivalent yielding and ultimate stresses are used to determine the parametern. It should be noted that if plastic strain at the point of yielding is zero, it is not possible to determine the parametern and, therefore, εp1 is considered 0.002.εpi=(σH)1n,log(εpi)=1nlog(σiH)i=1,21n=log(εp2εp1)log(σ2σ1)The strain and stress values of steel SS400 are substituted in the equation as follows:1n=log(0.22−0.001440.002)log(400288)=14.289In the tangent modulus theory, the tangent modulus (Et=dσ/dε) is used instead of the elastic modulus (E), in contrast to the Euler's equation (Pcr=π2EI/(kL)2). In this theory, the basic assumption is the increase of axial force at the moment of buckling (P→P+ΔP). The result of this assumption is that compressive stress must increase in all cross-sections, so that the tangent modulus can be applied for all axes in the cross-section [where Ir, L and k are the moment of inertia, the radius of gyration, the length and effective length factor, respectively. The tangent modulus is derived from the Romberg-Osgood behavioral model as follows:σcr=π2Etr2(kL)2⇒σcr(1E+1nH(σcrH)1n−1)=π2r2(kL)2⇒L=πrkσcrE+1n(σcrH)1nThe required spacing for the restraints to achieve critical stress is determined based on the tangent modulus theory using Eq. The double modulus theory has a more impeccable logic than the tangent modulus. In this theory, it is assumed that the compressive axial load remains constant over the buckling. Accordingly, due to the bending occurred at the moment of buckling, the stress rises on the concave side of column (compression region) and declines on the convex side of column (tension region). The stress continues to increase in the concave part with the slope (Et), but it drops in the convex part (unloading region) with the slope (E). In this theory, the critical force is also determined based on the Euler's equation through replacing the elastic modulus by the reduced modulus in the buckling equation []. Therefore, the general solution of the problem for different boundary conditions is:In order to calculate the reduced modulus, it is necessary to determine the position of neutral axis of the cross-section by Eq. , where QC and QT are the first moment of section for concave and convex parts, respectively.The reduced modulus will be obtained using Eq. where IC and IT are the moments of inertia for the compression and tension regions around the neutral axis obtained from Eq. and I is the moment of inertia for entire section around its central axis., Er for a rectangular section is equal to:The results of Romberg-Osgood equation are employed to calculate the reduced modulus.The reduced tangent modulus of a rectangular section is substituted in the critical stress equation as follows:The required spacing to achieve critical stress will be obtained from the equation above, based on the double modulus theory in the rectangular section. The calculations of double modulus theory are more complicated and time-consuming for cruciform sections. In this case, there are two probable positions for the neutral axis (a and b). Each position depends on the growth of strain and the amount of tangent modulus; one position along the large restrained length where the tangent modulus does not reduce significantly and another position along the small restrained length. In the following, the reduced modulus will be calculated for each state.Assuming that cb=X, ab−1=Y and EEt=Z, it is concluded that:The values of c and t are obtained by solving the quadratic equation above and Er is eventually determined by the equations below. It is worth mentioning that the acceptable root of this equation should satisfy the inequality a2<c<a+b2.Er=EtIC+EITIIC=bc33+(a−b)(c−a−b2)33,IT=bt33+(a−b)(t−a−b2)33EtQC+EQT=0⇒Et[c2b2+(a−b)b(c−a2)]−E[t2b2]=0⇒(E+Et−2Et)c2−2[(E+Et)a−Etb]c+[(E+Et)a2−Etab]=0(E′−2Et)(cb)2−2(E′ab−Et)(cb)+ab(E′ab−Et)=0To simplify and calculate the roots of quadratic equation above, it is assumed that E'ab−Et=W:(E′−2Et)(cb)2−2Wcb+abW=0⇒cb=W±WEt(2ab−1)E−Etcb=(E+Et)(ab)−Et±[(EEt+Et2)(ab)−Et2](2ab−1)E−Et⇒X=(1+Z)(Y+1)−1±[(Z+1)(Y+1)−1](2Y+1)Z−1The root derived from the quadratic equation should also satisfy the inequality a+b2<c<a.Er=EtIC+EITIIC=bc33+(a−b)b312+(a−b)b(c−a2)2,IT=bt33Finally, when Er is determined for both states, the restrained length can be obtained from Eq. Obviously, numerical solutions are required for the cruciform section, opposed to the rectangular section. Double modulus theory proposes an upper bound of buckling resistance due to the constant Et despite the strain variations in the buckling moment []. Therefore, distance for the restraints in Eqs. ) is expected not to be predicted conservatively.In this section, the reduction of mortar volume is investigated numerically in the cyclic behavior of BRBs. The volume of mortar is reduced in the experimental model presented in the validation section []. Here the analytical results of inelastic bucking theories are described. Since the increased moment of inertia in the core may impose a significant impact on the results, square and cruciform sections with constant areas are used for the core modeling. The dimensions of these equivalent sections are given below ():where AR, AS and Ac are the area of rectangular, square and cruciform sections, respectively, and IR, IS and Ic are the moment of inertia for the rectangular, square and cruciform sections, respectively. As can be observed, the moments of inertia of square and cruciform sections increase by more than 4.5 and 9 times that of rectangular section through the conversion, respectively. After determining the dimensions of the core, the restrained length must be calculated using the tangent and double modulus equations for square and cruciform sections.The restrained length of square section 41 mm long is presented based on fixed-end boundary conditions and behavior curved defined for the steel, the tangent modulus theory in Eq. ⇒Eq.8k=0.5L=π×0.041230.5×σcr200000+14.289(σcr444.918)14.289⇒L=π×0.0413σcr200000+42.866(σcr444.918)14.289⇒Eq.15k=0.5L=2π×0.0413σcr200000+42.866(σcr444.918)14.289+3σcr200000According to the dimensions and fixed-end boundary conditions in the cruciform section, the restrained length is calculated using Eq. in accordance with the tangent modulus theory.L=πrkσcrE+1n(σcrH)1n⇒k=0.5L=π×0.01660.5×σcr200000+14.2888(σcr444.9182)14.2888where the Gyration radius (r) of cruciform section is obtained by Eq. r=ICAC=a3+a−bb2122a−b=77.33+77.3−12×122122×77.3−12=16.6mmA numerical solution is required to determine the restrained length of cruciform section based on the double modulus theory. Given the dimensions of cruciform section, the answer of quadratic equations presented in section cb=4.141080E−2.296420Et±1.2135923.627406EEt−0.658503(E2+Et2)E−Etcb=6.4375(E+Et)−Et±76.445313(EEt+Et2)−11.875Et2E−Et) are the first and second modes of probable position of neutral axis in cruciform section, respectively.Given the dimensions of cruciform section, the roots of first and second equations are acceptable only in ranges of 38.625mm<c<44.625mm and 44.625mm<c<77.25mm, respectively. It should be noted that the positive roots under root symbol never fall in these ranges for both equations and, therefore, only negative roots under root symbol are acceptable., the critical stress and strain are shown in terms of variations in the restrained length for square and cruciform sections, where S and C represent the square and cruciform sections, respectively, and TM and DM are the abbreviations of the tangent modulus and double modulus, respectively. As observed, the restrained length must be reduced in order to increase the amount of critical stress or strain.For example, according to the curves in , the restrained length required for prevention of bucking at strain of 0.04 in a square core is 10 and 19 cm, respectively, based on the tangent and double modulus theories. However, these values are 14 and 33 cm for cruciform section at the same amount of strain, respectively, due to the increase in moment of inertia compared to the square section.The result validation is conducted here for numerical analysis. The BRB proposed by Watanabe et al. [] is modeled by Abaqus finite element software for result verification () comparing the experimental and numerical results of cyclic performance.It is so important to select the suitable plastic behavior model for steel members under cyclic loading. A number of behavior models have been already proposed by researchers [], among which the Armstrong-Frederick model is the most important []. A few years later, this behavior model was modified by Chaboche to be applied for the prediction of behavior of different metals. As a basis for their studies, many researchers employed this behavior model included also in numerous commercial software packages []. In general, three fundamental factors considered to describe the plastic behavior of metals are yield function (mostly Von Mises yield criterion), flow rule (mostly associated plastic flow) and hardening rule. This last rule encompasses three conditions of isotropic hardening (uniform increase of yield surface in all directions of stress space), kinematic hardening (displacement of yield surface in stress space by back stresses) and combined hardening. The non-linear kinematic hardening model proposed by Chaboche can predict the behavior of metals under cyclic loading with appropriate accuracy. In this model, the material parameters of Ci and γi are required in addition to initial yield stress, where i represents the number of back stresses. The combination of non-linear kinematic and isotropic models (the material parameters of Q∞ and b) can improve the accuracy for the prediction of behavior of metals.Each parameter is calibrated by tests on metal coupons. Jia and Kavamora calibrated the material parameters of SS400 steel for the Prager (linear kinematic hardening) and Chaboche (nonlinear kinematic hardening with/without isotropic hardening) behavior models [ presents the SS400 steel calibrated parameters used in this article.The BRB consists of a core with a rectangular section 90 × 19 mm and a tube with a box section 150 mm long and 4.5 mm thick. The core and outer tube are made of steel SS41 (JIS1) with a yielding stress of 288 MPa and steel TSk50 (JIS) with a yielding stress of 370 MPa.Since mechanical properties of the core governs the hysteresis curve of experimental specimen, it is necessary to apply an appropriate and accurate plastic behavior model for its simulation. Since the mechanical properties of steel SS41 is not available, the steel SS400 is used as its equivalent. Three behavior models given in are utilized for the simulation in order to choose an alternative most compatible with experimental results. Since the behavioral properties of filling mortar are not introduced, the concrete with strength of 25 MPa is used. It should be noted that the hysteresis curve shows no sensitivity to the strength of concrete, according to the result validation. The plastic damage behavioral model is utilized for the concrete to address the potential of failure. In this behavior model, the failure of concrete is simulated using decreased hardness of elements, caused by crushing under compression or cracking under tension.Boundary conditions of the BRBs are considered fixed on one side of the core and a controlled displacement is applied to the other side along the degree of axial freedom while other degrees of freedom are restrained. Based on experimental model presented in Ref. [], distance between the steel core and the concrete in the restrainer is 3 mm in the finite element models. It is very important to consider the influence of imperfections on the inelastic buckling []. To activate the buckling modes, a buckling eigenvalue analysis is performed and a deformation similar to the first mode of buckling with the maximum amplitude of 3 mm is imposed on the core as the imperfection []. The elements are of the type C3D8R (8-node linear brick, reduced integration, hourglass control) and both normal (hard contact) and tangential (penalty) behaviors with coefficient of friction of 0.15 are employed to define the interaction between the core and the concrete casing.The value selected for the coefficient of friction leads to the most compatibility with test results. As the coefficient of friction rises, the ratio of maximum forces in compression to tension regions increases. This occurs due to the collision of the core with the casing after bucking and transfer of some compressive forces.It is worth mentioning that axial forces cause internal bending in the steel core because of its bucking. Hence it is necessary to provide conditions for the distribution of bending-induced strain through the thickness of the core by placing some mesh layers along the thickness of the core. Accordingly, three mesh layers are applied along the thickness in this article. shows the finite element model of BRB components. represents the validation results of finite element model for different plasticity models. According to a, the Romberg-Osgood model shows the highest compatibility (for which the multi-linear kinematic hardening is applied) and the Prager model has the least compatibility with experimental model due to linear kinematic hardening behavior. b exhibits a comparison between the results of experimental and chaboche models. Obviously, the calibrated parameters of Chaboche model consider the effect of Isotropic hardening (shown with IH afterward) slightly higher than the experimental results. To achieve a better compatibility, the parameters of isotropic section of Chaboche model are thus modified by trial and error and the results are given in b (Q∞=227.8MPa,b=3.8 for the first trial; Q∞=127.8MPa,b=3.8 for the second trial).According to the cyclic curve of experimental and numerical models (a and b), it is clear that there is a good match between the results and, consequently, the reliability of modeling and numerical results is ensured. shows the yielding parts of the core and local buckling created in the finite element model on a scale of 3 to 1 (c). As can be observed, due to lack of connection between the casing and the steel core, on one side local buckling has intensified.Since the Romberg-Osgood and Chaboche-with IH-It2 models are best compatible with the behavior of experimental model, they are used to define mechanical behavior of the core. It must be noted that the Romberg-Osgood behavior model is just used for the core of modified conventional BRB and both behavior models are used for the core of modified all-steel BRB due to the great number of models and high-volume processing required for each case.Five BRB models with square steel core and different mortar contents are studied. In the first model, the mortar casing is used along the entire length of the tube (a) and in models 2 to 5, the number of mortar segments is reduced from 13 to 9 (b–e). The first and last mortar segments are 15 cm long while the middle segments are 10 cm long. The length of the mortar segment should somehow be determined not to get damaged from the impact force, as well as to provide the core with fixed boundary conditions. The reduced volume of mortar and back-to-back distances between segments (restrained length) are obtained for the model with 13 mortar casing segments using Eqs. where VT and VC are the total volume of tube and the volume of mortar, respectively. In , the reduced volume of mortar and restrained lengths are given for each model.For the cruciform section, a model with entire mortar casing (a) and 3 models with 8, 9 and 11 mortar casing segments are simulated and evaluated (c, e and f). The decreased number of segments for the cruciform section is because of the increase in its moment of inertia and stability compared to the square section. For instance, illustrates the interior of proposed finite element BRB model with a square core.As expected, the behavior of models does not change under tension and they all withstand a certain level of forces, while compressive strength declines as restrained length increases in the compression region. In the case with square core and 9 mortar segments (64% reduction in mortar volume), the strength loss equals 24% (Eq. ) and in the case with cruciform core and 8 mortar segments (67% reduction in mortar volume), the strength decreases by 8% (Eq. ). In the case with square core and 11 and 13 mortar segments and also the case with cruciform core and 9 mortar segments, no strength loss occurs and the results can be considered the same as those for braces with completely mortar-filled tube.PM−All−PM−9PartPM−All=57.9−43.857.9×100=%24PM−All−PM−8PartPM−All=57.9−53.257.9×100=%8a and b, the inelastic buckling is shown for the case with square core and 9 mortar segments and the case with cruciform core and 8 mortar segments, respectively., the restrained length for BRB with 11 mortar segments is 15.75 cm. Given the changes in last cycle of loading and its corresponding strain (ε=δ/L=4.723/319=0.01481), this value is obtained 17.1 cm for the square section from the tangent modulus theory. Moreover, the restrained length for 9 mortar segments is 20.09 cm, while this value is obtained 24 cm for the last cycle strain in the cruciform section based on the tangent modulus theory. However, the restrained length equals 31.3 and 53.3 cm for square and cruciform sections, respectively, at this amount of strain. Obviously, despite the use of more impeccable arguments in the double modulus theory, the results of more conservative tangent modulus theory seems more compatible with reality. This is due to the lack of factors such as imperfection, eccentricity of forces and residual stresses in these theories. The reports also suggest that the tangent modulus theory better justifies the behavior of short columns. On the other hand, the uniform distribution of axial strain along the core is not a reasonable assumption and strain concentration occurs in some parts of the core because of high buckling modes in the core and its collision with the casing. Therefore, it seems more reliable to apply the tangent modulus theory which has a higher safety factor.The results demonstrate that when restrained length exceeds the values proposed by the tangent modulus theory, strength loss begins in the cycles. As restrained length increases, the strength loss becomes more severe in the compression region. One of the main factors in determining the restrained length is the core strain demand, so that as the core experiences larger strains, the tangent modulus declines more and strength loss increases. For example, in cycles with a displacement of 2.4 cm which is equivalent to a strain of 0.073 in the bracing system, no strength loss happens in the BRBs with square and cruciform cores and various numbers of mortar segments. Given the tangent modulus theory, the restrained length of square core is 25.77 cm for this amount of strain, which is more than the length of 20.09 cm considered for 9 mortar segments. Given the direct relationship between the drift and the strain in bracing system, a reasonable estimation of drift demand may have a direct effect on the estimation of distances between the restrainers. On the other hand, as effective length of the core increases, ultimate strain decreases and the design becomes more economical.As explained previously, the uniform distribution of axial strain along the core is not a correct assumption and can be only an initial criterion for estimating the distance between the constraints. shows the maximum compressive axial strain versus the number of loading cycles for the modified BRBs. Typically, this strain is maximum in regions close to end of the core as shown in with arrows for square and cruciform sections. Evidently, there is a significant difference between the assumptions of uniform distribution of strain along the core and each strain value read from the most critical element along the core. Since no damage model is considered via the software, the results are acceptable for the models where maximum strains do not exceed the strain corresponding to necking initiation, which equals 0.22 for SS400 steel []. As observed in the last cycle, the axial strain for the cases having a square core with 9 and 8 mortar segments and the case having a cruciform core with 8 mortar segments is more than the defined value and their results are not acceptable.BRBs with discontinuous mortar segments pose problems such as difficult construction process and need for shear connectors to avoid the separation of discontinuous mortar segments. On the other hand, the failure of angular corners of discontinuous mortar segments may degrade the boundary conditions considered in analytical equations. Moreover, the use of some steel plates as a substitution for mortar segments can reduce the weight of the BRBs. To solve the problems, the steel plates welded to a steel tube are used instead of discontinuous mortar. The steel tube may consist of two channels connected by welding or bolting (when the plates are connected to its inner face). The steel plates are 1.5 cm thick and the geometry of the gap allows the cruciform core to be placed between them and according to Ref. [] The distance between the core and the lateral plate is assumed to be 3 mm. The thickness of the lateral plate is obtained by a trial-and-error process, so that it transmits contact force to the restrainer without experiencing nonlinear behavior. The results of previous studies suggest that the non-uniform distribution of tensile and compressive strains increases and the shear rupture conditions occurs sooner in the core if it is connected to the casing at the end or if there is no connection []; thus, the core is connected to the casing using a stopper plate at the center for this model. We assume that the stopper plate is welded to the steel core and the restrainers. illustrates the finite element model of this BRB.In this all-steel BRB, both Romberg-Osgood and Chaboche behavior models are considered for the core and then subjected to cyclic loading in accordance with the AISC-341-16 loading protocol []. According to the protocol, not only the maximum amplitude of cyclic loading should be higher than inter-story drift of 2%, but also the cumulative ductility of BRB under cyclic loading must be higher than 200. The ductility in each loading cycle with the same amplitude μi, will be estimated based on the following relation:Where Ni is the number of cycles for the same loading amplitude and Δe and Δui are respectively the yield and ultimate displacement of each cycle. represents the specification of cyclic loading applied to the BRB in accordance with the BRB dimensions given in reference []. As observed, since the cumulative ductility is smaller than 200 for 10 cycles equivalent to a drift of 2%, 4 cycles equivalent to a drift of 1.5% are added to the end of loading in order to increase the cumulative ductility to 272 (in the first two cycles, the value of 0.48 cm is equivalent to yield displacement of the BRB). shows the results of compressive and tensile axial strains for the most critical elements (the locations of axial true strains are shown in ), hysteresis curves and energy dissipation by the core. According to a and b, the compressive and tensile axial strains are smaller than the necking strain. Given the high bucking modes in the compression region under loading, on the other hand, the level of compressive strain is higher than the level of tensile strain; so that the ratios of maximum compressive strain to maximum tensile strain for the Romberg-Osgood and Chaboche behavior models are 0.0845/0.0210=4.02 and 0.1186/0.038=3.12 respectively. The results also suggest that the IH applied in the Chaboche model makes the non-uniform distribution of strain more critical along the core in comparison with the Romberg-Osgood multi-linear model. c illustrates cyclic curve of the BRB for both behavior models. Obviously, given the characteristic of isotropic hardening in Chaboche behavior model, as loading cycles increase in terms of number and amplitude, the level of generated forces is higher and the hysteresis loops are larger than those for the Romberg-Osgood model. Given the area under the cyclic curves and d which indicates the amount of energy dissipated by nonlinear behavior of the core, it is found that more energy dissipation occurs in the chaboche model in spite of more non-uniform distribution of strain, compared to the Romberg-Osgood behavior model (about 20%)., the inelastic buckling and maximum compressive and tensile axial true strains are shown for the modified all-steel BRB.In this study, the impact of discontinuous casing on the behavior of conventional and all-steel BRBs with square and cruciform cores was investigated. Thus, equations were derived to determine the distance between restrainers using the inelastic buckling, tangent and double modulus theories. After the result validation based on experimental results, 11 models were simulated using Abaqus finite element software and evaluated under cyclic loading. Prager, Romberg-Osgood and Chaboche behavior models were also compared to each other to select the appropriate plasticity behavior for the core. Finally, the results of numerical analysis were compared to those of analytical equations.Despite small differences in cyclic curves for the validation section, the results suggest that the Romberg-Osgood and Chaboche behavior models simulate the experimental results more accurately than the Prager model. But the results of all-steel BRBs indicate that as the cycles increase in number, the difference between Romberg-Osgood and Chaboche behavior models increases.Results of inelastic buckling theories show that the double modulus theory presents higher values for the distance between the restraints at a given strain level, while the finite element results are more compatible with those of the tangent modulus theory.Finite element models indicate that it is possible to reduce the mortar volume up to 57% for a steel core with square section, while compressive strength of the bracing system remains unchanged compared to that of the entirely mortar-filled tube. Moreover, for the cruciform section, the reduction of mortar volume up to 64% does not lead to strength loss in cyclic behavior of the bracing system.If the spacing between restrainers exceeds the values presented based on the tangent modulus theory in finite element models, the cyclic load results in strength loss in the compression region. In the case with square core and 10 mortar segments, the restrained length is 18.09 cm. This value is obtained 17.1 cm for the square section and the tangent modulus theory showing a decline in compressive strength.According to the Romberg-Osgood behavioral model, the tangent modulus decreases continuously as strain rises. Therefore, as strain level increases, the critical buckling stress and spacing between restrainers decline. For example, the spacing between restrainers equals 17.1 and 25.77 cm for strain levels of 1.5% and 0.73%, respectively, based on the tangent modulus theory.The Romberg-Osgood and Chaboche behavior models for all-steel BRBs were chosen for plastic behavior of the core, as the most compatible cases with the experimental results. Each BRB was subjected to cyclic loading that could satisfy the cumulative ductility of 272 for acceptable strains. The results show that the distribution of axial strains along the core is more non-uniform for the Chaboche model compared to the numerical model leading to a high level of compressive and tensile strains in the core. Given the isotropic hardening in the Chaboche model, the increased level of forces results in greater hysteresis curves and higher energy dissipation.Study of stellite-6 deposition by cold gas sprayingCold gas spraying (CGS) has been used to generate coatings using ductile materials which are easily deformed with the impact generated by the high kinetic energy of the process. The deposition of less ductile materials is being a challenge.The present work is intended to study the deposition behavior of a stellite alloy whose high mechanical strength hinders its plastic deformation. For this purpose, we evaluated the influence of spraying parameters such as distance and, gas temperature and pressure on the properties of cold sprayed stellite 6 coatings deposited onto steel substrates. Various sets of parameters were tested in order to optimize the porosity, thickness, and deposition efficiency of the stellite coatings and thereby achieve coatings with demonstrated hardness and corrosion and wear resistance.The results show that the two most important parameters for CGS are distance and gas pressure. These two parameters are correlated to coating quality in the way that higher distance and pressure produce lower deposition efficiencies (DEs) and increased porosity contents. Temperature, the third parameter in importance, is positively correlated to quality, thus an improved coating (i.e. dense and with higher DE) can be achieved by increasing this factor.Cobalt-based alloys can generally be described as wear-resistant, corrosion-resistant, and heat resistant materials. Stellites belong to a Co/Cr group of alloys, which show ideal low-friction under high-load sliding conditions, thus making them suitable for sealing the surfaces of gate valves. The corrosion resistance of stellite is provided by Cr while it is also the main carbide former; further resistance to friction, abrasion and erosion is conferred by the addition of W and/or Mo together with Ni, Fe, C, Si and B, which lead to the development of carbides, borides and intermetallic phases. Thus this alloy has extensive applications in the oil industry (critical components of drilling), the electrical industry (energy-generating turbines), the automotive industry (coatings on exhaust parts), and others Several technologies, such as laser cladding The tribological performance of stellite coatings is determined by the formation and shearing of an hexagonal close-packed (hcp) phase; at certain stress levels, the common face-centered cubic (fcc) stellite phase can transform to the hcp structure typical of pure cobalt through a martensitic transformation Stellite-6 has a lower ductility than other fcc metals and its properties must be evaluated to assess its critical velocity. Although the use of this alloy for CGS purposes has not been addressed, other cobalt alloys, such as CoNiCrAlY, have been used successfully The present work is a preliminary study with the aim to obtain pore-free and adherent coatings. For this purpose, a factorial design was performed with spraying distance, temperature and pressure as the main factors. Future studies will address the wear and corrosion performance of these coatings.The stellite powder used as feedstock was a − 45 + 15 μm Diamalloy 4060NS from SULZER company, obtained by an atomization process (); the nominal composition (wt%) Co 28Cr 4 W 3Ni 3Fe 1.5Si 1C 1Mo is typical of stellite-6. The powder particles show a spherical morphology with some satellites (); aqua regia etching revealed dendrites that were formed during fabrication process (b). The substrates used were low alloy carbon steel G41350 UNS coupons, which were previously degreased and ground, since a roughness of 5Ra.The Cold Gas Spray equipment was a KINETICS® 4000 (Cold Gas Technology, Ampfing, Germany), with a maximum operating temperature of 800 °C, pressure of 40 bar, and propellant gas limited to nitrogen. In addition, this apparatus was equipped with a prechamber of 60 mm in length connected to a WC-Co D24 gun nozzle. Powders are heated up by the hot gas in this chamber for a longer time.During the experiments, some spray conditions were kept constant, such as powder feed rate (40.3 g/min), gun speed (250 mm/s) and impact angle (90°), based on some preliminary experiments. A factorial design was used to study the effect of stand-off distance, and temperature and pressure of the propellant gas. The objective of this approach was to estimate the effects of the individual parameters and their interactions. The relevance of these parameters for CGS was evaluated by measuring the thickness, porosity and deposition efficiency of the coating. A matrix of the experiments is given in ; the levels were chosen on the basis of our previous results using stellite and on those of other studies Deposition efficiency is the ratio of the weight of the powder deposited to the net weight of the powder consumed. The coating thickness was measured using optical micrographs and Image Tool software, while porosity was determined with Matrix Inspector software, following ASTM E2109 recommendations.Cross-sections were mounted using an epoxy resin, grinded using Buehler wet SiC grinding papers, and polished using diamond solution and silica both with polishing cloths. The samples were examined in a Scanning Electron Microscope (JEOL 5310 microscope, Japan, Tokyo) operated at 20 kV and with an Optical Microscope (Leica DMI 5000 M, Wetzlar, Germany). The coating microstructure was revealed by etching with a mixture of acids (15 ml HNO3, 15 ml CH3COOH, 60 ml HCl and 20 ml of H2O).Tensile strength was evaluated on the basis of the ASTM C-633 standard and microhardness by means of a Matsuzawa MTX-α (Japan) Vickers apparatus, following the ASTM E384-99 standard. The mean values are from at least 20 indentations performed at a load of 100 gf in the polished cross-sections of the coatings.In order to study the porosity of the optimized coatings, open-circuit corrosion tests were performed in 80 mL of an aerated and unstirred 3.4% NaCl solution. A conventional three-electrode cell was used, with a saturated Ag/AgCl/KCl as the reference electrode, a Pt-wire as counter electrode, and the as-sprayed and polished samples as the working electrode. The coated sample was placed at the bottom of the electrochemical cell, exposing 1 cm2 to the solution. A PC-programmed EG&G 263A potentiostat/galvanostat (Princeton Applied Research, UK) was used. shows the optical micrographs of the coatings according to a 23 experimental design. At a spray distance of 40 mm, delamination and porosity were observed, while at 20 mm the occurring porosity can be assumed to correspond to the preparation step since pores were highly spherical and therefore produced by detachment of single particles from the coating. Thus, it is foreseen that the spraying distance has a considerable influence on the final structure of the deposit.The effect of the factors examined and their interaction with the variables are described below. shows the deposition efficiency results of the experimental design, and the corresponding Pareto chart. The deposition efficiency results indicate that the C factor (distance) is the most important parameter, followed by B (pressure). Increasing both parameters had a negative effect on quality making Deposition Efficiency (DE) decrease, while A (temperature) showed a positive effect (b). These observations imply that an increase in distance and pressure results in a poorer coating quality, whereas the opposite happens with increasing temperature. Therefore the best result was achieved at high temperature, and low distance and pressure. Such conclusion also corresponds to the findings on coating thickness and porosity.Regarding the coating thickness, in contrast to the effect to DE, this time pressure was more important (). However, the difference between the two effects (pressure and distance) was small. is the corresponding Pareto chart for coating porosity and differs from the other two in the sense that distance and pressure (still being the most important effects) were positive, implying that an increase in these variables enhances porosity. The opposite was observed for temperature (b); that variable now is not as important as it was on the other cases, and now its effect is negative, meaning that an increase in this parameter produces less porosity.Considering the interactions between variables (c), they were weak for DE and coating thickness. Their values in the Pareto chart fall below the t-Student Parameter and the slopes of the lines were very similar, so they will not be studied.Regarding porosity however, the interactions between the variables were stronger (c); for example, the interaction between pressure and distance had a greater effect than temperature alone, and while the slopes of pressure and distance differed considerably, they remained below the t-limit. By observing the microstructures, it can also be concluded that spraying at the lower temperature leads to poor cohesion during the different passes, whereas the porosity at the higher temperature is caused by voids, rather than being produced while spraying due to the experimental conditions, as shown in The effect of increasing distance can be explained as follows; it is known that the particle velocity increases outside the nozzle but there is a maximum where the particle velocity starts to decrease. If such a maximum is overcome, the kinetic energy upon impact is lower and, in some cases, may not be enough to overcome the critical particle velocity, thus generating a poor coating; but also at very short distances, the velocity might be lower because of the bow-shock effect The same happens with pressure above a certain value. In general, an increase in gas pressure leads to an increase in particle velocity, and thus higher deposition efficiency and lower porosity Temperature influences the CGS process in several ways. First, an increase in stagnation temperature causes greater gas velocity, and accordingly an increased impact velocity of the particles. Second, the elastic and plastic properties of materials depend on the temperature of the process. Therefore the temperature of the materials can be changed by using a higher gas temperature and also by preheating the substrate. An increased temperature of the materials may enhance thermal softening, which is crucial for bonding From the above results, it can be seen that by increasing the spray distance from 20 to 40 mm, the DE decreased by 3.5%, while a change in pressure or temperature resulted in DE enhancement of only 2.9 and 1.6%, respectively. The effect of spraying distance on coating thickness and porosity as well is not usually so evident. In general terms, the higher the spraying distance, the lower the particle velocity. Therefore, the achievement of strong bonding is influenced by whether the critical velocity for the material is surpassed The aim of the previous factorial design was to optimize the spraying conditions with the lowest number of experiments possible. The best coating was achieved at a temperature of 800 °C, a distance of 20 mm and a pressure of 38 bar. That may be discussed in terms of the high critical velocity for such material. Despite not being able to simulate and calculate particle velocities, a rough approximation in comparison to other face-centered cubic metals can be done. According to the equation proposed by Schmidt et al., critical velocities depend directly on the flow stress, heat capacity and melting temperature and are inversely dependent on material density shows the etched coating; the particle boundary network is revealed in a. Detailed features of the dendrite deformation within each particle are shown in b. Although the substrate was ground slightly before spraying, the interface was not smooth, and clearly showed the rounded profile of the particles deposited. This observation is attributed to stellite being harder than the steel substrate.In the present work, as also reported by other authors, the porosity was more evident in the outer region of the coating, while the inner part showed a relatively dense structure. This might be attributed to a tamping effect at the inner part of the coating, which is the densification of the existing coating layers by peening during the deposition of a new layer.On the top, the lately bonded particles seem to have deformed less, which may be corroborated by the observation of the surface morphology of the coating (b), which is in fact dependent on the mechanical properties of the material sprayed The first impinged particles still find the influence of the mechanical properties of the substrate but, when some layers are already built up, the larger stiffness and hardening of the previously deposited material makes the critical velocity value to be higher. This, combined to the spraying parameter effects as already explained i.e. lower particle velocities at lower particle temperatures and lower substrate temperature at larger distances, etc., might produce spallation and weak cohesion. Such hardening can be illustrated at the work of Levin et al. In addition, direct observation of the cross-section of the optimized coating revealed high compacity; however, a good way to be sure of the internal coating cohesion avoiding interconnected paths is performing open-circuit potential tests ). The values at which the potential was stabilized were found to be much higher than those corresponding to the uncoated specimen, thereby indicating that the coating showed a sufficient degree of compactness to prevent electrolyte penetration. The coating tensile strength was 53 ± 4 MPa and the failure was in a cohesive mode.The HVOF technique has also been used to produce stellite-6 coatings with noticeable structural differences. The occurrence of these differences depends on the type and flux of fuel gases as a result of the inherent melting produced during conventional thermal spray processes. Even in HVOF, the external part of the metallic particles is oxidized during their residence in the jet and subsequent solidification Here we demonstrate the capacity of CGS technology to produce dense stellite-6 coatings. The most relevant factors in CGS within the range of the two-level study were distance and gas pressure, and when increased both led to poorer coating quality. Although the effect of gas temperature in the range studied was not as relevant as that of the other parameters, an increase in this variable enhanced deposition efficiency.Despite a relatively low deposition efficiency, the resulting coatings showed satisfactory adherence and interparticle cohesion, as demonstrated by the open-circuit potential tests. Future research will involve testing the wear- and corrosion-resistance of these coatings in order to facilitate comparison with those produced by conventional thermal spray processes.Active displacement field in the Suez–Sinai area: the role of postseismic deformationBy means of a spherical viscoelastic model of co- and postseismic deformation we compute the postseismic displacement associated with the November, 1995, Mw=7.2, Aqaba (Jordan) earthquake. We compare our results with the observational data obtained by a GPS campaign performed in a wide portion of Sinai between November 1997 and May 1998. Though the original purpose of the campaign was to explain the tectonic features of the region, the displacement values deduced from the GPS observations are hardly reconcilable with any of the proposed tectonic models of Sinai. Our hypothesis is that the detected deformation field could be due more to the postseismic relaxation following the Aqaba earthquake rather than to tectonic movements. Our results show that both GPS observational data and the postseismic simulations predict a compressional regime in the Gulf of Suez though the contraction detected by GPS is generally larger. The best agreement with the data is obtained for an asthenospheric and lower crust viscosity of 1018 Pa s and an absence of aseismic afterslip on the fault plane. We conclude that the contribution coming from the postseismic viscoelastic relaxation of the ductile shallow layers following the 1995 Aqaba earthquake is likely to play an important role in determining the present deformation field in Sinai. The transient postseismic relaxation seems to play a more important role than the secular tectonic deformation.From November 1997 to May 1998 two GPS surveys in the Sinai peninsula have been performed to shed light on the tectonics and kinematics of that area. The GPS network crosses the Sinai peninsula from the Suez Gulf to Elat (Israel, inner Aqaba shore). The data from the two campaigns have shown that Sinai undergoes a large significant motion with displacement rate of the order of 3 cm yr−1 with respect to the African shore of Gulf of Suez, in absence of significant contemporary seismic activity In November 22, 1995 Sinai was struck by the largest event (known as the Aqaba or Nuweiba earthquake) which has occurred along the Dead Sea transform during the last centuries. This event was strongly felt in almost the whole Middle East; it reached a VIII maximum intensity with substantial damage over an area greater than 1000 km2 and was followed by intense aftershock activity with about 200 events of Ml≥4.0 Some GPS surveys, carried out on a network located in Sinai before and after the strong seismic event, estimated 16.6 cm coseismic horizontal displacement at the closest GPS site (DAHA, 26 km from the epicenter, at 246° azimuth) ), whilst, as we pointed out above, the large compressional axis estimated for the Gulf of Suez results in apparent contrast with the widely accepted knowledge about the long-term tectonics of the area.Our hypothesis is that the detected deformation field in Sinai could be mainly due to the postseismic effects of the Aqaba earthquake, namely viscoelastic relaxation of the shallow ductile layers (lower crust and upper mantle asthenospheric layers) and possibly aseismic afterslip on the fault. Our goal in this work is to test this hypothesis computing the postseismic deformation field adopting an appropriate model and comparing it with the GPS-detected field.Postseismic effects after major earthquakes are presently widely recognized as capable of driving deformation field detectable with GPS-INSAR technique and there are several works finding a good agreement with the observational data and synthetic results (e.g. Several geological and seismological investigations assert that the area surrounding the Gulf of Suez displayed, in the past, extensional tectonics with large deformation rate (e.g. The tectonics of the Sinai peninsula and the Gulf of Aqaba is strongly dominated by the active boundaries between the African and the Arabian plates which are separating one from the other. According to the current literature, from Neogene to Late Miocene, this area was subjected to different phases of motion. At the beginning, the north eastward drift of the Arabian peninsula yielded the opening of the Red Sea; subsequently, the opening propagated toward north, along the Gulf of Suez area. In the end, the Suez Gulf opening probably slowed and the stresses of the Red Sea rift were transferred along the Aqaba–Levant area, generating a NNE left shear motion with minor extensional component.The Sinai peninsula has been recognized as sub-plate of the African plate Geological studies show that the oldest movements of the Aqaba–Dead Sea fault zone are surely younger than those in the Suez basin, thus suggesting the end of the extension of the Gulf of Suez and the transfer of the motion along the Aqaba–Levant fault zone about 10 Myr ago ) and tectonic subsidence; on the contrary, the Aqaba–Levant transform system displays a higher rate of motion with geological evidences suggesting an average value of about 8–9 mm/yr The Dead Sea–Jordan fault system extends over about 450 km in an approximately NE direction, from the Gulf of Aqaba toward the thrust components of the Taurus arc. This structure is considered a sinistral transform as a whole, but is broken in a series of en-echelon left lateral strike slip faults that die out to the north by bending toward north-east The GPS data considered in this paper are the horizontal displacements estimated from a GPS network of 12 sites: seven located on the Sinai peninsula, other four on the west shore of the Gulf of Suez and the last in the inner part of the Gulf of Aqaba (the permanent station of ELAT) (see ). Each vector represents the coordinate differences estimated for each site on the local tangent plane, keeping fixed the coordinates of one site of the network.The estimation of the horizontal displacement field comes from the analysis of two GPS campaigns carried out in 1997, from November 20 to December 2, and in 1998, from May 25 to 31 The analysis of the Sinai GPS observations is reported extensively in Riguzzi et al. GPS observation processing by the BERNESE 4.0 software comparison between the two network solutions by using a statistical analysis to evaluate the significance of the observed coordinate differences;computation of the displacement vectors and error ellipses on the local tangent plane at 95% confidence level The analysis performed on the vertical component did not show any significant height difference. On the contrary, the analysis on the horizontal component detected as significant exclusively all the coordinate differences pertaining to the seven sites located on the Sinai peninsula, while the remaining five sites exhibited differences within the errors The 2D vector displacements, their azimuths and the corresponding errors computed on the local tangent plane at 95% confidence level were computed with respect to HURG (For our simulation we use a model of postseismic deformation developed taking into account the effects of spherical geometry, self gravitation, linear viscoelastic rheology of the asthenosphere and lower crust, physical and chemical discontinuity between the elastic shallow layer (crust) and the two viscoelastic layers (lower crust and asthenosphere) In all the following computations we will keep fixed the scalar moment and the focal parameters of the earthquake (those given by the CMT catalogue), the length of the fault ) and we will discuss their consistency with the observational data. The problem of the viscosity of the uppermost part of the mantle and of the lower crust is still unresolved and the current estimates vary by about three orders of magnitude ( (columns 3–7) we show the synthetic postseismic displacement in the time window spanned by the GPS data, computed using our model. The six panels refer to different viscosity and thickness configurations of the lower crust and asthenosphere. We have also considered two different depths of the fault, since this parameter is the less constrained by seismological results Four of the six models are characterized by a lower crust viscosity of 1018 Pa s (models 1–4). This value results from several previous analyses performed for different earthquakes ), the final rates exhibit a modest decay for the first five years after the earthquake. This is an important point, in fact a fundamental feature in order to discriminate between transient postseismic deformation and long-term tectonic motion would be just the extremely different decay times involved. This means that future GPS investigations (performed more than 5 yr after the Nuweiba event) should evidence a decay in the deformation rates in the Sinai–Suez area (incidentally we would note that, effectively, very preliminary results from a new GPS campaign in Sinai indicate a decay in the rates of deformation in that area [Mahmoud, personal communication]).Postglacial rebound analyses and some works on the postseismic relaxation of the major earthquakes of this century found viscosity values greater than 1018 Pa s for the shallow ductile layers, typically ranging from 1019 to 1020 Pa s (e.g. is that, differently from tectonic models and in agreement with the GPS data, all the six models under examination predict a compressive postseismic deformation field across the Gulf of Suez. The magnitudes of postseismic displacements predicted by the «low viscosity models» (, models 1–4) are directly comparable with the detected GPS data while the «high viscosity models» predict much lower relaxation rates, hardly comparable with the detected displacements. The maximum differences between GPS and postseismic data are localized in the western side of the Gulf of Suez where all the African sites are predicted to move in the opposite direction with respect to the observed one. In addition to the considerations expressed above, in this particular area, the presence of the Gulf of Suez, i.e. the separation area between the African plate and the Sinai sub-plate The purpose of this section, keeping in mind the considerations expressed above, is to test the possibility of discriminating between the proposed models in terms of data fitting and possibly to assess the eventual role of other postseismic deformation processes beyond the viscoelastic relaxation (i.e. aseismic afterslip on the fault plane) in determining the final displacement field.To quantify the agreement between the computed displacement field and the observational data, we have computed the chi-square merit function χ2:where XGPS, YGPS and Xtheor, Ytheor are the GPS and postseismic component of the displacement, respectively, ΔXGPS, ΔYGPS are the errors associated with the observations (that we remind have been taken as 2σ) and N=12 is their number. takes into account the quality of the observational data, since the relative contribution of the square deviation associated with a GPS datum with a low uncertainty is increased and vice versa. In column 2 of are shown the chi-square function values for the six models described in . The chi-square function ranges from 1.24 (model 1) to 1.47 (model 6), with a degradation in the quality of the fit of about 50% All the previous considerations have been stated without taking into account any further deformation cause than viscoelastic relaxation, nevertheless we know that also another source of postseismic deformation could be active in the time scale under analysis, namely an aseismic afterslip on a fault plane. Beyond this, also a tectonic deformation field is likely to be active in Sinai (see ). To discern if the presence of these additional deformation engines would affect the agreement between the synthetic and GPS data, for each of the six models we have computed the displacement field associated with a constant-rate aseismic slip on the fault evaluating the impact of this field on the chi-square function. We have also considered the effect of a possible tectonic deformation scenario on our displacement rates. To obtain the displacement rates due to tectonic deformation on the GPS sites we have interpolated the tectonic data field given by Steckler et al. are displayed the results. The contribution of aseismic afterslip in addiction to postseismic viscoelastic relaxation leads to a decrease of the chi-square function only for the high viscosity models 5 and 6 (, column 3). The contribution of the tectonic field leads even to a deterioration of the fit for five of the six models (It is instead noteworthy to observe that four of the six models exhibit a lower value of the chi-square function when the joint effect of tectonic and aseismic displacements (in addition to postseismic viscoelastic relaxation) is taken into account. Some speculations could be made about the fault plane adopted to simulate the aseismic displacement field. A straightforward possibility would be the same plane of the seismic rupture (indeed this is our choice) but alternative choices are possible. In particular the aseismic source might extend to the south much more than the seismic fault inferred for the Nuweiba earthquake. A magnitude Mw=6.1 took place in 1993 in the Aqaba fault, about 50 km south of the Nuweiba fault and the 1993 segment might remain unwelded until 1995 as suggested by the aftershocks distribution of the 1995 event. We have investigated also this possibility imposing an aseismic motion on the plane of the 1993 rupture and alternatively also on a plane connecting the two seismic ruptures. We obtained that for the low viscosity models 1–4 the introduction of this further aseismic motion results in an extremely marginal improvement in the quality of the fit (<1%), while for the high viscosity models 5 and 6 the values of χ2 increase with about 10%. our final results are summarized: in column 2 the minimum chi-square value is reported for the corresponding model of column 1; in columns 3 and 4 the conditions are specified under which this minimum value was obtained. The best value has been obtained using model 2 in presence of the tectonic field and without any contribution due to aseismic afterslip on the fault plane. Rows 5 and 6 of show that to minimize the chi-square function the high viscosity lower crust and asthenosphere models require very high rates of aseismic slip.We have investigated the kinematics engine of the deformation field, detected by recent GPS campaigns, in Sinai. Our speculations started from the observation that the proposed tectonic configuration of the area hardly reconciles with the detected deformation field (both in shape and magnitude of the deformation field). Since that area has been struck by a magnitude 7.2 earthquake in 1995 we have tested the hypothesis of a postseismic contribution to the deformation field. Adopting a model recently developed, we have computed the postseismic displacement field associated with the viscoelastic relaxation of the ductile shallow layers. It resulted in that the compressional deformation field, detected by the GPS campaign and opposed to the proposed tectonic configuration, was in better agreement with the computed postseismic deformation field. The viscosity values of the lower crust and asthenosphere maximizing the postseismic deformation rates at the time of the GPS campaigns are around 1018 Pa s. Even adopting this viscosity value, the postseismic deformation rates show a tendency to be lower than the detected ones especially in the west shore of the Suez Gulf. Stimulated also by this evidence we have investigated the possible role of another potentially important long-term postseismic deformation engine: the aseismic afterslip on the fault plane. Though the presence of the aseismic afterslip improves the quality of the fit in presence of a high viscosity asthenosphere and lower crust the best fit has been obtained by a model with a low viscosity of the ductile layers, namely 1018 Pa s and in absence of aseismic slip. The introduction in our synthetic rates of the small tectonic deformation field, proposed by Le Pichon and Gaulier Sharp lateral viscosity variations in the shallower ductile layers beyond those due to the contrast between oceanic and continental settings.Biasing effects due to a non-linear viscoelastic rheology.The validity of this last explanation would imply that the threshold for the linear behavior of the ductile layer commonly accepted (typically from 1 to 100 MPa, e.g. Ranalli Identification of a friction model for modelling of orthogonal cuttingNumerical approaches to high-speed machining are necessary to increase the productivity and to optimise the tool wear and the residual stresses. In order to apply such approaches, rheological behaviour of the antagonists and friction model of interfaces have to be correctly determined. The existing numerical approaches that are used with the current friction models do not lead to good correlations of the process variables, such as the cutting forces or the tool–chip contact length. This paper proposes a new approach for characterizing the friction behaviour at the tool–chip interface in the zone near the cutting edge. An experimental device is designed to simulate the friction behaviour at the tool–chip interface. During this upsetting-sliding test, an indenter rubs in a specimen with a constant speed, generating a residual friction track. Contact pressure and friction coefficient are determined from the test’s numerical model and are then used to identify the friction data according to the interface temperature and the sliding velocity. These initial findings can be further developed for implementation in FEA machining models in order to increase the productivity.High-speed machining is submitted to economical and ecological constraints. Optimization of cutting processes must increase the productivity, reduce the tool wear and control the residual stresses in the workpiece. Developments of numerical approaches to simulate accurately high-speed machining process are therefore necessary since in situ optimisation is long and costly. To get this purpose, rheological behaviour of antagonists and representative friction models at tool–chip interface has to be studied at very intense plastic strains (from 1 to 5), high strain rates (until 105

s−1), and high temperature (until 1400 K) as encountered during high-speed machining process.Linear friction models (such as Coulomb, Coulomb–Orowan, and Tresca) and non-linear relations A set of different friction testing stand can be used to identify the friction parameters at the tool–chip interface. Pin-on-disc system, which is the most commonly known, does not simulate contact conditions of the machining process. The pin always rubs on the same friction track. The modified pin-on-disc device proposed by Olsson et al. The contact pressure and the plastic strains are evaluated with the finite element simulation of high-speed machining. According to the numerical approaches of orthogonal cutting Two specific zones can be discerned in the tool–chip interface (). A low sliding velocity combined with a contact pressure value higher than 1 GPa is characteristic at the beginning of the cutting. The second one suffers from lower contact pressures levels but a sliding velocity up to the speed of the chip. Contact conditions at the tool–chip interface in the near cutting edge zone (with a low sliding velocity, a contact pressure on the tool tip higher than 1 GPa, and a high interfacial temperature) are not reached with the friction device designed by Bonnet.This paper proposes a new approach to characterize the friction behaviour in these sliding, pressure and temperature conditions. The study is led with AISI 1045 steel and an uncoated carbide tool. The following work is restricted to the first zone near the cutting edge. Many steps are necessary for the friction analysis. Thermo-mechanical parameters of machining process are firstly considered as the characteristic contact conditions to be reproduced on a testing stand. The contact pressure and the interfacial temperature are assessed with the finite element modelling of high-speed machining. The contactor penetration and the specimen temperature are the parameters to be determined in order to perform tests in concordance with the characteristic contact conditions. A numerical model of the test allows us to estimate these friction parameters. Several tests are then performed to provide the experimental friction data. The ratio between the tangential and the normal force is defined as a friction index. The numerical model of the test is required to get the friction coefficient. An iterative method is used to determine Coulomb's coefficient by minimizing the differences between the experimental and the numerical efforts. Tribological data are thus used to define the friction coefficient versus the contact pressure, the sliding velocity, and the interfacial temperature.An upsetting-sliding test (UST) had been previously designed to study the cold forming processes This test is used to simulate the specific contact conditions of the interface zone near the cutting edge. This specific device composed of a moving and a fixed part is set on a standard tensile machine. The moving set-up is supported by the load cell linked to the crosshead whereas the other part is fixed on the tensile machine table. The specimen is positioned on a v-block special stand () and totally clamped. The moving part enables one to carry away the contactor with a relative penetration p into the specimen.Specimen and contactor temperatures are regulated. The specimen is heated by means of an induction coil (a) and the inside temperature, measured by three thermocouples, can reach up to 1525 K. The contactor is heated by a regulated heating cartridge up to 575 K (b). The UST parameters are the relative penetration of the contactor into the specimen, the contactor geometry, the sliding velocity of the contactor, and the contactor and the specimen temperatures.During the test, the contactor penetrates the specimen and slides along its surface with a constant sliding velocity to generate a residual friction track. The sliding velocity is regulated by a hydraulic jack up to 0.5 m.s−1. Both normal and tangential forces are recorded on a computer. The tangential load is measured by the load cell of the tensile machine whereas a special sensor located behind the contactor makes possible the normal force measurement. is a schematic representation of the contactor/specimen contact at halftime of the test.When the test is over, 3D optical surface profile measurements are carried out on the specimen to determine the actual penetration, which will be used for the numerical model of the upsetting-sliding test.This friction test involves the specimen and the contactor, which represent the chip and the tool, respectively. The contactor and the specimen are machined in the tool material and in the workpiece, respectively. The mechanical parameters of the contact (mainly the contact pressure, the interfacial temperature, and the sliding velocity) are adjusted by using the test parameters.Finite elements model of the upsetting-sliding test leads to the simulated contact parameters at the specimen–contactor interface. Considering the high strains involved during this test, an Arbitrary Lagrangian-Eulerian formulation has been chosen to avoid computation problems. A 3D model including the thermo-mechanical interactions has been implemented with ABAQUS explicit formulation. The zone submitted to deformation is only meshed (). The hexagonal C3D8RT elements have been selected in order to enable heat transfer modelling. Smaller elements, located in the contact zone, have a 0.3 mm size.The purpose of this work is to identify friction data according to the contact pressure, the interfacial temperature, and the sliding velocity. In order to obtain relevant interfacial temperature, the heat transfer between the contactor and the specimen is needed. The model includes the heat generation induced by plastic deformation and friction. The interfacial behaviour between contactor and the specimen is modelled by a Coulomb’s friction model. The friction coefficient introduced in the model is set constant for the interface between the contactor and the specimen.A front bulge results from specimen plastic deformations during the friction test. The mechanical work due to plastic deformations is converted into heat by the ratio of the Taylor–Quinney coefficient. This heat source generates a rise in temperature. The heat equation involving the plastic deformations, the heat, and the Taylor–Quinney coefficient is expressed bywith β as the Taylor–Quinney’s coefficient, σm the mean stress, εpl the plastic strain, ρ the density, cp the specific heat, and T the temperature. In agreement with the literature The heat flux generated by friction depends on the shear stress, the sliding velocity, and the ratio of the friction energy converted into heatwhere ϕ is the flux density generated by friction, η is the ratio of the friction energy converted into heat, τ is the shear stress, and x is the displacement. In this work, the ratio η is set equal to 100%. The heat flux due to friction phenomena is divided between the specimen and the contactor in accordance with their thermal effusivities and 60% of the heat flux generated affects the specimen.A Johnson–Cook model (equation below) describes the flow stress of the AISI 1045 steel according to the strain, the strain rate, and the temperatureσ=[A+Bεpl]n[1+Cln(ε̇plε̇0)][1−(T−TroomTmelt−Troom)m]with σ as the flow stress, A the yield strength, B the hardening modulus, εpl the plastic strain, n the hardening coefficient, C the strain rate sensitivity coefficient, ε̇pl the plastic strain rate, ε̇0 the reference plastic strain rate, T the temperature of the workpiece, Troom the room temperature, Tmelt the melting temperature of the workpiece, and m the thermal softening coefficient.The Johnson–Cook parameters come from the works of Jaspers and Dautzenberg . The material flow characteristics are obtained by the split Hopkinson pressure bar. Unfortunately, this testing device cannot provide either high strain rates or high temperatures. The Johnson–Cook parameters are presumed to be reliable for cutting conditions. The thermo-physical properties of the specimen and the tool are summed up in As far the contactor is concerned, the thermo-physical properties of uncoated carbide H13A are chosen in accordance with Kalhori’s works Displacement and thermal boundary conditions used for the antagonists are shown in . The contactor is totally fixed whereas the sliding velocity V is applied to the inflow boundary. The contact is assumed as thermally perfect for the heat transfer computing by taking into account a high thermal conductance (106

K w−1

m−2). Tool boundaries far away from the contact zone are retained at the initial temperature (Tinit). Other surfaces of the workpiece are dealt without any heat loss either by convection or by radiation.The test parameters namely the specimen temperature T and the contactor penetration p are obtained from the finite elements model of the upsetting-sliding test. Several computings are achieved with penetration p ranging from 0.05 to 0.2 mm, specimen temperatures T ranging from 300 to 1000 K, Coulomb’s friction coefficient of 0.2, and a sliding velocity of 0.4 m.s−1.The targeted mean contact pressure temperature can also be defined, thanks to the surface dependent on both penetration p and specimen temperature T. These two last parameters are extracted from the outlines of these two surfaces (). A rise in contact pressure and in interfacial temperature drop are observed with increase in penetration or with decrease in specimen temperature. The upsetting-sliding test parameters are then adjusted from these graphs to simulate the contact conditions of high-speed machining process.Tests are performed in order to determine the friction data according to the interface temperature, the contact pressure, and the sliding velocity. The antagonists are AISI 1045 steel specimen and an uncoated carbide contactor (Sandwick H13A). The numerical simulation of orthogonal cutting with these configuration of materials, for a cutting speed of 100 m.min−1, a feed of 0.1 mm.rev−1, a depth of cut of 3 mm, a rake angle of 0°, and a relief angle of 4°, lead to the values of the contact pressure, the interfacial temperature, and the sliding velocity (Parameters of the UST are then determined from graphs plotted on and from contact conditions described on ) are proposed to study the influences of sliding velocity, penetration, and specimen temperature on friction data. Tests are performed three times each because of scattering.Normal and tangential forces are reported on for the sixth configuration (penetration of 80 μm, specimen temperature of 750 K, and sliding velocity of 400 mm s−1). These plots show the good reproducibility of tests. After a fast rising, strength values become stationary before decreasing when the contactor goes from the specimen. gives the results of average strengths obtained for the three tests of each configuration. Mean values are held from the stationary zones. It can be noted that sliding velocity has a great influence on the frictional index Ft/Fn. It significantly drops when the sliding velocity increases whatever may be the penetration and/or specimen temperature values. As an example, results for a specimen heated to 654 K and tested under a penetration of 71 μm show a decrease in the frictional index from 0.42 to 0.30 (about −30%) when the sliding velocity raises from 200 to 400 mm.s−1 (configuration 1 against 3).The friction coefficient gets also weaker when the penetrations values increase. The frictional index then varies from 0.42 to 0.39 (about −7%) for a specimen temperature of 654 K combined with a sliding velocity of 200 mm.s−1 when the penetration ranges from 71 to 94 μm. The frictional index values are less dependent on penetration than on the sliding velocity. In opposition to the decrease in frictional index observed for increased penetration and sliding velocity, values become lower when the specimens are the most heated. An increase of 40% of the frictional index can also be noted for an increase of about 200 K.These trends are dependent on input parameters of the upsetting-sliding test and the numerical approach of test is needed to analyse contact conditions generated by them on the frictional coefficient.Contact conditions such as contact pressure, interfacial temperature, sliding velocity, and Coulomb’s friction coefficient are determined with the numerical model of the upsetting-sliding test. The optimal friction coefficient of the Coulomb arises from an iterative method, which minimizes the gap between the experimental and the numerical by the following equation:f=(Ftsim−FtexpFtexp)2+(Fnsim−FnexpFnexp)2+((Ft/Fn)sim−(Ft/Fn)exp(Ft/Fn)exp)2where f is the function to minimize taking into account the experimental forces (FtexpandFnexp), the calculated ones (FtsimandFnsim), and also the ratios of them, which correspond to the frictional index.This part deals only with the numerical analysis of the test according to the configuration number 6. These conditions are a penetration of 84 μm, a sliding velocity of 400 mm.s−1, and a specimen temperature of 752 K. shows the measured experimental forces and the numerical ones, which are obtained for an optimal friction coefficient (μ=0.24).Local contact variables like contact pressure, interfacial temperature, and sliding velocity can now be extracted from the numerical modelling., for the sixth configuration. The maximum contact pressure located in front of the contact is around 1.5 GPa and the average contact pressure is about 1 GPa.The temperature fields on specimen and contactor are quite similar and the maximum temperature is anyway located at the back of the contact. Maximum temperatures of 1185 and 1120 K are observed on the contactor and on the specimen, respectively. The average of temperatures in the contact zone reaches 835 K for the contactor against 925 K for the specimen. This agrees with an approximate rise in temperature of 540 K for the contactor and of 175 K for the specimen. The mean interfacial temperature of 880 K, which is equal to the average of mean surfaces temperatures of antagonists, thus results from the modelling of the sixth configuration. shows also the heterogeneity of the sliding velocity field. At the end of the contact, the sliding velocity reaches the displacement speed (400 mm s−1). The average sliding velocity is about 340 mm s−1. This drop of 15% compared with the contactor displacement speed is related with the adhesion phenomena in the contact and this phenomenon has been also observed by other authors Finally, numerical modelling achieved with an optimal frictional coefficient of 0.24 provides for this configuration a contact pressure of 1 GPa, an interface temperature of 880 K, and a sliding speed of 340 mm s−1.Coulomb’s friction coefficient can be formulated according to the contact pressure, the interfacial temperature, and the sliding velocity by this frictional lawwhere c1, c2, c3, and c4 are the constants to be determined.Determinations of contact parameters and optimal friction coefficients are carried out again for each configuration and enable to quantify the constants of the proposed friction law. gives these coefficients for the studied configuration.Analysis of this equation shows clearly the influence of contact parameters on the value of friction coefficients. It decreases further when the pressure and the sliding velocity are higher. On the contrary, the friction coefficient takes a higher value when the interfacial temperature increases. These trends of variations have been observed during friction tests performed on the couple 40CD4 steel/carbide ISO P30 This paper has presented the upsetting-sliding test specially dedicated to the characterization of the friction coefficients along the tool–workpiece contact in the forming processes. This tribometer enables one to reach the contact conditions at the tool–chip interface in the near cutting edge zone. This device has been applied to the case of the machining of AISI 1045 steel with an uncoated carbide tool in dry conditions. Several tests have been performed that have clearly shown the influence of the displacement speed and the contactor penetration on the friction index (Ft/Fn). A significant drop of the friction index is observed when the speed decreases. The results of the friction index are also lower when the penetration increases.A numerical model of the upsetting-sliding test enables one to extract the contact conditions such as the contact pressure, the interfacial temperature, the sliding velocity, and Coulomb's friction coefficient. A friction law according to variables like contact pressure, interfacial temperature, and sliding velocity has been proposed and the constants have been identified. Finally, the interfacial law can be implemented on a finite element model of machining in order to improve the numerical prediction of dry machining of AISI 1045 steel.The original contribution of this work consists in determining a friction law by taking into account the two zones in the tool–chip contact. The present work is limited to the zone near the cutting edge for which low sliding velocity combined with high pressure value is observed. The sliding velocity obtained with the upsetting-sliding test does not exceed 0.5 m.s−1. A specific device has been designed and set on a high-speed machining machine to study the frictional phenomena with velocities up to 1000 m min−1. Other works deal currently with the simulation of the friction behaviour at the tool–chip interface moving away the cutting edge.Experimental and numerical investigation of die designs in biomass pelleting and the effect on layer formation in pelletsDesign parameters of a pellet mill die for pellet production are essential for running optimal pellet production in terms of energy consumption and quality of the pellets. In this study, the effects of the countersink angle and depth are investigated through experimental tests and Computational Fluid Dynamics (CFD) simulations. Inlet die designs with angles 0°, 60°, and 100° and three different depths, were tested via single pelleting tests with spruce. A new design parameter, AR, is suggested for comparison of the dies performances. The parameter is derived from the die's surface area, and is the ratio of the die's inlet area vs. total surface area and values tested here ranged 0.35 to 1.Specific energy consumption and mechanical pellet durability were measured experimentally, and the feedstock layer profiles in pellets were qualitatively analyzed via image processing. The layer profiles in the pellets were simulated with a CFD model using a simple Bingham viscosity model. The model was validated by comparing the simulated and experimentally obtained layer profiles. The results show that the lowest energy consumption was obtained with a 60° countersink and an AR value of 0.6–0.8. Furthermore, an AR value in this range were found to be optimal with respect to pellet durability. Analysis of the layer profiles shows interesting differences in the layer profiles of the pellets, and evaluation of the kurtosis of the layer profiles suggests that this can be used to predict the pellet durability and, thereby, the quality of the die design.Ratio of active and transition area to the total surface area of the die [−]Axial velocity in the press channel [ms−1]Radial velocity in the press channel [ms−1]y-coordinates of the data points for the layer profileLongitudinal axis of the press channel [−] illustrates the general design of a press channel, which consists of a conical countersink with the inlet angle β and depth h, and a cylindrical channel with the diameter d and length l. In the pellet press, feedstock is compressed between a roller and the rotating die. The feedstock is pressed into the press channels in layers, causing each pellet to consist of multiple layers of compressed feedstock. also shows a conceptional illustration of the feedstock layers in the die press channel, where a layer is formed each time a new layer of feedstock is pressed into the press channel.The size of the countersink is limited by the spacing between the openings of the press channels in the die. illustrates a sectional view of a die surface, where the press channels are distributed in a hexagonal pattern with spacing X. The area designated by the dotted red line represents the total area that geometrically belongs to the centre press channel. The total area can be divided into three subareas; active, transition, and an inactive area (, for a single press channel, the active area is the cross-sectional area of the channel, the transition area is the projected area of the countersink, and the inactive area is the remaining area. The size of the transition area is directly correlated to the dimensions of β and h of the countersink. Industrial ring dies are typically designed to have an active area composing 30–40% of the total area.From an industrial point of view, the share of active area is a tradeoff between having a high active area, while still retaining sufficient die strength to resist the compressional force that appears between die and roller during pelleting. This tradeoff is based on the assumption that high compressional forces appear between the roller and the inactive areas since this feedstock is pressed towards the nearest press channel.Research studies of the pelleting process have shown how the process temperature, moisture content, feedstock particle size, etc., affect pellet durability and energy consumption of the pellet press (). In addition to process and feedstock parameters, the effect of the die design has been researched, where especially the length to diameter ratio of press channels has been highlighted as a key process parameter ( studied the energy consumption in experimentally single pelleting tests, and found that 74% and 66% of the energy consumption for beech and pine are allocated for pressing the feedstock through the inlet. Similar to their findings, , pp. 550–558) found from 1D simulations of single press channels that 50% of the energy consumption of 0.1491–0.1874 J kg-1, corresponding to 37–48 kWh t-1, were consumed within the upper 4.5 mm of four different press channels. The press channels were all 50 mm long and 6 mm in diameter, where one channel was a pure cylinder, and the other had countersink designs. The energy consumptions reported by , pp. 550–558) thus showed an increase of 26% from the press channel consuming 37 kWh t-1 to the press channel consuming 48 kWh t-1, and even higher relative differences were observed for the pelleting pressure.In addition to the studies of energy consumption in the countersink of the press channel, a few studies have provided indications of the countersink's effect on mechanical pellet durability. From single pelleting tests of refuse-derived fuel, found that pellets produced in dies with β=28o had a higher durability and lower pelleting pressure compared to pellets produced in dies with 0°, 4° and 14° countersinks. The higher durability of the pellets produced in the wide countersink was explained by the feedstock being more interwoven, compared to pellets from the more steep countersinks. Similar results were found in a study by also found that pellets produced with the β=37.6° die were stronger and better bonded than pellets from the cylindrical channel. The few previous studies of the countersink angle have not been continued in the studies of the countersink depth, h, and its effect on the pelleting process (The use of Computer-Aided Engineering (CAE) tools in published research of the biomass pelleting process is minimal. Whereas other and similar processing industries, such as metal extrusion (), often use Computational Fluid Dynamics (CFD) for simulations and optimisations. Simulations of flow fields in all types of applications can enable optimizations and provide a better understanding of how different parameters affect the process. This may also apply to the pelleting process, where experimental observations inside the pellet press between die and roller are almost impossible due to the harsh environment. The difficulties of doing these observations may be the reason why the feedstock motion between die and roller, and its flow into the press channels, have not been studied. To the knowledge of the authors, the same applies to the interweaving of fibres and its effect on pellet durability, which are not apparent in the scientific literature.This contribution is intended to provide a better understanding of how the countersink inlet in dies affect the pelleting process in terms of energy consumption and durability of the pellets. The study is based on experimental single pelleting tests using spruce, where seven different countersink inlet designs are analyzed in terms of energy consumption and pellet durability. Also, a method of investigating the layer formation in pellets is presented, where the layer profiles in pellets are evaluated from image processing of photographs of pellet cross-sections. Via qualitative analysis of the pellets, a correlation between the layer profiles, the pellet durability, and the die design is set up.Using CFD, simulations of the feedstock motion in the dies are performed. The presented CFD model is validated with the feedstock layer shapes derived from the image processing analysis. The CFD simulations are single-phase simulations with a simplified Bingham plastic model to model the viscoplastic behavior of the wood fibres. With the CFD model in the present study, countersink designs can be assessed in terms of producing pellets with feedstock layers that can facilitate high durability. Thereby it may facilitate the optimisation of die designs and introduce layer profiles in pellets as a new parameter in terms of understanding the pelleting process and differences between different die designs.The CFD simulations in the present study were performed in Ansys Fluent 19.0. The model geometry was set up as a 2D axis-symmetric domain representing the void of the single pelleting setup used in the experiments. The setup and dies are described in detail in section illustrates the void geometry of a die used in the simulations and experiments, with the applied boundary conditions for the simulation.The models solve the continuity equation in Eq. , which are written in cylindrical coordinates.ρ(vrδvrδr+vzδvrδz)=−δpδr+η[1rδδr(rδvrδr)−vrr2+δ2vrδz2]ρ(vrδvzδr+vzδvzδz)=−δpδz+η[1rδδr(rδvzδr)+δ2vzδz2]), z and r are the axial and radial orientation of the press channel, ρ is the feedstock density, vz and vr are the axial and radial velocity, η is the non-Newtonian viscosity, and p is the pressure.In this study, the compressed feedstock was assumed to be an isotropic continuum, and in terms of viscosity, its constitutive behavior was modeled as a simplified Bingham plastic with the yield stress, τ0 (). The Bingham model is a commonly used idealisation of viscoplastic fluids (). The constitutive model of the pelleting feedstock is based from ideas developed from simulations of powder flow, where the Drucker–Prager yield criterion have been used (). The yield stress criterion defines the amount of shear stress that a material can sustain before plastic deformations appear. Comparable to viscosity models in fluid dynamics, the yield criterion in this study is treated as a constant yield stress, which is a characteristic of the Bingham model. When the feedstock is exposed to shear stresses below its yield point, it appears as a rigid solid, while above the yield point, it behaves as a fluid. The ideal Bingham fluid is discontinuous at the point of the yield stress, which causes computational challenges when solving the interface between solid and fluid zones (). The issues of discontinuity have been solved by applying a bi-viscous model, where a critical shear rate is introduced to make the model continuous between the solid at fluent state (The intention of the present model was to simulate the effect of the die geometry on the feedstock layer profiles in the press channel. Therefore, the Bingham model was reduced, so the viscosity in the Bingham model was set to zero, leaving the viscosity model to depend only on τ0. The viscosity model was calculated via Eq. , where γ˙ is the shear rate, and γ˙cis the critical shear rate (η={τ0γ˙forγ˙≥γ˙cτ0(2−γ˙/γ˙c)γ˙cforγ˙<γ˙cThere is no exact definition of how to determine the magnitude of γ˙c, but it needs to be small enough to reproduce the flow behavior, but large enough to guarantee numerical stability of the simulation (As no experimental methods are capable of determining the value of τ0in the present study, the value was determined by computer optimisation. The applied settings for the CFD simulations are listed in The models were discretized with structured hexahedral elements. To ensure grid independence, a surface integral of the inlet pressure was calculated for different mesh sizes, until a stable value was reached. The coupled solver was used for the simulations, together with a second order and second order upwind scheme for the pressure and momentum equations.The pelleting process involves both static and dynamic friction effects caused by the start-stop motion of the compressed feedstock in the die (). However, to reduce complexity, the transient effects were neglected, and the models were set up as steady-state simulations where the inlet velocity of feedstock is set to a constant rate, equal to 1.25 mm s-1, which is the velocity of the pressing piston in the experimental tests.In terms of the wall treatment, the feedstock was assumed to move as a plug, in the cylindrical part of the press channel, causing no velocity gradients. To model this phenomenon, a slip condition with a wall shear stress, τw, was applied to the wall of the press channel. The magnitude was based on the assumption that the pellet moves as a plug in the press channel, and therefore τw was set to be less than the yielding stress, τ0. The method of applying wall slip conditions in fluid flow analysis is commonly used for viscoplastic fluids (). The walls upstream of the conical inlet to the press channel were also modeled with a slip condition with the wall shear stress was set to zero. An isothermal condition was assumed for the model, thus frictional heating in the die was neglected.The experimental work presented in this paper is performed at the Department of Energy Technology, Aalborg University, Esbjerg, Denmark.Spruce (Picea abies) was used as feedstock for the pelleting tests. shows the particle size distribution of the feedstock. The particle size distribution was analyzed by vibrational sieving using a 150 g sample for 10 min with the following sieve sizes: 0.125 mm, 0.25 mm, 0.5 mm, 1 mm, 1.4 mm, and 2 mm.The moisture content of the spruce was adjusted to 15% dry basis, by adding water to the feedstock and after that, it was stored in a fridge at 5° C for 48 h. The final moisture content of the feedstock is 15.3% d.b., which is measured by drying a 50 g sample at 105° C for 24 h.In order to analyse the layer profiles in the pellets, two spruce samples coloured with water-based ink. Feedstock samples of 100 g was moistened with 100 ml red and blue coloured ink, and thereafter they were dried at 105° C for 24 h. The red colour was carmine with E120, and the blue was brilliant blue E133 from the European codes for substances used in food. The moisture content of the dried samples was adjusted to 15% d.b. similar to the uncoloured spruce. shows photos of both coloured and uncoloured spruce samples, where it can be seen that the sample coloured with the blue ink, appears to green after drying.Pellets were produced using a LLOYD LR50K mechanical press. The pelleting tests were performed in a single pelleting die setup, designed for continuous pelleting and manufactured for the present study. illustrates the single die setup with exchangeable die system, where a and b illustrate the complete setup and c and d illustrate the single dies. The diameter of the pressing piston in b is 10.1 mm, which gives an active area of 35.3%, which is equivalent to industrial ring dies, and similar to values that have been used in previous single pelleting tests (The die setup was made from the steel type S355. The single dies were designed to have different countersink angles and depths, and lists the design parameters of the dies used in the test. The countersink depths, h, were selected to test different ratios of the inlet and transition area vs. total area. For this purpose, a design parameter for the area ratio on the die surface, AR, was calculated for the dies via Eq. . The parameter was based on the areas that are illustrated in , where the total area was the sum of the active, transition, and inactive area per press channel.The pelleting tests are performed according to the procedure used by . The die setup was heated to 130° C during the tests, to create conditions similar to those in industrial pellet mills. The compression speed of the pressing piston was 75 mm s-1, and the piston was stopped 1.00 mm above the die surface when pressing the feedstock layers into the die.The dies were tested once, where each test included 19 piston punches. First, 14 layers each consisting of 0.30 g uncoloured spruce are pressed into the die, which produces a total of six pellets for each die, where each pellet consists of two layers. After pressing the 14 layers of uncoloured spruce, another five 0.10 g layers of coloured spruce were pressed into the die to evaluate the shape of the feedstock layers in the die. The procedure for testing one die was:Layer 1–2: 0.30 g uncoloured spruce layers, which filled the die.Layer 3–8: 0.30 g uncoloured spruce layers, which were used for reaching a steady pelleting pressure. The three pellets produced from these layers were not used for durability analysis.Layer 9–14: 0.30 g uncoloured spruce layers, which were used for measuring pelleting pressure and specific energy consumption. The three pellets produced from these layers were used for the durability analysis.Layer 15–19: 0.10 g coloured layers, which shifted between red and blue. These layers were used for creating coloured layers in the die, for evaluation of the layer profiles.Pelleting pressure, energy consumption, and pellet durability were measured as an average of the six layers 9–14. The pelleting pressure was evaluated at the peak pressure between the static and dynamic friction regime, where the motion of feedstock in the press channel was initiated. Energy was measured as mass-specific energy consumption, where the energy was calculated by numerically integrating the recorded force vs. displacement of the press piston (The durability of the pellets was measured with an Andritz pellet tumbler, certified for ISO 17831-1:2015 (). The three pellets produced of the layers 9–14, were tumbled one at the time for 10 min at 50 PM, which has been proven to be a valid method of measuring the durability of single pellets (The layer profiles in the pellets were evaluated from the coloured feedstock layers (layers 15–19). After pressing the layers into the die, the coloured feedstock sat the die press channel as a cast. The casting was then ejected by pressing the compressed spruce from the back of the die. The feedstock cast was embedded in epoxy resin and hardened for 48 h to prepare it for further processing. The embedded castings were then sanded until a cross-sectional view of the feedstock layers was obtained.The images of layer profiles were processed in Matlab. illustrates the steps in the image processing, where d shows the filtered binary image. Based on the RGB colour scale, binary images of the pellets were generated by cropping the green layers from the image. A filter was then applied to the binary images to remove all minor areas, so only the primary layer structures appeared.The average specific energy consumptions of the tested dies are plotted in a, where the error bars represent the standard deviation.a, the specific energy consumption of the β=100o dies was higher than the β=60o dies for all three values of AR, while the energy consumption of the blank die, β=0o, was between the β=60o and β=100o dies. The standard deviation of the β=100odies were higher compared to the β=60odies. a also shows that the energy consumption for the β=60odies decreased when AR increased from 0.60 to 0.80, while the die with AR=1.00 had an energy consumption similar to the 0.80 die. For the β=100o dies an opposite effect for the ARvalue was observed, where the die with AR of 1.00 had the highest energy consumption.b shows the results of pellet durability measurements. The pellets with highest durability were produced in dies with AR of 0.60 and 0.80, while the two dies with AR=1.00 produce pellets that were slightly less durable. The blank die, with AR of 0.35, produced the pellets with the lowest durability. The durability of pellets produced in dies with β=60o was slightly higher and more consistent for AR of 0.80 and 1.00 compared to the β=100o dies. However, the effect of the countersink angle on pellet durability was relatively low compared to the effect of AR. During pellet tumbling, it was observed that all three pellets produced in the blank die broke into two smaller pellets, while all other pellets remained intact.The raw photos used for analysis of the pellets layer profiles are shown in shows the layer profiles that were found via image processing of the pellets produced in the tested dies. The layer profiles of the three dies with β=60o are illustrated in a, and the β=100o dies are illustrated in For dies 1, 2, and 4, which are the dies with the lowest values of AR, areas with stagnant feedstock appeared on the inactive area at the top of the die inlet, which was seen by the presence of uncoloured feedstock. The boundary of these areas indicates that the shear stress at these locations exceeds the yielding stress of the feedstock. It is also noticeable that in the countersink inlet of die 6 and 7, both with β=100o, stagnant regions with uncoloured feedstock were apparent. The stagnant areas in the countersink generates a secondary β angle, that were defined by the boundary stagnant and moving feedstock. shows a pellet produced in the blank die and die no. 4 (β=60o and AR=1.00), before and after tumbling. By comparing the end shapes of the two pellets, before and after tumbling, it can be seen that more feedstock was released from the pellet produced in the blank die after tumbling, compared to the pellet produced in die no. 4. The end profiles of the pellets, after tumbling in , are somehow similar to the layer profiles produced by the same dies in b. For the pellet produced in die no. 4, the breaking profile appears to follow the layer profiles of the pellet, and no significant differences in the shape of the pellet end were observed before and after tumbling, resulting in better durability. The observation of the parabolic breaking profiles of the pellets, were similar to the profiles found by , where they found the breaking profile of pellets produced in a pellet press, to be affected by the countersink inlet of the die. shows results from the CFD simulations of die no. 2. The simulated layer profiles in the die are shown in b, which shows the streamlines coloured by the feedstock retention time. The simulated layer profiles were derived from the position of the feedstock across the press channel at the retention time before the feedstock exits the model domain. a illustrates the velocity contours of die no. 4, where it can be seen that the feedstock moves as plug flow in the cylindrical part of the press channel. This can also be seen in c, from the shear rate contours, where the dark blue areas are the solid zones, obeying γ˙<γ˙c. Comparing the experimental result of die no. 2 in b and the simulated shear rates, a high shear rate appear on the boundary where the stagnant feedstock above the countersink inlet was observed in the experiments. Also the velocity contour shows a very low velocity in this zone.The presented CFD model was validated by comparing plots of the simulated and experimental layer profiles of the pellets. These plots are shown in . Generally, the CFD models were capable of reproducing the layer profiles of the seven dies. However, as seen on the photos in , the pellet layers vary from layer to layer, which likely is to be caused by the feedstock not behaving as a continuum due to the feedstock being granulate with varying particle sizes.The durability of pellets is related to different types of inter-particular bonds of particles in pellets (). Calculation of these bonds is highly complex, and no calculation procedure for particle bonding strength in biomass pellets has been developed for CAE simulation tools. In this study, durability was neither simulated nor calculated. Instead, correlations between the shape of the simulated layer profiles, the die's AR value, and the pellet durability are presented. The shape of the pellet's layer profiles was quantified by calculating the kurtosis, Kurt. The parameter is calculated via Eq. , pp. 89–110), by assuming the layer profile is an upward facing distribution., Yi is the y-coordinates of the data points for the layer profile, Y¯ is the mean of the y-coordinates, N is the number of data points, and s is the standard deviation of the profile distribution. shows the calculated kurtosis values for the layer profiles, the pellet durability, and the AR values. In a, the layer profile kurtosis, and pellet durability data are plotted, and a 2nd degree polynomial function fitted to the data points with r2 = 0.73. The correlation shows that the highest durability was produced from the layer profiles with a kurtosis of 2.00–2.05. The pattern of the data in b, where the highest durabilities were observed for AR in the range 0.6–0.8.b shows the corresponding values of kurtosis and AR, and a fitted linear function with r2 = 0.72 and a p-value = 0.016, showing that there is a significant relation between AR of the die design and the layer profile kurtosis.This paper presents results that gives new insight to the effects of the die countersink, and how it affects the pellet durability and energy consumption.By presenting a new die design parameter for the area ratio of the active and transition area on the die surface, AR, seven die designs with different inlet designs were selected and tested.The results show that the three dies with β=60o consume the least energy. Energy consumption was relatively low for the 60° countersinks with an ARvalue of 0.80 and 1.00, and relatively high for the 100° countersinks. The energy consumption for the die without a countersink was in between the level for the 60° and 100° countersink dies.The presented CFD model is one of the first contributions, if not the first, to apply this technique to simulate feedstock motion in press channels. The simulated layer profiles in the pellets qualitatively match the profiles found in the experiments. A linear relation was found between the die's AR and the kurtosis of the layer profiles, and the highest pellet durability was measured for the pellets with a layer kurtosis of approximate 2.00–2.05.With the presented findings, experimental analysis and CFD simulations of layer profiles in pellets can be used for evaluating countersink designs in terms of their effect on pellet durability.The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.Generation and characterization of carbon nano-fiber–poly(arylene ether sulfone) nanocomposite foamsIn this study, carbon nano-fibers (CNFs) were used to increase the compressive properties of poly(arylene ether sulfone) (PAES) foams. The polymer composite pellets were produced by melt blending the PAES resin with CNFs in a single screw extruder. The pellets were saturated and foamed with water and CO2 in a one-step batch process method. Dynamic mechanical thermal analysis (DMTA) was used to determine the reduced glass transition temperature (Tg) of the CNF–PAES as a result of plasticization with water and CO2. Sharp transitions were observed as peaks in the tan

δ leading to accurate quantitative values for the Tg. By accurately determining the reduced Tg, the foaming temperature could be chosen to control the foam morphology. Foams were produced which ranged in density from 290 to 1100 kg/m3. The foams had cell nucleation densities between 109 and 1010

cells/cm3, two orders of magnitude higher than unreinforced PAES foam, suggesting that the CNFs acted as heterogeneous nucleating agents. The CNF–PAES foam exhibited improved compressive properties compared to unreinforced PAES foam produced from a similar method. Both the specific compressive modulus and strength increased by over 1.5 times that of unreinforced PAES foam. The specific compressive strength of 59 MPa for the CNF–PAES foam is similar to that of commonly used high performance structural foam, poly(methacrylimide foam).The development of lightweight, structural materials is important in aerospace, automotive, marine, rail, and wind energy applications In order to increase the strength to weight ratio of polymers, microcellular foams were developed In an effort to improve the mechanical properties of microcellular foams, microcellular nanocomposite foams have been produced by combining nano-clays and polymer matrices, including polystyrene The dispersion and exfoliation were also important for increasing the tensile and compressive properties of the nanocomposite foam. Two studies were performed, one involving polystyrene and one involving PMMA. The tensile properties of the nanocomposite foams were lower than the unfoamed polymer, regardless of the clay dispersion, even if the tensile properties were normalized to account for the lower density. However, the tensile properties were improved when compared to the neat polymer foam as long as good dispersion of the clays was observed While nano-clays have been shown to improve the mechanical properties of several microcellular foams, incorporation of the nano-clays into polymers with high glass transition temperatures (Tg) is difficult. Nano-clays are often organically modified to enhance the dispersion in polymer matrices Carbon nano-fibers have also been incorporated into polymer matrices and then foamed using supercritical carbon dioxide as the foaming agent. Shen et al. Both tensile and compressive properties of microcellular polystyrene foams which were reinforced with carbon nano-fibers (1 and 5 wt.% loading) were reported Foams of poly(arylene ether sulfone) (PAES) have demonstrated relatively high compressive properties. Microcellular foams of PAES were first produced by Sun et al. The objective of this research was to determine whether foams produced from CNF reinforced PAES over a range of foam densities, would exhibit enhanced compressive properties, tensile modulus, and impact strength compared to the neat PAES foam A second objective of this research was to more fully exploit the use of the blowing agents of water and CO2, which both plasticize the polymer, to control the cell size and density. In particular, dynamic mechanical thermal analysis (DMTA) is utilized to more accurately determine the suppression of the Tg, when compared to differential scanning calorimetry, and thereby more carefully select temperatures at which foaming occurs.Poly(arylene ether sulfone) (PAES, Radel® R-5800) was generously supplied by Solvay Advanced Polymers (Alpharetta, GA). The glass transition temperature (Tg) and density of the polymer were 220 °C and 1.29 g/cm3, respectively. Heat-treated, vapor grown carbon nano-fibers (PR-19-XT-LHT) were obtained from Pyrgograf Products (Cedarville, OH). The fibers had an average diameter of 150 nm and a length of 50–200 μm. Carbon dioxide was obtained from Airgas, Inc.Prior to melt blending, the PAES pellets and carbon nano-fibers were weighed and dry mixed with an industrial blender. The mixture was dried at 100 °C for 18–24 h under vacuum to remove the moisture. The dried PAES and carbon nano-fibers were compounded with a Killion extruder (L/D = 18, barrel diameter = 25.2 mm, and variable screw diameter from 16.6 mm at the feed to 21.45 mm at the exit) with a temperature profile of 310 °C–330 °C–350 °C, a die temperature of 350 °C, and screw speed of 25 rpm. A 3 mm diameter capillary die was used to produce a strand. The strand was drawn down to a diameter of 1 mm, cooled in a 1 m water bath, and fed into a pelletizer.The PAES foams were produced using a one-step batch process method. A cylindrical stainless steel mold measuring 3.0 cm in diameter by 12.5 cm in length was filled with the PAES resin and liquid water (a 2:1 w/v ratio was used for polymer:water). The mold was placed inside a pressure vessel which was sealed and charged with a predetermined amount of carbon dioxide (4.5 MPa). The pressure vessel was heated to 265 °C causing the pressure to increase to between 10 and 11 MPa. A saturation temperature of 265 °C was used to facilitate the sintering of the pellets during the saturation process, yielding a foamed specimen without weld lines after the foaming process. The gas was allowed to diffuse into the PAES for 1 h. The temperature was decreased to the desired temperature (165–227 °C), and the pressure was increased to 10.3 MPa using a high pressure pump. The pressure vessel was held at the desired temperature for one hour to assure full saturation. The pressure was rapidly released (less than 2 s) and the mold was removed from the pressure vessel. The mold was allowed to cool to room temperature before removing the foamed specimen.Differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and DMTA were conducted on CNF–PAES samples which had been saturated with water and carbon dioxide. CNF–PAES was saturated with scCO2 and water at 265 °C and 10–11 MPa for 1 h. The temperature was cooled to 220 °C and pressure regulated to 10.3 MPa, and the sample was saturated for an additional hour. The temperature was cooled to room temperature to eliminate the loss of blowing agents due to foaming, and the CNF–PAES was removed from the vessel. The saturated specimen was immediately tested upon removal from the pressure vessel. However, experiments proved that no appreciable loss of blowing agents occurred when the saturated specimen was subjected to ambient temperature and pressure for up to an hour after release.CNF–PAES plaques were compression molded, prior to saturation, for DMTA testing. A Carver Laboratory Press was used to produce 2 mm thick sheets of CNF–PAES. The polymer pellets were placed in a rectangular mold and placed inside of the press, which was heated to 300 °C. A pressure of 11.5 MPa was applied to the mold for 10 min. The mold was cooled to room temperature, and the plaque was removed.A DSC (TA Instruments, model Q1000) was used to determine the Tg of the samples. Scans were conducted under nitrogen from −20 °C to 260 °C at a heating rate of 10 °C/min. High volume DSC pans with rubber seals (TA instruments) were used to minimize the loss of blowing agents during testing.A TGA (TA Instruments, model Q500) was used to determine the amount of blowing agents present in the PAES resin. Samples were run from 25 °C to 600 °C at a heating rate of 10 °C/min in a nitrogen atmosphere.DMTA was performed on a Rheometrics RMS-800. Strips measuring 45 mm long, 4 mm wide, and 2 mm thick were cut from the plaque of CNF–PAES that was saturated with water and CO2. A dynamic torsional test was conducted at a frequency of 1 s−1 and 1% strain leading to the measurement of the storage (G′) and loss (G″) moduli from which the tan

δ was determined as a function of temperature from 50 to 240 °C.The foam density was determined using the water displacement method. A foam specimen was weighed and submerged in water. The displaced water was measured to determine the volume of the foam. Because the foam has a thin skin layer on the surface and a predominately closed cell structure, water uptake is negligible during the measurements.The cell size and structure of the foamed polymer were determined using a Leo 1550 field emission scanning electron microscope (FE-SEM) operated at 5 kV. The foam specimen was freeze fractured and sputter coated with 20 nm of gold. The SEM images were analyzed using ImageJ (National Institute of Health) image processing software. Typically, micrographs containing 25–50 cells were used to determine the average cell diameter and 100–200 cells were used to determine the cell nucleation density.The cell nucleation density, No, was calculated using the method reported by Kumar and Weller and given by Eq. , n is the number of cells in the micrograph, M is the magnification, A is the area micrograph in cm2, and Vf is the void fraction of the foam. Vf can be estimated from Eq. , where D represents the average diameter of the cells.The tensile modulus of the foam was determined using an Instron 4204 and ASTM D638 was used as a guide for testing. Due to sample size limitation the ASTM test method was not followed exactly. Five rectangular samples measuring 45 mm in length, 10 mm in width, and 3 mm in thickness were cut from a large specimen of the PAES foam. The gauge length was set to 20 mm and the samples were tested at a constant speed of 1.27 mm/min. The strain was calculated from the displacement of the crosshead. The modulus was determined by applying a least-squares fit through the initial linear region of the stress–strain curve. The modulus represents an average of five foamed specimens.The compressive properties of the foam were measured using an MTS (model 826.75) 50,000 lbs servo hydraulic test system. ASTM D1621 was used as a guide for testing. However, due to sample size limitations, the test method was not followed exactly. Five cylindrical samples measuring 30 mm in diameter and 40 mm in length were cut from a large specimen of the PAES foam and the foam properties were determined from the average of the five samples. A lathe was used to cut the samples to ensure the cuts were perpendicular to the cylinder wall. The samples were compressed at a rate of 2.5 mm/min. The strain was calculated from the displacement of the crosshead and the modulus was determined by applying a least-squares fit through the initial linear region of the stress–strain curve.The impact strengths of the foams were determined using ASTM D256-06a as a guide. Five samples measuring 63 mm long, 12.7 mm wide, and 3.2 mm thick were cut from a large specimen of the PAES foam. A sharp notch was cut into the sample using a Tinius Olsen Model 899 specimen notcher (Horsham, PA) turning at a high rotational speed. The notched specimens were tested using a Tinius Olsen 897 machine (Horsham, PA). Because the specimens were thinner than the ideal ASTM thickness, care was taken to ensure the samples did not buckle during impact.The production of CNF–PAES foams using water and CO2 as the blowing agents and the associated mechanical properties are addressed in three parts. First, the amount of blowing agents absorbed under various conditions and their plasticization of the CNF–PAES are considered. Secondly, based on the information obtained in the first part of the research, the conditions for foaming of the CNF–PAES to obtain various degrees of density reduction and cell size are discussed. In particular, results from DMTA helped to refine the foaming process by quantifying the plasticization of the CNF–PAES with the water and CO2. By understanding the thermal transitions, foams were produced by releasing the pressure at varying temperatures to control the cell morphology and foam density. We then conclude this section with a presentation of the mechanical properties obtained for the CNF–PAES foams of various morphologies (cell size and densities).Thermogravimetric analysis was conducted to determine the amount of water and CO2 that diffused into the CNF–PAES polymer composite during saturation. In order to induce a large thermodynamic instability during foaming, a large solubility is desired that ∼7.6% of water and CO2 were able to diffuse into the CNF–PAES matrix during the 2 h saturation time, at 10.3 MPa. Similar amounts of water and CO2 were able to diffuse into the neat PAES DSC was used to determine how much the Tg of the CNF–PAES polymer composite was reduced by the presence of the 7.6% water and CO2. VanHouten and Baird ) reduce the Tg of the CNF–PAES to approximately 160 °C. A large endothermic peak was observed directly after the Tg inflection. It was difficult to quantify the degree of suppression of the Tg of the polymer due to plasticization using DSC because the endothermic peak was much larger than the inflection due to the Tg.To better quantify the plasticization of the CNF–PAES with water and CO2, DMTA was conducted. Dynamic torsional testing was conducted on strips of CNF–PAES. The storage modulus and tan

δ are shown in for CNF–PAES saturated with 7.6% CO2 and water and CNF–PAES which had not been saturated. The data from the storage modulus suggests that the bulk of the sample remained saturated with the blowing agents until the CNF–PAES was heated to the lowered Tg due to plasticization. If a considerable amount of blowing agents were able to diffuse out of the CNF–PAES matrix, an increase in the storage modulus would be observed. Because no appreciable amount of blowing agents are lost during the DMTA testing of the PAES saturated with water and CO2, DMTA was a viable option for quantitatively determining the plasticization of the polymer.The Tg can be observed as either a rapid decrease in the storage modulus or a peak in the tan

δ. The storage modulus and tan

δ exhibited only one transition in the CNF–PAES samples containing no blowing agents. This transition was observed at 227 °C, which was close to the Tg of the PAES. When the CNF–PAES sample was saturated with CO2 and water, three distinct transitions were observed as peaks in the tan

δ. The first transition was observed at 160 °C, which is attributed to the plasticized Tg of the CNF–PAES due to the presence of both the CO2 and water. Once 160 °C was reached, the CO2 was able to rapidly diffuse out of the PAES matrix while a majority of the water remained in the polymer. The broadening of the decrease in the storage modulus at 160 °C is due to the loss of the CO2. This loss of CO2 from the PAES matrix led to an increase in the Tg, which yielded another transition at 189 °C. This transition is attributed to the plasticized Tg due to water. Once 189 °C was reached, the water was able to escape by both diffusion and nucleation of bubbles from the PAES matrix. Because the water completely escaped from the PAES matrix, a transition at 227 °C was observed, which is the Tg of the CNF–PAES matrix without blowing agents.DMTA was used to determine the effect of the release temperature on the diffusion and solubility of the blowing agents. During the saturation process, the temperature was decreased from 265 °C to the desired temperature for pressure release and held for an hour. Because the temperatures varied greatly, the solubility of the blowing agents could be affected. To prepare the DMTA samples, the CNF–PAES sample was saturated at 265 °C and 10.3 MPa for 1 h. The temperature was lowered to either 165 °C or 220 °C, the pressure regulated to 10.3 MPa, and CNF–PAES sample was saturated for an additional hour. The DMTA results for the samples saturated at 165 and 220 °C are shown in . From this figure, it can be seen that the decrease in temperature from 220 to 165 °C, for the last hour, does not affect the diffusion or solubility of the blowing agents as both curves exhibit the same transitions.Using blowing agents, which also plasticized the CNF–PAES, allowed for better control of the foam morphology. Samples were foamed at five different release temperatures to control the cell size and optimize the compressive properties of the foams. The release temperature is defined as the temperature of the pressure vessel at which the pressure was released. Temperatures were chosen based on the DMTA results ranging from nucleation with minimal cell growth (165 °C) to significant cell growth without foam collapse (227 °C). Release temperatures of 180 and 200 °C were chosen to assess the effect of the second observed Tg transition on the cell morphology. A release temperature of 220 °C was utilized so the foam morphology and mechanical properties could be compared to previously reported values of neat PAES foam produced from a similar process The SEM micrographs of these samples, shown in , show the effect foaming temperature had on cell morphology. It can be seen that as the foaming temperature is increased, cell size increases. When the release temperature is close to the plasticized Tg of the CNF–PAES, the cells do not have a lot of time to grow before vitrification is induced because the viscosity is becoming infinitely large. As the release temperature is increased, the cells have a longer time to grow and cell coalescence can occur, leading to larger diameter cells. Cell coalescence occurs when the growth of two or more cells impinge on each other and the cell walls become so thin that surface tension can no longer keep the cells separate. Evidence of cell coalescence can be seen in the SEM micrographs when the pressure was released at a temperature of 180 °C or higher. It is inferred that cell coalescence occurred because lines, which are indicative of coalesced cell walls, are observed in the larger cells. At the higher temperatures, cell coalescence occurs more frequently. Cell coalescence which led to macrocellular size cells occurred when the pressure was released at a temperature of 227 °C. Despite the cell coalescence at the higher temperatures, cells less than 1 μm are present for all temperatures. The number of the cells less than 1 μm decreases as the foaming temperature is increased.The presence of a broad distribution of cell sizes can be seen in . In all of the micrographs, small cells (>1 μm) can be seen in the cell walls of the larger cells. The presence of distinctly different diameter cells suggests that there is more than one nucleation mechanism present during the foaming process. Upon rapid release of the pressure, the cells first nucleate due to the supersaturation of the CO2 in the PAES matrix. Nucleation due to the supersaturation of the water occurs after the CO2 nucleation. The bimodal distribution of cell sizes occurs because the two blowing agents nucleate the cells at different rates.The DMTA confirms that two nucleation processes could occur during foaming when water and CO2 are used as the blowing agents. The nucleation processes can be seen by the distinct transitions in the DMTA. At 160 °C, the CO2 is able to be released from the PAES matrix. At this temperature, the CO2 can begin to nucleate cells, while the water is still stable in the PAES matrix. When the temperature reaches 189 °C in the DMTA, the transition due to the water is observed. At this temperature, the water is unstable in the PAES matrix and can begin to nucleate cells. The difference in the stabilities of the blowing agents in the PAES matrix confirms that nucleation due to water and CO2 occurs separately during the foaming process.The cell nucleation density was calculated from the SEM micrographs, and it was determined that cell nucleation density was affected by the temperature at which the pressure was released. A plot of cell nucleation density is shown in . As the temperature of pressure release increased, the cell nucleation density decreased. The cell nucleation density decreased because of cell coalescence during the cell growth. As the cells grow together, the population of the cells decreases and this was observed as a decrease in the cell nucleation density.For the CNF–PAES foam, the cell nucleation density ranged between 109 and 1010

cells/cm3. The cell nucleation density was two orders of magnitude higher than neat PAES foam produced with water and CO2 under the same saturation and foaming conditions . In the micrograph, it can be seen that a CNF protrudes from the initially nucleated cell. The presence of heterogeneous nucleation produces a larger population of smaller cells, which can lead to better mechanical properties While the temperature of pressure release could be used to control the cell size, there was a tradeoff between cell size and the foam density. The effect of release temperature on the foam density is shown in . As the release temperature was increased, the foam density decreased. CNF–PAES foams were produced with a reduction in foam density ranging from 290 to 1100 kg/m3, a 78–15% density reduction, by only controlling the temperature at which the pressure was released.The tensile, impact and compressive properties of the CNF–PAES foams were tested and are shown in . The temperature in the sample name refers to the release temperature at which the corresponding foam was produced. Previously reported values to determine the effect the CNFs had on the mechanical properties of the foams. All of the values are specific values, normalized by the foam density, to eliminate differences in the mechanical properties due to foam density. Because the samples were foamed in a cylindrical mold, the cells were oriented in the direction parallel to the cylinder wall.The effect of both the cell morphology and the addition of the CNFs on the tensile modulus can be seen in . By comparing the PAES foam to the CNF–PAES foam (both foamed at 220 °C) it was determined that the addition of the CNFs yielded no effect on the foams because both foams exhibited tensile moduli which were statistically similar. Through comparison of the CNF–PAES foams produced at different release temperatures, the effect of the cell morphology on the tensile modulus of the foams was determined. The tensile modulus improved slightly as the cell size increased. As the foaming temperature was increased, up to 220 °C, the thickness of the cell walls also increased. The higher release temperature caused the cells with thin walls to coalesce. At a release temperature of 220 °C, a majority of the cell walls appeared to be greater than 1 μm, thus yielding a higher specific tensile modulus than the foams produced at the lower release temperatures. The increase in the cell growth, at a release temperature of 227 °C, led to a decrease in the cell wall thickness. The decrease in cell wall thickness led to a slight decrease in the specific tensile modulus. It should be noted that the improvement in the specific tensile modulus due to the foam morphology was minimal.The addition of the CNFs to the PAES yielded foam which had a significantly lower specific notched izod impact strength. When compared to unreinforced PAES foam, the specific impact strength of the CNF–PAES foam decreased by approximately 40%. The decrease in the impact strength from the addition of the CNFs was due to the strengthening characteristics of the CNFs. The CNF–PAES was more rigid than the unreinforced PAES foam. The rigidity of the foam allowed energy transfer to occur more easily in the foam. Therefore, the sample did not recoverably deform, and little energy from the impact was lost due to deformation The compressive properties, modulus and strength, were most affected by the addition of the CNFs to the PAES. Both the specific compressive modulus and specific compressive strength increased over 1.5 times that of the unreinforced PAES foam to values of 1.5 GPa and 59 MPa, respectively. The CNF–PAES foam compared well with commercially available structural foams. The commercial structural foams that have high compressive properties have specific compressive moduli and strength values around 1.4 GPa and 70 MPa The specific compressive properties of the CNF–PAES foam were also affected by the foaming temperature. Similarly to the specific tensile modulus results, a higher release temperature, up to 220 °C, produced foam with greater specific compression modulus and strength than the lower release temperatures. As was argued for the tensile modulus, this increase was attributed to the greater cell wall thicknesses observed in the foam produced at 220 °C. However, at 227 °C the compressive properties were greatly decreased. The large reduction in the specific compressive properties is attributed to the inclusion of many macrocellular cells.DMTA was demonstrated to be a more useful method than DSC to quantitatively determine the reduced Tg, due to plasticization, of the CNF–PAES saturated with water and CO2. In the DMTA, two distinct Tgs were observed for the plasticized samples. The sharp peaks in the tan

δ provided more quantitative results than in the DSC. The loss of the blowing agents yielded a large endothermic peak did the DSC thermograms, which overlapped with the reduced Tg, and hindered quantitatively determining the Tg.The DMTA results were used to quantitatively determine the thermal transitions of the saturated polymer and yield a better understanding for choosing different foaming temperatures. The different foaming temperatures, corresponding to the thermal transitions observed in the DMTA, were chosen to control the cell morphology and foam density. Both the cell diameter and cell nucleation density were greatly affected by the temperature at which the pressure was released. As the temperature was increased, the cell size increased and the cell nucleation density decreased. The increase in the cell size was attributed to the longer cell growth times and cell coalescence. Cell coalescence accounts for the decrease in the cell nucleation density. The foam density was also significantly affected by the temperature at which the pressure was released. At 165 °C, the foam density was the greatest because the cells did not have time to grow. At 227 °C, the cells had a longer time to grow and the foam density was reduced by 78%.The addition of the CNFs where shown to greatly increase the compressive properties while slightly decreasing the impact strength of the foams. By adding in only 1% of the CNFs, both the specific compressive modulus and specific compressive strength were increased by over 1.5 times the modulus and strength of the unreinforced PAES foam. The specific compressive modulus and strength are greater than several commercial polymeric structural foams. However, the CNFs decreased the specific impact strength of the foams. By adding the CNFs to the PAES, the foam was much more rigid and less energy was absorbed by the sample bending during impact testing.Effect of fitted position on stress distribution and strength of a bonded shrink fitted joint subjected to torsionRecently, joints combining shrink fit with anaerobic adhesives (bonded shrink fitted joint) have been appeared in order to increase the joint strength. This paper deals with stress analysis and strength estimation of the bonded shrink fitted joints in which a ring is fitted at the end of a hollow shaft subjected to torsion. The objective of the paper is to examine the effect of fitted position on the characteristics of the bonded shrink fitted joints. The stress distributions at the interface of the joints are analyzed using axisymmetric theory of elasticity. The effects of outer diameter, height and stiffness of the ring on the interface stress distributions are examined in the numerical calculations. In numerical calculations, it is found that a rupture of adhesive layer initiates from the edge of the interfaces close to the end of the shaft to which a torsional load is applied. Using the interface stress distributions, joint strength was predicted. Furthermore, experiments to measure the joint strength were carried out. The numerical results of the joint strength show more conservative values than the experimental results. In addition, the stress distributions in the present study are compared with those in which a ring is fitted at the middle of a shaft. It is found that the effect of shrink fitted position is negligibly small and the strength of the bonded shrink fitted joints is greater than that of shrink fitted joints without adhesives.inner radius of finite hollow cylinder I (shaft), II (adhesive layer), III (ring) (i=1,2,3)outer radius of finite hollow cylinder I, II, III (i=1,2,3)height of finite hollow cylinder I, II, III (i=1,2,3)origin of the coordinate for finite hollow cylinder I, II, III (i=1,2,3)Young’s modulus of finite hollow cylinder I, II, III (i=1,2,3)Poisson’s ratio of finite hollow cylinder I, II, III (i=1,2,3)Shear modulus of finite hollow cylinder I, II, III (i=1,2,3)interference of shrink allowance (=b1–a3)the first kind of modified Bessel function of order kthe second kind of modified Bessel function of order kthe first kind of modified Bessel function of order nthe second kind of modified Bessel function of order nthe sth positive roots satisfying with the equation J(αsIb1)=0(s=1,2,3,…)the sth positive roots satisfying with the equation C2(αsIIa2)=C2(αsIIb2)=0the sth positive roots satisfying with the equation C2(αsIIIa3)=C3(αsIIIb3)=0coefficient of the normal stress σr which governs the shear stress (see Shrink fitted joints have been widely used in mechanical structures such as railway vehicles, automobile and so on. Some investigations In this paper, in order to investigate the effects of fitted position on a position where a rupture of adhesive layer initiates and joint strength, the stress distributions at the interfaces of the joints are analyzed using axisymmetric theory of elasticity as a three-body contract problem shows a bonded shrink fitted joint of a hollow shaft with the inner diameter 2a1 and the outer diameter 2b1, which is fitted with a ring at the end of a hollow shaft, subjected to torsional load Tw. The ring of the inner diameter 2a3 and the outer diameter 2b3 is fitted at the end of the hollow shaft with the interference (shrink allowance) on which an anaerobic adhesive is applied. shows the dimensions of each component in the bonded shrink fitted condition. shows a model for analysis of the bonded shrink fitted joint, in which a ring is fitted at the end of a hollow shaft, subjected to torsional loads Tw. The origins of the hollow shaft, the adhesive layer and the ring are denoted as , respectively. By analyzing each model shown in and superposing the stress distribution of , the stress distribution of the bonded shrink fitted joint, in which a ring is fitted at the end of a hollow shaft, subjected to torsional loads Tw is obtained. In , the hollow shaft, the adhesive layer and the ring are replaced with finite hollow cylinder [I], [II] and [III], respectively. The inner diameter, the outer diameter, the height, Young’s modulus, Shear modulus and Poisson's ratio of finite hollow cylinder [I], [II] and [III] are denoted as 2a1, 2b1, 2h1, E1, G1, ν1, 2a2, 2b2, 2h2, E2, G2, ν2, 2a3, 2b3, 2h3, E3, G3 and ν3, respectively. In the analysis, it is assumed that a torsional load Tw acts annularly on the region (a1≦r≦b1) of the upper end (z=h1) of the hollow shaft [I] as a liner shear stress distribution . Thus, the torsional load Tw is expressed by the following equation:The displacement in the circumferential-direction νθ is assumed to be fixed at the outside diameter (r=b3) of finite hollow cylinder [III]. The analyses of the models shown in are carried out as three-body contact problems taking account the adhesive (hollow cylinder II). The models shown in are analyzed exactly by using axisymmetric theory of elasticity as a three-body contact problem , where ur is the displacement in the r-direction and wz is the displacement in the z-direction and superscripts I, II and III indicate finite hollow cylinder [I], [II] and [III], respectively.At the interface between [II] and [III]:Expanding the stress distribution F(r) into a series of Bessel functions C1(αsIr) indicate coefficients in series of Bessel functions.At the interface between [II] and [III]:where Cn(γsIr)=Jn(γsIr)−JI(γsIb1)/Yn(γsIr)/Y1(γsb1). Jn(αsr) is the first kind of Bessel function of order n and Yn(αsr) is the second kind of Bessel function of order n. The method for analysis is the same as the bonded shrink fitted joint in which a ring is fitted at the middle of a shaft . The obtained stresses and displacements are equated to the boundary conditions described in . Thus, 48N+20 and 18N+15 simultaneous equations are obtained in the case of the bonded shrink fitted joint in which a ring is fitted at the end of a hollow shaft shown in , respectively, where N is a number of the series. On the other hand, in the case where a ring is fitted at the middle of a hollow shaft, 24N+9 and 18N+15 simultaneous equations are obtained when the model for analysis is bonded shrink fitted state and torsional load is applied, respectively.It has been known empirically that joint strength increases as the interference (shrink allowance) increases in shrink fitted and bonded shrink fitted joints. This means that the fitting stress (normal stress) σr and the joint strength increase as the interference increases. Thus, it is impossible to apply the conventional failure criterion for estimating joint strength such as the maximum shear stress theory, Mise’s theory and so on. In this study, the torsional load Tw is defined as the joint strength when a rupture occurs at the interfaces by a load Tw. A rupture of adhesive layer occurs at the interface area (r=a2,z3=h3) when the shear stress reaches a critical value τ0. Assuming that the critical value τ0 depends on the normal stress σr, the value of τ0 is expressed by the following equation: are obtained from analogous test shown in before the analysis. The shear stress τa represents the strength of the adhesive without the fitting stress σr. The joint strength can be estimated by using the normal stress and the shear stress obtained from the numerical analyses. Thus, the relationship between the normal stress σr and the shear stress τrz is examined in order to estimate the strength of the bonded shrink fitted joints. In addition, it is difficult to determine the adhesive thickness under a given interference. Thus, the adhesive thickness was determined by the measurements described in the In this study, the relationship between the normal stress and the shear stress described above (in shows schematics of the experimental setup for obtaining the relationship between σz and τzθ (this is called analogous test) and dimensions of the test specimens. It is assumed that the relationship between the normal stress σz and shear stress τ is analogous to that of the normal stress σr and the shear stress τrθ in the bonded shrink fitted joints shown in . The normal stress σr is varied by changing the bolt clamping force Ff and the contact area. The bolt force was measured by two strain gauges attached to the shank of M16 bolt. In order to examine the effect of the contact area in the test, the specimens of the inner diameter 2a=54 and 57 mm were fabricated. It can be assumed that a variation in the contact stress distribution is small at the smaller contact area. The surface roughness of the specimens Rmax was less than 2.0 μm in the circumferential direction. The two specimens were clamped by a M16 bolt after they were bonded by an anaerobic adhesive (Loctite14486). The clamped specimens were subjected to torsion T by using a hydraulic ram until a rupture of cured adhesive initiated at the interfaces. The torsion T was measured by using a torque transducer. The shear strength τzθ was calculated as the average shear stress under the maximum torque measured. Thus, the relationship between σz and τzθ can be obtained. shows the dimensions of test specimens () in the torsional tests. The shafts and the rings shown in was manufactured in order to fix the bonded shrink fitted joints and was made of steel (S45C, JIS). The maximum surface roughness Rmax of the contact surface of the shafts (r=b1) and the rings (r=a3) was measured as 1.56–10.62 μm and 4.0–10.8 μm, respectively. The outer surface of the rings was manufactured as shown in . The interference was given between −0.021 and 0.007 mm. The dimensions of the shaft were chosen as 2a1=7 mm, 2b1=34.970–35.021 mm, 2h1=50 mm and those of the ring as 2a3=34.968–35.029 mm, 2h3=20 mm and 2b3=80 mm, respectively. Prior to assembly, the rings were heated up to approximately 200°C and then assembled to the shafts on which the anaerobic adhesive (Young’s modulus E2=3.82 GPa, Poisson's ratio ν2=0.39) was applied. Then, the bonded shrink fitted joints were cooled to ambient temperature for 48 h. The joints were placed on the testing equipment shown in and a torsional load T was gradually applied to the joint by using a hydraulic ram. The maximum torsional load was measured as the joint strength by using a torque transducer.The numerical calculations were carried out choosing a number N of terms in the series as 50 and 60, respectively. The difference in each stress between the series of 50 and 60 is found to be less than 5%. Thus, good convergence was expected to choose the number of the term as 50. The stiffness of the joint, the outer diameter of the ring and the engagement length (the ring’s height) are important for designing the cylindrical joint components. Thus, in the numerical calculations, the effects of Young’s modulus of the ring, the outer diameter of the ring and the height of the ring on the interface stress distributions are examined. In addition, the effect of shrink fitted position (a ring is fitted at the end/middle of a shaft) is also important from a reliable design standpoint. Thus, the effect of shrink fitted position on the interface stress distribution is also examined. show the interface stress distributions at the adhesive layer of the bonded shrink fitted joint shown in are the normalized fitting stress σr×a2/(δaE2) in the state of are the normalized shear stress τrθ/(2Tw/πb13) in the state of . The abscissa is the normalized distance z2/h2. The numerical calculations were carried out in consideration of the dimensions of the specimens used in the experiments, that is, 2b1=35 mm, 2h1=50 mm, E1=203 GPa, G1=68 GPa, ν1=0.3, 2a2=35 mm, 2b2=35.003 mm, 2h2=20 mm, E2=3.82 GPa, G2=1.27 GPa, ν2=0.39, 2a3=35 mm, 2b3=80 mm, 2h3=20 mm, E3=203 GPa, G3=68 GPa, ν3=0.3 and Tw=98 N m. The interference of the bonded shrink fit δ(=δs−δa) is expressed as the sum of designed interference δs(=b1−a3) and the adhesive thickness δa(=b2−a2), where δs is chosen as 0.0 mm and δa is as 0.03 mm. In this paper, the interface stress distributions of the bonded shrink fitted joints are shown at the inner surface of adhesives layer (r=a2) since it is noticed from the numerical calculations that a rupture of the bond line will initiate at the interfaces between the inner surface of adhesive layer (r=a2) and the outer surface of the shaft. shows the effect of Young’s modulus ratio E3/E2 on the normalized fitting stress distribution σr×a2/(δaE2) and the normalized shear stress distribution τrθ/(2Tw/πb13) at the inner surface of the adhesive layer. In , it is found that the fitting stress increases as the ratio E3/E2 increases. In , the shear stress shows stress singularity at the edge of z2/h2=+1.0. In addition, it is seen that the normalized shear stress τrθ/(2Tw/πb13) increases as the ratio E3/E2 increases. From the above results, it is indicated that the joint strength increases as the rigidity of the ring increases in comparison to that of the adhesive. shows the effect of the outer diameter ratio on the normalized fitting stress distribution σr×a2/(δaE2) and the normalized shear stress distribution τrθ/(2Tw/πb13) at the inner surface of the adhesive layer. shows that the effect of the ratio b3/b1 on the normalized fitting stress distribution σr×a2/(δaE2) (compression) increases as the value of b3/b1 increases. shows that the effect of the ratio b3/b1 on the normalized stress distribution τrθ/(2Tw/πb13) is small and the shear stress increases near the upper end where the torsional load is applied (r=a2,Z=+h2). Thus, it can be assumed that the joint strength increases as the outer diameter 2b3 of the ring increases in comparison with the outer diameter 2b1 of the shaft. shows the effect of the engagement length 2h3 (the ring’s height) on the normalized fitting stress distribution σr×a2/(δaE2) and the normalized shear stress distribution τrθ/(2Tw/πb13) at the inner surface of the adhesive layer. The effect of the value h3/b1 on the normalized fitting stress distribution σr×a2/(δaE2) at the edge of the interface is small. However, the normalized fitting stress distribution σr×a2/(δaE2) increases as the value h3/b1 increases at the middle of the interface. The stress singularity at the edge of the interface decreases as the value h3/b1 increases. As the results, it can be concluded that the joint strength increases as the engagement length 2h3 increases. shows the effect of bonded shrink fitted position, where the solid line indicates the case of the bonded shrink fitted joint in which a ring is fitted at the end of a shaft, and the dotted line shows the case of the bonded shrink fitted joint in which a ring is fitted at the middle of a shaft. It is observed that the fitting stresses are decreased in the case where a ring is fitted at the end of a shaft (z2/h2=−1.0). However, the effect of the shrink fitted position on the normalized stress is small. It can be assumed that the effect of the shrink fitted position is negligibly small. Thus, when the joint strength is estimated by using the interface stress distributions, the model for analysis is available where a ring is fitted at the middle of a shaft. The computation time for analyzing the model of the bonded shrink fitted joint where a ring is fitted at the middle of a shaft is smaller than that of . From the above results, it can be concluded that the joint strength increases under the following conditions: (1) Young’s modulus of ring E3 is greater than that of adhesive E2, (2) the outer diameter 2b3 of the ring increases, (3) the engagement length 2h3 (the ring’s height) increases. In addition, from the results of and the relationship σr and τrθ, it can be predicted that a rupture of the bonded shrink fitted joint initiates from the inner interface of the upper end (z2/h2=+1.0) where the torsional load is applied.In this paper, the joint strength estimation is carried out by using the numerical results and analogous test which has been done to obtain the relationship between the normal stress σr and the shear stress τrθ. Since the adhesive thickness will be changed by the interference (shrink allowance) of shrink fitted. Thus, the relationship between the adhesive thickness δa and the interference δs was measured by experiments. Fifteen bonded shrink fitted joints were assembled and their sections were cut. Then, the adhesives thickness was measured by a micrometer at many sections. The average of adhesive thickness was obtained. Thus, the relationship between the interference δs and the adhesive thickness δa is expressed by the following equation from the experimental results:Furthermore, in order to estimate the joint strength of the bonded shrink fitted joint, the results of the analogous test were used. The results of the analogous test, which was described in , was obtained by the following equation:where σr is the normal stress which corresponds to the bolt clamping stress σz. When the fitting stress σr is zero, which means only bonded without fitting, the shear strength of the bond is obtained as 69.3 MPa. Thus, it is found that joint strength increases as the fitting stress σr increases. Thus, the joint strength can be assumed for a given fitting stress σr and when the shear stress in the bonded shrink fitted joints reaches the value τ0 described in shows an example of twist-angle diagram in the torsion tests. The ordinate is the torsional load and the abscissa is the torsional angle of the shaft. Prior to the maximum value of the torsional load Tw, the slope of the curve is decreased slightly as shown in . This is thought due to a micro-fracture that has occurred near the upper end of the interfaces. With further application of the torsionl load Tw, a microscopic fracture increases and a rupture then occurs. In this paper, the joint strength is predicted under the following two methods: (1) A torsional load Tw (the results is shown by the solid line) is determined as the joint strength when the shear stress τrθ at the position z2/h2=+0.98 reaches the shear strength described in , (2) The value of Tw (indicated by dotted line) is determined when the shear stress τrθ at the position z2/h2=+0.86 reaches the shear stress 0. In Hattori’s study shows the comparisons of the joint strength between the estimated and the experimental results, where the ordinate is the joint strength Tw and the abscissa is the normalized interference δs/b1. It is found that the effect of the interference on the joint strength of the bonded shrink fitted joint is small. That is, the joint strength is independent of the interference because the adhesive thickness changes due to change in the interference. As the results, both the joint strength estimation by using the stresses at the edge of interface z2/h2=+0.98 and that of z2/h2=+0.86 are safety estimated because of the effect of the fitted temperature that is higher than mating temperature (about 150°C) in general. However, the results of the joint strength estimation rule (z2/h2=+0.98) is good for estimating the strength of the bonded shrink fitted joint. shows the comparisons of the joint strength between the bonded shrink fitted joint and the shrink fitted joint without an adhesive in which a ring is fitted at the end of a shaft. The stress analysis was done in the shrink fitted joints as a two-body contact problem by using axisymmetric theory of elasticity. The estimated values are obtained by using the stress at the position z2/h2=+0.98. In the shrink fitted joint, the analogous tests provided the relationship between normal stress and shear stress as the equation 0=0.416σr

MPa. From the results, it is observed that the joint strength of the bonded shrink fitted joint is greater than that of the shrink fitted joint. shows the comparisons of the joint strength of the bonded shrink fitted joint in which a ring is fitted at the middle of a shaft between the numerical and the experimental results. The estimated values are obtained by using the stress at the position z2/h2=+0.98 which is as same as in . From the results, it can be concluded that the joint strength is well estimated by using the stress at the position of z2/h2=+0.98 that can be safety estimated from a reliable design standpoint. In addition, from the results of , the effect of the bonded shrink fitted position (a ring is fitted at the middle/end of a shaft) on the joint strength is small. Thus, the analysis for the bonded shrink fitted joints in which a ring is fitted at the middle of a shaft is available.This paper dealt with the stress distributions and the strength estimations of the bonded shrink fitted joint in which a ring is fitted at the end of a shaft subjected to torsional load. The results obtained are as follows:By replacing a hollow shaft, an adhesive layer and a ring with finite hollow cylinders, a method for analyzing the interface stress distribution of the bonded shrink fitted joint subjected to torsion is demonstrated as an elastic three-body contact problem.In the numerical calculations, it is found that the fitting stress increases as Young’s modulus ratio E3/E2 between the ring and the adhesive, the outer diameter ratio b3/b1 between the ring and the shaft and the engagement length 2h3 (the ring’s height) increases. It is also found that the effect of Young’s modulus ratio E3/E2 and the outer diameter ratio b3/b1 on the shear stress at the interface are small. From the interface stress distributions obtained from the present analysis, it can be predicted that the joint strength increases under the following conditions: (1) when Young’s modulus ratio E3/E2 increases, (2) when the outer diameter ratio b3/b1 increases, (3) when the engagement length 2h3 (the ring’s height) increases.It is estimated that a rupture initiates from the interfaces of the upper end (z2/h2=+1.0) where torsional load is applied.In the experimental results of the joint strength, it is obtained that the joint strength is well estimated by using the stress at the position of z2/h2=+0.98 and it can be safety estimated. Furthermore, it is found that the joint strength is independent of the interference. It is also demonstrated that the strength of bonded shrink fitted joints is greater than of shrink fitted joints.From the comparisons of the results between the bonded shrink fitted joint in which a ring is fitted at the end of a shaft and the bonded shrink fitted joint, in which a ring is fitted at the middle of a shaft, it is found that the effect of the shrink fitted position is small. Thus, it is noticed that the interface stress distribution and the joint strength can be estimated by using the model where a ring is fitted at the middle of a shaft. The computational time for analyzing the case where a ring is fitted at the middle of a shaft is more reduced than that of the joint shown in Crack tip plasticity in single crystal UO2: Atomistic simulationsThe fracture behavior of single crystal uranium dioxide under mode-I loading is studied using molecular dynamics simulations at room temperature. The initial cracks are introduced as elliptical notches on either {1 1 1} or {1 1 0} planes. Two crack tip shielding mechanisms, dislocation emission and metastable phase transformation are identified. Crack extension is observed for cracks residing on {1 1 1} plane only. The dislocations have a Burgers vector of 〈1 1 0〉/2 and glide on {1 0 0} planes. Two metastable phases, Rutile and Scrutinyite, are identified during the phase transformation, and their relative stability is confirmed by separate density-functional-theory calculations. Examination of stress field near the crack tips reveals that dislocation emission is not as an effective shielding mechanism as the phase transformation. The formation of new phases may effectively shield the crack if all phase interfaces formed near the crack tips are coherent, as in the case of cracks residing on {1 1 0} planes.Uranium dioxide (UO2) is the primary nuclear fuels in today’s reactors. Its favorable properties include the stability under the extreme environment of heat and stress in nuclear reactors The fracture behavior of UO2 has been extensively studied since the 1960s In this work, attempts are made to investigate the fracture behavior of UO2 using molecular dynamics (MD) simulations, targeting the atomic-scale phenomena at the crack tips. In this study, we focus on the fracture behavior in single crystal UO2, or the intragranular fracture that occurs in the grain interior. In the following, we first describe the simulation method in Section . Finally, we summarize our conclusions in Section To simulate fracture in UO2, we used a periodic single crystal simulation cell with an initial notch in the center, as shown in . The dimensions of the cell in its three axial directions were 96.5, 3.1 and 37.8 nm respectively. The initial notches were created by removing ions with the O/U ratio of 2.0 to maintain charge neutrality. The notch was of elliptical shape, with 8.0 nm in width and 1.0 nm in height. The crack planes, the planes on which the initial crack resides, were chosen to be either {1 1 1} or {1 1 0}. These two planes were selected for being the two planes of the lowest surface energies. For the crack on the {1 1 1} plane (referred to as the (1 1 1) crack), the X axis was [2¯11], and the Y axis was [011¯]. The corresponding axes for the crack on the {1 1 0} plane (the (1 1 0) crack) were [1¯10] (X) and [0 0 1] (Y).To describe the interatomic interaction, the rigid ion type Basak potential was used in the present study Φij(rij)=ZiZje2rij+f0(bi+bj)expai+aj-rijbi+bj-cicjrij6+f0Dijexp-2βijrij-rij∗-2exp[-βij(rij-rij∗)]Here subscripts i and j represent the ith and jth ions. Z is the effective partial charge. r and r∗ are the interatomic distance and the bond length of anion–cation pair in vacuum. Among other parameters, D and β denote the depth and shape of the potential. f0, a, b and c are fitting parameters, and a, b and c are ion-specie dependent. The first and the second terms on the right hand side of Eq. describe the Coulombic interaction and the core repulsion between ions. The third term represents the van dar Waal’s interaction. The last term denotes the Morse type interaction which applies only to anion–cation pairs. The parameters used in the potential can be found elsewhere To calculate the Coulombic energy, we adopted the Wolf summation After being constructed, the simulation cell was equilibrated at 1800 K (about 0.6

Tm; Tm is about 3100 K suggested by experiments As a typical ceramic oxide, UO2 is expected to experience cleavage fracture at low temperature, with the {1 1 1} plane being one of the natural cleavage plane To represent the load–displacement curves, the responses of nominal stress σzz and system volume V with respect to nominal strain εzz are presented in . The volume is normalized by the initial system volume V0. In the elastic range, the Basak potential gives the elastic moduli of 146 GPa along the 〈1 1 1〉, and 172 GPa along the 〈1 1 0〉 directions at 300 K, as extracted from the linear response range. Due to the strain dependence of the elastic moduli For both the (1 1 1) and the (1 1 0) cracks, the onset of stress relaxation (defined by the maximum nominal stress) takes place along with an abnormal change in system volume. Under the displacement controlled loading condition, such abnormal changes in system volume are usually attributed to structural change such as phase transformation. In addition, as can be seen in , the responses of the two crack configurations to applied loading differ considerably. First, the stress relaxation of the (1 1 0) crack starts at a much lower critical stress (strain) than that of the (1 1 1) crack. Second, the magnitude of stress relaxation differs with orientation. The global stress σzz drops much faster for the (1 1 0) crack, to a plateau of about 2.0 GPa. While for the (1 1 1) crack, a slower drop in σzz takes place and a plateau of about 5.0 GPa is reached under about 7% strain. This plateau remains almost constant with up to 9% strain, and after that the stress drops again. These differences in stress–strain behavior suggest that different deformation mechanisms may operate.The energy release rate for crack extension Gc can be obtained from the stress–strain curves if the critical strain or stress at the onset of crack extension is known. Assuming ideal mode-I fracture, the energy release rate is given by Gc=∫0εcLzσzzdεzz. For the (1 1 1) crack, the critical strain is about 6.2%, as obtained by monitoring the atomic configurations. Integration along the stress–strain curve gives a Gc of 9.1 J/m2. This result is much larger than the theoretical prediction of 2.04 J/m2 (twice the surface energy of (1 1 1) surface), however it is in the range of the scattered data by previous experiments The configurational changes around the crack tips of the (1 1 1) crack during the loading is summarized in . For this purpose, the atomic configurations were quenched for structural analysis, and were projected onto the (011¯) plane. We used the common neighbor analysis (CNA) method Under periodic boundary conditions, initially all non-FCC U ions belong to the notch surfaces (). At the onset of stress relaxation, new non-FCC U ions appear at both crack tips (a) as signs of energy dissipation processes. The zoom-in view of the area near the right crack tip displays a dislocation configuration with edge characteristics. The Burgers vector, as characterized by the missing vector to complete the Burgers circle, was determined to be [0 1 1]/2. Once being emitted from the crack tip, the dislocation immediately glides away from the crack tip along (1 0 0) plane (b). Dislocation emission from crack tips has been commonly observed in atomistic simulations of fracture in many materials, particularly metals On the other hand, the non-FCC U ions at the left crack tip was characterized as a new phase of UO2. In reference to the Fluorite phase, the zoom-in image in f displays a distinct lattice structure, which is further characterized as the so-called Scrutinyite (α

−

PbO2) phase. As shown in c, the crack extension takes place along the interface between the Fluorite and the newly formed Scrutinyite regions (c) at 6.2% strain. As the crack extends, the Scrutinyite region in c transforms back to the Fluorite phase, and new lattice structures develops around the crack tips (d) at 7.0% strain. Three distinct lattice orderings present near the left crack tip (g) under 7.0% strain, and they are identified as three different phases of UO2. In addition to the Fluorite phase (represented by FCC U ions), the lattice structure in the left of g belongs to the Scrutinyite structure, having a different orientation with that in f. On the other hand, the lattice structure just below the crack tip is characterized as the Rutile phase. Therefore, the atomic configurations in g displays the coexistence of three phases of UO2. Similar coexistence of multi-phases is also observed near the right crack tip after the dislocation emission (d). Under compressive pressure, recent DFT calculations have shown that UO2 can take several metastable phases The phase transformation processes presented in a–d display two interesting features. First, the newly formed phases are metastable and exist only in the regions of high stress, e.g., near crack tips or dislocation cores. A similar behavior has been observed in previous MD simulations, in which the Scrutinyite phase nucleated from grain boundaries only c and d, and all Rutile regions take the same orientation. It appears that the choice of orientation is determined by the structural relationship between different phases. The new phases tend to orientate such that coherent interfaces form between the different phases. Across coherent interfaces, the U sublattices from different phases match perfectly with each other. As shown in f and g, most phase interfaces are coherent with perfect matching of the U lattice across the interfaces. The exception is the lower interface in f, along which the crack extends. The structural relationship also determines the growth manner of the new phases, which usually expand along the coherent interfaces. The Scrutinyite region in c expands along the (1 0 0)F plane. Similarly, the Rutile region in d grows along the (1¯11)F plane. Here the subscript F in the notation represents the Fluorite phase. To distinguish the different phases, future notation will be given with the subscript F, R, S, initials of phase names.The character of phase interfaces has significant effect on the fracture behavior of UO2. As can be seen in c, the crack propagated along the non-coherent interfaces, and no crack propagation along the coherent interfaces were observed. To elucidate this behavior further, the corresponding unit cell structures of the three phases are illustrated in , with the lattice parameters obtained from the Basak potential. As mentioned earlier, U ions in the Fluorite phase form an FCC sublattice. Each corner U ion forms a tetrahedron with its three nearest U neighbors at face centers, and each tetrahedron contains an O ion at the center (a). The U sublattice of the Scrutinyite phase has a shifted face-centered-orthorhombic (FCO) structure (b). The (0 2 0)S plane is shifted along the [1 0 0]S direction for about 0.15a. The O ions are also shifted from the tetrahedron centers. Consequently the cubic symmetry of FCC structure is absent in the Scrutinyite phase. In contrast, the U ions are of body-centered-tetragonal (BCT) structure in the Rutile phase (c). O ions are located along the diagonals on the (0 0 1)R plane. The (1 0 0)R plane is symmetrical to the (0 1 0)R plane, but not to the (0 0 1) plane. The possible coherent interfaces can be predicted by planes with similar U arrangement, i.e., (1 0 0)F and (0 1 0)S. Both planes exhibit a face-centered structure, and the maximum lattice mismatch is 11% (6.05 vs. 5.45 Å). The lattice mismatch may be further reduced under a deformed state, facilitating the formation of coherent interfaces.Indeed, most interfaces formed during phase transformations are between planes with similar U arrangement, and are therefore coherent. Considering the atomic configuration shown in f, the Scrutinyite phase shares the Y ([011¯]F or [101¯]S) axis with the Fluorite phase. In a two types of interfaces identified were the (1 0 0)F//(0 1 0)S and the (0 1 1)F//(1 0 1)S interfaces (a). Both (1 0 0)F and (0 1 0)S planes exhibit the face-centered structure (), forming a coherent (1 0 0)F//(0 1 0)S interface. On the other hand, the U arrangement of (0 1 1)F and (1 0 1)S are different, due to the shift of the (0 2 0)S plane. Therefore the (0 1 1)F//(1 0 1)S interface is non-coherent. Instead, the atomic arrangement across the interface displays a likely semi-coherent interface with mismatched dislocations; as shown in f. As an indication of the different interface nature, the potential energy profile near the crack tip is plotted in c. Here the potential energy is calculated in quenched images and is partitioned to each UO2 formula (one U and two O). Only U ions are plotted, and each of them carries 1/3 of the potential energy per formula. As shown in c, U ions near the (0 1 1)F//(1 0 1)S interfaces are of high energy, in accordance with the non-coherent nature. The non-coherent interface is prone to decohesion and it serves as a crack extension path, similar to that observed at the crack tips in atomistic simulations of body-centered-cubic (BCC) iron Similarly, three types of interfaces form in the regions where three phases coexist in g. The shared Y axis is [011¯]F, or [1 1 0]S, or [0 0 1]R. This coexistence takes place at 7.0% strain, accompanied by a plateau in the stress–strain curve (). The interfaces are characterized as (1 0 0)F//(0 0 1)S, (1 0 0)R//(0 0 1)S, and (110)R//(1¯11)F respectively. The (0 0 1)S plane is of a shifted face-centered (b) structure, slightly different than the face-centered (1 0 0)F. However, a low energy interface (d) still forms under the deformed state. The (110)R//(1¯11)F interface is analogous to the BCC–FCC interface under the Nishiyama-Wasserman relation ). Correspondingly, the (1 0 0)R//(0 0 1)S interface is of higher energy than the other two (d). However, this interface is nearly perpendicular to the crack plane, and therefore it is not favorable for crack extension under mode-I loading. Furthermore, since the other two interfaces are coherent with low energies, the crack extension is delayed until about 9.0 % strain, in accordance to the stress plateau shown in After establishing the structures of phase interfaces, we now demonstrate the path of the phase transformations, with the help of atomic displacement maps. Specifically, the displacement of each ion is calculated in reference to its initial position, and is represented by a vector starting from the initial position. The atomic images are projected to the plane parallel to the Burgers vector and normal to the gliding plane. As shown in a forms by relative shear along [0 1 0]F on (1 0 0)F plane. After this shearing process, the (1 0 0)F plane becomes a (0 1 0)S plane, forming an (1 0 0)F//(0 1 0)S interface. Similarly, the Scrutinyite phase in b forms by relative shear along [0 1 0]F on (0 0 1)F plane, creating a (1 0 0)F//(0 0 1)S interface. Both transformation processes correspond to a Schmid factor of 0.33, with the loading applied along [1 1 1]F. For reference, the Schmid factor for 1/2[0 1 1]F(1 0 0)F dislocation emission is 0.47. However different barriers may exist for the phase transformation and dislocation emission, which occur under the same strain level (a). On the other hand, the formation of the Rutile phase in b is by relative shear along [2 1 1]F on (1¯11)F planes, with a Schmid factor of 0.31. This process is analogous to the reverse of the BCC–FCC transformation path observed experimentally in carbon steel The effect of interface structure on the crack extension can be further demonstrated by analysis of the atomistic stress. According to the linear elastic fracture theory, the stress profile along the X direction is given by σzz(x)=K/x+σzz0a. Indeed, the stress profile before onset of stress relaxation follows a similar trend with the analytical solution. A least square fitting gives the critical stress intensity factor K to be 0.54

MPam0.5, close to the experimental value of 0.2–0.45

MPam0.5 in sintered UO2 where intragranular fracture is dominant a), since the new structure forms primarily along the (1 0 0)F planes, 54° from the X((2¯11)F) direction. However, the shape of the stress field changes as a result of the phase transformation (a–c). High tensile stress develops along the non-coherent (0 1 1)F//(1 0 1)S interface, which serves as easy crack extension path under further loading. No stress concentration develops along the coherent (1 0 0)F//(0 1 0)S interface. At the right crack tip the emission of the dislocation relieves the stress concentration temporarily (c), however this effect vanishes and the stress field recovers as the dislocation glides away (The above presented deformation mechanisms clearly illustrate why the energy release rate obtained in MD simulations is much higher than theoretical prediction of the cleavage failure based on the Griffith theory ), with a higher surface energy than that of {1 1 1} planes. The newly formed phases are metastable and exist under tensile stress only. Once the local stress is relieved, e.g., by crack extension, they transform back into the Fluorite phase. However, this transient phenomenon has significant effect on the fracture behavior of UO2.Compared to the (1 1 1) crack, the results on the (1 1 0) crack display two differences: (1) the relaxation takes place at earlier portion of the loading and the resulting drop in the stress level is much larger, and (2) no crack extension is observed up to 10% strain. To understand these differences, the configurational evolutions of the (1 1 0) crack were summarized in . For the (1 1 0) crack, stress relaxation occurs by phase transformations (a and b). Both Scrutinyite and Rutile phases are identified at the crack tips, and they form simultaneously at about 3.3% strain (As discussed in the case of the (1 1 1) crack, the crack extends if non-coherent interfaces form near the crack tips. To explain the absence of crack extension, the interface structures near the (1 1 0) crack tip are presented in a. Two types of interfaces form near the crack tip, namely the (0 1 0)S//(1 0 1)R and (1 0 1)R//(0 0 1)F. Both interfaces are analogous to the BCC-{1 0 0}//FCC-{1 1 0} interface in Bain orientation, as observed in Ag/V multilayers d), and the low energy nature of the interface (b). Experimentally, the (0 1 0)S//(0 1 1)R interface has been observed in TiO2, where Scrutinyite and Rutile phases coexist The Scrutinyite phase forms by shear displacement of the (1 0 0)F planes along the [0 1 0]F direction, as shown by the displacement map in c, where the atomic image is projected onto the (0 0 1)F plane. Such shear displacement corresponds to a Schmid factor of 0.50 with the load applied in the [1 1 0] direction. After phase transformation, the Y axis becomes [0 0 1]S (from [0 0 1]F). Similarly, the Rutile phase forms by successive shear displacement of the (1 0 0)F plane along the [0 1 0]F direction (d), similar to that proposed for Rutile to Scrutinyite phase transformation in TiO2 is similar to that for the Fluorite to Scrutinyite transformation of the (1 1 1) crack (). Both processes take place by 〈1 0 0 〉F/{1 0 0}F shear, and should correspond to similar critical resolved shear stress (CRSS). Regarding the much larger Schmid factor for the phase transformation of the (1 1 0) crack, a much lower global stress is required, in accordance with the much lower maximum stress of the (1 1 0) crack in . Specifically, the maximum stress is about 7.1 GPa for the (1 1 1 crack. Correspondingly the CRSS is 2.4 GPa with a Schmid factor of 0.33. For comparison, the maximum stress of the (1 1 0) crack is about 5.6 GPa. Multiplication with the Schmid factor (0.50) gives a CRSS of 2.8 GPa, close to that for the phase transformation of the (1 1 1) crack. Therefore, the difference in maximum stress is a result of the different Schmid factors for the phase transformation processes. We note that stress is concentrated near the crack tip. The local resolved shear stress is much higher than that predicted from the Schmid law.Since no non-coherent interfaces form near the (1 1 0) crack tips, the local stress concentrations are effectively relieved. Consequently, no crack extension occurs up to 10% strain. Following the same procedure of , the stress profile near the (1 1 0) crack tips are plotted in . Before phase transformation starts, the stress profile shows clear concentrations at both tips, as shown in a and b. As new phases form at the left crack tip, the corresponding stress concentration is reduced (a and c). A similar stress drop is observed at the right crack tip, as a result of the phase transformation (a and d). Due to the significant relief in stress concentration, no crack extension is observed with up to 10% strain.Two new phases, in addition to the ground state Fluorite phase, have been identified for UO2. The formation of Scrutinyite phase has previously been reported and validated by DFT calculations The results on phase stability are plotted in in the form of energy-volume curves. The data is normalized with the number of UO2 formulas, and shifted by taking the Fluorite phase as the reference state. As shown in a, the Basak potential predicts that the Scrutinyite and Rutile phases are more stable than the Fluorite phase as the volume expansion is beyond certain critical points. Furthermore, the energy minimums for the Scrutinyite and the Rutile phases are close to each other, in accordance with their coexistence in . For reference, the energy minimums corresponding to the Scrutinyite (with fixed relative ionic positions, ISIF5) and the Rutile phases also exist in DFT calculations with both the GGA and LDA + U approaches, indicating their possible existence as metastable phases. However, activation of ionic relaxation predicts no stable structure for the Scrutinyite phase. It transforms into the Fluorite phase under low expansion, and the Rutile phase under high expansion, as shown in b, putting some doubts on its existence in reality. Furthermore, the LDA + U calculations with shape change allowed predict that the Fluorite phase starts to deform at high volume and transforms into the Rutile phase, as shown in b, in agreement with the phase transformation process observed in MD simulations.Both the Scrutinyite and the Rutile phases have larger molar volumes than that of Fluorite phase. Transformation from the Fluorite phase to the other two leads to volumetric expansion and stress relief at the crack tips, and consequently shields the crack. As shown in , MD simulations and DFT calculations predicts similar volumetric expansions for the phase transformation processes. For MD simulations with the Basak potential, the cell volume increases by about 10% and 12% through transformation from the Fluorite to the Scrutinyite and the Rutile phases, respectively. The increases are 16% and 18% from DFT calculations with the GGA approach, and 12% and 18% respectively with the LDA + U approach. On the other hand, the energetic differences of the Scrutinyite and the Rutile phases over the Fluorite phase are much larger as given by DFT calculations than by MD simulations. For instance, the energy minimum is only 0.05 eV for the Rutile phase in MD calculations, in contrast to that of 0.59 eV from the DFT calculations with the GGA approach, or 0.72 eV with the LDA + U approach. The much higher energetic differences predicted by DFT calculations may undermine the prominence of phase transformation in shielding the crack tips.The results obtained from MD simulations are limited by the reliance on the empirical potential and the extremely high loading rates. As shown above, the energetic differences between different phases predicted by the Basak potential are much smaller than those predicted by DFT calculations. A larger energetic difference requires higher critical stress to trigger the transformation. The above results suggest that the phase transformations may be less favored than predicted by MD simulations, in competing with other energy dissipation processes such as dislocation emission. However, the conclusion is open to further study since the barrier for dislocation emission is unknown. On the other hand, the dislocation emission may be delayed by the high loading rates; so may the phase transformations too. It has been observed in MD simulations that the phase transformations take place by relative shear displacements analogous to dislocation slip. Furthermore, using the same potential, previous atomistic simulations have shown that the nucleation time of phase transformation from Fluorite to Scrutinyite in bicrystal UO2 increases with decreasing applied stress In spite of the potential and loading rate issues, the significance of the current results shall not be undermined very much. First of all, two possible crack shielding mechanisms are dynamically observed in MD simulations around the crack tips in UO2. The dislocation configuration is in agreement with previous experiments and the existence of metastable phases is confirmed by separated DFT calculations. Second, though the relative importance of these two shielding mechanisms is not clear yet due to the inaccuracy of the Basak potential in predicting the energetics of metastable phases, some other aspects of the results shall not be limited by the potential and loading rate issues. Both MD simulations and DFT calculations predict the existence of a new metastable phase, i.e., the Rutile phase of UO2. The existence of Rutile phase is expected to play an important role on the fracture behavior of UO2. For instance, the phase interfaces may serve as easy crack propagation paths. In addition, the phase interfaces and the phase transformation mechanisms elucidated by MD simulations will help to understand the formation and coexistence of the metastable phases studied here. The phase transformation mechanisms by themselves are of great interests to be explored. The current results should not be limited to UO2 systems, and they may be applicable to crystals with similar structures. For instance, the phase interfaces demonstrated by has previously been observed experimentally in TiO2In summary, the room temperature fracture behavior of single crystal UO2 was simulated using molecular dynamics with the Basak potential. Instead of cleavage behavior, two shielding mechanisms were identified at crack tips, emission of 1/2〈1 1 0〉{1 0 0} dislocation and phase transformation from Fluorite to either Scrutinyite or Rutile phases. The dislocation glided on {1 0 0} planes, and was ineffective in shielding cracking. The newly formed phases may effectively shield the crack if only coherent phase interfaces form near crack tip, such as for cracks residing on {1 1 0} planes. For the crack on {1 1 1} plane, non-coherent phase interfaces formed during phase transformation, and they served as paths for crack extension under higher strain.Decoupling of the softening processes during rapid tempering of a martensitic steelThe increased adoption of martensite-containing advanced high strength steels, such as martensitic and dual-phase steels, into automotive applications has led to concerns among practitioners with respect to softening during rapid tempering cycles such as those experienced during laser welding. Past studies on rapid tempering have successfully modeled the rapid tempering process; however, the activation energies and softening rates calculated did not match the classic literature values associated with martensite tempering. The present study examined rapid tempering data for a martensitic steel and separated the softening process into two stages: carbide nucleation and carbide coarsening or growth. The activation energies calculated for each process were found to be consistent with classic literature values for diffusion controlled nucleation and growth of carbides during martensite tempering.initial concentration of solute atoms in the matrixpre-exponential factor for grain boundary diffusion coefficientpre-exponential factor for volumetric diffusion coefficientchange in material hardness due to particle coarseningenergy barrier to material softening (JMAK equation)geometric constant for grain boundary particle growthconversion factor from Vickers hardness to yield strengthinitial time for particle coarsening equationparticle surface energy per unit area of interface with matrixAutomotive manufacturers are widely required by legislation to improve vehicle fuel economy AHSS derive their high strengths from complex microstructures comprising mixtures of various volume fractions of martensite, ferrite, bainite and retained austenite Limited work has been done on quantifying the effects of thermal history, microstructure and steel chemistry on martensite softening kinetics using rapid heat treatments consistent with those associated with laser welding All experiments were carried out using an industrially fabricated 1.8 mm thick M220 grade martensitic steel. The as-received microstructure was produced via a continuous annealing line. The M220 chemical composition and as-received hardness can be found in . Microhardness traverses conducted on the sheet cross-sections revealed that there were no significant hardness variations across the sheet thick thickness.All rapid tempering heat treatments were carried out using a Gleeble 3500 (Dynamic Systems Inc., Poestenkill, NY, USA). Samples comprised 100 mm×12 mm coupons with the rolling direction parallel to the sample long axis. During tempering, average sample heating and cooling rates were approximately 2200 °C/s and 4100 °C/s, respectively. These heating and cooling rates allowed the rapid tempering cycles to be considered isothermal, as verified via a Hollomon-Jaffe analysis . However, it should be noted that tempering times of 20 s and 50 s were used only for tempering temperatures of 420 °C or less.All microhardness measurements were made using a Vickers indenter on metallographically prepared sample cross sections. In all cases, a 500 gf load and 15 s dwell time were employed. Testing locations were separated by at least three indentation widths in accordance with ASTM E384-11 The microstructures of selected samples were examined using optical (OM) and scanning electron microscopy (SEM). In all cases samples were sectioned, mounted, and polished using standard metallographic methods. SEM samples were etched with 2% nital and gold coated before imaging with a JEOL JSM-6460LV SEM (JEOL Ltd., Tokyo, Japan) using an acceleration voltage of 20 keV. Optical microscopy samples were etched with Marshall׳s reagent. Grain size measurements utilized the linear intercept method All carbide equivalent diameters were measured from carbon replicas from samples tempered at either 500 °C or 600 °C viewed via transmission electron microscopy (TEM). Replicas were made using standard methods, as described in From past work it has been shown that softening in DP and martensitic steels can be modeled using a sigmoidal curve starting at the as-received alloy hardness and transitioning to a minimum hardness as heat input, temperature or tempering time increase where HBM is the as-received (base material) alloy hardness, H is the instantaneous measured hardness and H∞ is the minimum alloy hardness, defined as the hardness after a 1 h furnace heat treatment at 650 °C. From this definition, ϕ progresses from 0 in the as-received condition with no softening, to 1, where tempering has been completed. In this form, the softening kinetics may be modeled using the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation where t is time, n the reaction rate exponent and k the energy barrier to softening as described by the Arrhenius equation:where Q is the activation energy for softening, R the universal gas constant, T is temperature and k0 a fitting parameter. Although the JMAK equation was developed to describe the growth of a daughter phase within a parent phase, it has been found to be suitable for the modeling of softening data with some minor modification ) was used successfully by the present authors to model isothermal tempering hardness data Although the JMAK equation was used previously by the present authors to successfully model M220 softening data, two issues were identified with respect to its use in modeling HAZ softening. Firstly, the values derived for Q and n (Eqs. ) were 28.3 kJ/mol and 0.10, respectively In order to determine if multiple processes occurred during softening, which would affect the derived Q and n values in this manner, n and k may be calculated directly from the slope and y-intercept of the ln[−ln(1−ϕ)] versus ln(t) plot, respectively. From , it can be seen that there are two distinct regions in the softening data, as characterized by the significant change in the slope of the 360–420 °C curves, suggesting that two distinct processes were operating for shorter and longer tempering times. These are referred to as Stage I and Stage II softening in and in the subsequent discussion. A more detailed examination of will reveal that the slopes of the Stage I portions of the curves are approximately parallel for all tempering temperatures as are the slopes of the curves for Stage II, indicating that similar processes are operating in each regime. In addition, the transition from Stage I to Stage II, as characterized by the time of the curve knee points, decreases significantly with increasing tempering temperature and was not able to be experimentally captured for temperatures higher than 420 °C. This latter is consistent with softening being a thermally driven process.To determine the relationship between the two process regimes highlighted in and the microstructural evolution of the samples as a function of tempering time, the microstructures of the as-received material and samples tempered at 400 °C and 500 °C were viewed via the SEM. The as-received base material comprised both non-tempered and tempered martensite grains, indicating that the as-received material had undergone some degree of autotempering during industrial thermal processing prior to welding (a). When tempered at 400 °C for times of 1 s or less, the microstructures were quite similar to those of the base material, as can be seen in b and c. These observations, combined with the kinetic data from , imply that the martensite decomposition had not been completed for these microstructures and that the tempering reaction was on-going. In the classic tempering process sequence, this would correspond to Stage 3 of tempering c–g) the microstructures comprised tempered martensite with a significant population of carbides. These observations and the change in slope observed for the softening data in suggest that carbide nucleation was complete and that carbide coarsening or growth was underway. This corresponds to stage 4 of the classic tempering sequence , it was determined that the average JMAK exponent (n) value for the 360–420 °C Stage I softening was 0.659±0.003, which is in good agreement with the accepted literature value of 0.67 for particle nucleation on dislocations ) was constructed using the k values derived from the 360 °C to 420 °C short-time tempering data in . From this construction, an activation energy, Q, of 113±7 kJ/mol was calculated. This value is in good agreement with the activation energy for C diffusion in ferrite of 80–122 kJ/mol It is interesting to note that the degree of softening (i.e. ln[−ln(1−ϕ)]) value for the samples tempered at 360–420 °C was approximately -1.15 at the curve knee point in , corresponding to a ϕ value of 0.27±0.05. Using a simple regression model, it may be calculated that for samples tempered at 500 °C, Stage I softening would be completed at approximately 0.06 s (see ). Timescales of this order are extremely difficult to capture experimentally and explain the lack of a visible Stage I softening from the experiments with tempering temperatures greater than 420 °C (see After the carbide nucleation stage was completed, show that the steel continued to soften through the martensite decomposition process. This could be due to a combination of three mechanisms: ferrite recrystallization, grain growth or softening associated with carbide growth. To investigate whether ferrite grain recrystallization or grain growth were significant factors in the softening process, a sample tempered at 500 °C for 0.2 s and a second sample tempered at 600 °C for 10 s were compared to determine if significant changes in the grain structure had occurred during the tempering heat treatments. These microstructures are presented in . Both samples exhibited a fine-grained, equiaxed microstructure where the average grain size for the samples tempered at 500 °C and 600 °C were 3.1±0.1 μm and 2.5±0.2 μm, respectively. The significantly smaller ferrite grain size of the sample tempered at 600 °C may be attributed to recrystallization, as reported by Speich From the above, it can be concluded that changes in the ferrite grain structure did not contribute significantly to Stage II softening (, it may be seen that these microstructures exhibited large populations of carbides. These carbides can block dislocation movement through a precipitation hardening mechanism The carbides observed in the tempered M220 were identified as cementite for all TEM replicas examined ), from which it may be then seen that mean diameter of the cementite particles in samples tempered at 600 °C grew more rapidly than those tempered at 500 °C.Cementite coarsening was consistent with the trends observed in the hardness data (), where particle size increased with increasing time and temperature, leading to a drop in precipitate density and decreased hardness. The contribution of carbide coarsening to the overall sample hardness can be calculated using a modified version of the Ashby–Orowan equation arising from Guo and Sha where ΔH is the change in hardness associated with precipitation hardening, G is the ferrite shear modulus (81 GPa, . The base hardness of the microstructure was assumed to be 92 HV from the hardness of ferrite plus contributions from solution strengthening alloying elements The influence of cementite particle size on hardness was calculated using Eq. for samples tempered at 500 °C as the carbide size data for samples tempered at 600 °C was too noisy for a confident evaluation of its effect (). When the calculated hardness due to carbide coarsening was compared to the measured hardness values for samples tempered at 500 °C, it can be seen that predictions followed the softening trend reasonably well (). The average error from this prediction was 11%, which is reasonable considering the wide size distribution of the cementite particles measured. The agreement between the precipitation hardening model and the measured hardness values suggest that carbide coarsening dominated Stage II softening.Although Stage II softening largely arises from interactions between the ferritic matrix and carbide coarsening during tempering, the kinetic parameters k and n may still be used to characterize the softening progression (). Using the analysis employed for Stage I softening, the average n value for carbide coarsening was determined to be 0.108±0.001. Using the Stage II k data from , it was determined that the activation energy for the carbide growth process was 35±4 kJ/mol. These values are in reasonable agreement with the values previously calculated for the entire softening process (28.3 kJ/mol and 0.10 Decoupling the carbide nucleation and coarsening processes from the overall softening process revealed the reasons for the activation energy (Q) and JMAK exponent (n) of the combined softening processes in , when the carbide nucleation process (Stage I in ) was separated from the overall softening process, the calculated activation energy (113 kJ/mol) and JMAK exponent (0.67) agreed well with the classic literature values for martensite tempering. From this, it can be concluded that Stage I softening of the present martensitic steel can be characterized as being equivalent to stage 3 (i.e. nucleation of cementite) of the well-established martensite tempering process A similar procedure applied to the Stage II portion of the tempering data in determined that the activation energy () and JMAK exponent for the carbide growth process were 35±4 kJ/mol and 0.108±0.001, respectively. However, it must be acknowledged that an inspection of these values would seem to be at odds with the rate controlling processes for carbide growth, in this case the diffusion of C and self-diffusion of Fe. To resolve this seeming inconsistency, cementite growth kinetics need to be established.Particle growth kinetics have been modeled by Lindsley and Marder where d is the particle equivalent diameter, kD is the diffusion dependent constant and m is the coarsening exponent, which depends on the dominant coarsening mechanism (i.e. m=0.2 for dislocation pipe diffusion, 0.25 for grain boundary diffusion and 0.33 for volumetric diffusion). By applying Eq. , it was observed that the dominant diffusion mechanism changed between samples tempered at 500 °C and 600 °C. When tempering at 500 °C, m was found to be 0.25±0.02, indicating that grain boundary diffusion was the dominant growth mode. However, at 600 °C, m was determined to be 0.29±0.05, indicating that cementite growth was due to a combination of grain boundary and volumetric diffusion. The effects of these different diffusion mechanisms on the microstructural evolution of the tempered martensite may be seen in , where cementite within the samples tempered at 500 °C formed primarily on the martensite block and lath boundaries, whereas in the samples tempered at 600 °C, cementite grew on the lath and block boundaries as well as throughout the bulk grains. The observation that the cementite growth mechanism can change with tempering temperature is consistent with the results of Bannyh et al. As it was observed that cementite grew by both bulk and grain boundary control, the rate of each growth mechanism must be understood. Volumetric diffusion controlled particle coarsening kinetics have been described by Lifshitz and Slyozov per where d is the particle diameter at time t, d0 the particle diameter at time t0, γ the surface free energy of the precipitate per unit area of precipitate-matrix interface, C0 the equilibrium concentration of solute atoms in the matrix, Vm the molar volume of the precipitate and Dv the volumetric diffusion coefficient. Speight where Dgb is the grain boundary diffusion coefficient, δ the grain boundary thickness and k1 a geometric constant.As it was shown, above, that Stage II softening was due to cementite growth, it is logical to believe that the activation energy of softening is correlated to the activation energy for carbide growth. However, as the diffusion mechanism(s) controlling particle growth changed with tempering temperature, the activation energy could not be calculated using a conventional Arrhenius plot. For this reason, literature values were used. Although cementite grows through diffusion of both C and Fe, the controlling process rate is the self-diffusion of Fe To determine how the activation energies for Fe self-diffusion relate to the apparent activation energy for softening, it must first be understood how the softening progression (ϕ) varies with particle diameter (d). After determining how ϕ changes with d, correlating ϕ to time may be done through Eqs. and the activation energy calculated per the methodology used in relates hardness both to lnd and the reciprocal of L, both of which increase as d decreases, it was decided that a more direct way to correlate ϕ to d could be obtained by plotting ϕ versus d, as shown in . From this, it can be seen that ϕ increases as a power function of particle diameter such that, ϕ may be calculated as a function of time. For this calculation γ was taken to be 2.48×10−5

J/cm2) when cementite growth is driven by bulk and grain boundary diffusion, respectively. These values match the measured activation energy for Stage II softening of 35±4 kJ/mol determined in the present study. When it is considered that the dominant diffusion mode was grain boundary diffusion, the low activation energy determined for Stage II softening was likely due to the non-linear relationship between d and ϕ.As with the correlation between the activation energies associated with cementite growth and softening, the correlation between the JMAK exponent, n (Eq. ), and the time exponent for particle coarsening, m (Eq. ) is not clear. To determine this relationship, it is best to simplify the relation between ϕ and d using Eq. . By substituting the appropriate form of d from Eq. ) for the 500 °C and 600 °C particle data into Eq. , the time exponent for ϕ would be 0.065 for the samples tempered at 500 °C and 0.075 for the 600 °C samples. However, in case of the JMAK equation (Eq. ), time is an exponential variable and is not easily isolated analytically. Thus, Eqs. were equated and n determined using non-linear regression. This technique yielded a JMAK equation n value of 0.112±0.001. This agrees well with the value of the JMAK exponent calculated from the hardness data during carbide coarsening (i.e. 0.108±0.001) and shows how the non-linear relation between ϕ and d as well as the exponential form of the JMAK equation changes the rate constants from those expected from Eq. The overall conclusion of this study is that decoupling the short-time/lower temperature (i.e. Stage I, ) carbide nucleation process from the longer-time/higher temperature carbide coarsening process (i.e. Stage II, ) allowed for the derivation of JMAK parameters for rapid martensite tempering consistent with the existing classic literature C-diffusion controlled models for martensite tempering. However, in most practical cases of rapid high temperature tempering, such as weld heat affected zone softening, the softening process can be efficiently modeled using kinetic parameters derived from the coupled process due to the dominant role carbide coarsening plays in this processes. However, it should be noted that in cases where rapid tempering takes place at low temperatures (i.e. T≤400 °C) for short times, the carbide nucleation stage must be taken into account in the softening model because this will occur over a significant portion of the tempering cycle when tempering on the order of seconds or tens of seconds. This explains the poor fit between the predicted and actual ϕ values for the softening data in for tempering temperatures of 400 °C or lower.This study examined the softening observed in a martensitic M220 steel during rapid tempering to resolve the disagreement between the activation energy and time exponent calculated by Biro et al. The softening process could be broken down into two sub-processes: carbide nucleation and carbide coarsening. These processes were separated within the overall softening data by transforming the softening versus time data.The carbide nucleation stage occurred very quickly and was experimentally observed only for relatively short tempering times and for tempering temperatures of less than 420 °C. The activation energy and time exponent for carbide nucleation, calculated from the hardness data, were determined to be 113±7 kJ/mol and 0.659±0.003, respectively, matching the classic literature values for the activation energy for C diffusion in ferrite (80–120 kJ/mol) and particle growth on dislocations (0.67) widely accepted for martensite tempering.The apparent activation energy and time exponent calculated for the carbide coarsening stage of softening were 35±4 kJ/mol and 0.108±0.001, respectively. These values did not match the classic literature values for the activation energy and time constant of 234 kJ/mol and 0.33 or 363 kJ/mol and 0.25 when cementite growth is dominated by volumetric and grain boundary diffusion, respectively.The apparent activation energy associated with the carbide coarsening stage was determined to be an artefact of the non-linear relationship between the particle diameter growth kinetics and the self-diffusion of Fe, which is the controlling mechanism for cementite growth. When the apparent activation energy of Stage II softening was calculated using the softening resulting from cementite growth due to grain boundary and bulk diffusion, the resulting activation energy matched the activation energy calculated from experimental data.The low time exponent associated with the carbide coarsening stage was due to the non-linear relation between the softening parameter (ϕ), cementite particle diameter and the exponential form of the JMAK equation.Although this work revealed that there are two separate processes occurring when softening during rapid tempering, it is believed that in most cases softening during rapid tempering may be modeled using a kinetic model dominated by the carbide coarsening process as this process dominates at practical timescales and higher welding heat inputs. However, in the case of short-time tempering at temperatures of 400 °C or less, the carbide nucleation stage must be taken into account in order to predict softening.The use of the isothermal tempering assumption in the modeling was verified via a Hollomon-Jaffe The relative contributions of the heating versus isothermal portion of the Gleeble simulation thermal cycles ((a,b)) on tempering damage was determined by calculating the tempered hardness of the material after tempering at 420 °C and 650 °C using two models for the thermal cycle: (i) a thermal cycle that comprised only the isothermal tempering temperature and time – i.e. a rectangular thermal profile and (ii) a thermal cycle comprising the heating portion of the cycle and the isothermal tempering temperature and time. Isothermal tempering times for the 420 °C and 650 °C data ranged from 0 s. (i.e. heating only without an isothermal hold) to 50 s. The effect of heating time on tempering damage was accounted for using the temperature domain method and Hollomon–Jaffe tempering parameter (c). To simplify the presentation of these calculations, the predicted isothermal tempered hardness was approximated by a third-order polynomial fit (R2=0.975). By overlaying the predicted hardness values of the tempering cycles accounting for and discounting the heating portion of the thermal cycles ((c)), it can be seen that there was no significant effect of excluding the heating portion of the cycle on the hardness, thereby validating the isothermal tempering assumption in the present analysis.Threshold stress intensity factor for hydrogen-assisted cracking of CR-MO steel used as stationary storage buffer of a hydrogen refueling stationIn order to determine appropriate value for threshold stress intensity factor for hydrogen-assisted cracking (KIH), constant-displacement and rising-load tests were conducted in high-pressure hydrogen gas for JIS-SCM435 low alloy steel (Cr-Mo steel) used as stationary storage buffer of a hydrogen refuelling station with 0.2% proof strength and ultimate tensile strength equal to 772 MPa and 948 MPa respectively. Thresholds for crack arrest under constant displacement and for crack initiation under rising load were identified. The crack arrest threshold under constant displacement was 44.3 MPa m1/2 to 44.5 MPa m1/2 when small-scale yielding and plane-strain criteria were satisfied and the crack initiation threshold under rising load was 33.1 MPa m1/2 to 41.1 MPa m1/2 in 115 MPa hydrogen gas. The crack arrest threshold was roughly equivalent to the crack initiation threshold although the crack initiation threshold showed slightly more conservative values. It was considered that both test methods could be suitable to determine appropriate value for KIH for this material.To ensure the safety of steel storage buffers of hydrogen refuelling station, a leak-before-break (LBB) assessment shall be performed in accordance with ASME BPVC 2013 Sec. VIII – Div. 3 Article KD-10 A low alloy steel of JIS-SCM435 (Cr-Mo steel) used as real stationary storage buffer of a hydrogen refuelling station was examined in this study. The storage buffer had a nominal outer diameter of 355.6 mm and nominal wall thickness of 40.5 mm. The material of storage buffer was quenched and tempered. Tensile test specimens with the diameter of parallel portion equal to 5 mm were fabricated from the mid-thickness position of the wall along the longitudinal direction, and then tensile tests were conducted in air at room temperature. The 0.2% proof strength (σ0.2) and the ultimate tensile strength (σUTS) were 772 MPa and 948 MPa respectively. The plane strain fracture toughness (KIC) obtained in accordance with JSME S001-1992 Wedge-opening-load (WOL) specimens for constant displacement tests were designed according to ASTM E1681-03 . The WOL specimens were oriented so that the loading and crack growth directions were parallel to the circumferential and longitudinal axes, respectively, of the storage buffer (C-L orientation). Side-grooves were machined along the faces of the WOL specimens prior to pre-cracking, which reduced the specimen thickness by 15%. Fatigue pre-cracking was introduced in air at test frequencies (f) of 10 Hz and 20 Hz with a stress ratio (R) of 0.1. The pre-crack length (a) was 0.5 W. Maximum stress intensity factor during pre-cracking (Kpre-crack) was 15 MPa m1/2. Strain gauges were attached on the back face of the WOL specimens as shown in , in order to measure loads caused by tightening bolts and to monitor crack growth during high-pressure hydrogen gas exposure. After the fatigue pre-cracking, the WOL specimens were statically loaded by a fatigue testing machine in order to calibrate the relationship between load (P) and back face strain (BFS) for the final crack length. Referring to the relationship, the loading bolt was tightened in air until the stress intensity factors reached the given values. The following equations fI(a/W)=(2+a/W)(0.8072+8.858(a/W)−30.23(a/W)2+41.088(a/W)3−24.15(a/W)4+4.951(a/W)5)/(1−a/W)3/2,The bolt-loaded WOL specimens were placed into a stainless steel pressure vessel, and then exposed to 35 MPa or 115 MPa hydrogen gas for 1000 h at room temperature. After the exposure, the variations of BFS during unloading by loosening bolts were measured, then the WOL specimens were statically re-loaded by a fatigue testing machine to determine the final load (Pfin). Subsequently, the WOL specimens were fractured by fatigue test and the final crack lengths (afin) were measured from the fracture surfaces. Crack arrest threshold stress intensity factors were calculated with Eqs. Compact-tension (CT) specimens were fabricated for rising load tests with dimensions shown in . The orientation of the CT specimens relative to the storage buffer was the same as the WOL specimens, i.e., C-L orientation. Side-grooves were machined along the side faces of the specimens in the same plane as the pre-crack starter notch, which reduced the specimen thickness in this plane by 15%. Fatigue pre-crack was introduced in air at room temperature at f of 20 Hz with a R of 0.1 to a of 0.5 W under Kpre-crack of 10 and 27.7 MPa m1/2. The reason why Kpre-crack has such wide range was that the crack initiation thresholds under rising load were found to be close to the Kpre-crack of 27.7 MPa m1/2. Therefore, Kpre-crack was decreased to 10 MPa m1/2 for some specimens. After the fatigue pre-cracking, two types of rising load tests, which were stepwise rising load test and monotonic rising load test, were conducted in high-pressure hydrogen gas at room temperature.Stepwise rising load tests were performed in accordance with ISO 11114-4 method B The procedure of monotonic rising load tests was similar to ASTM E399-09 (b). Because the displacement rate should be slow enough to detect the crack initiation, displacement rate was 2 × 10−5 mm/s. shows the optical microscope images of the microstructure of the surface normal to the longitudinal direction of the storage buffer. The specimen was etched with 3% nital. Since the storage buffer was quenched and tempered, it was considered that the microstructure was bainite or tempered martensite. However, the observation of microstructure revealed grains with white appearance (W microstructure) and grains with black appearance (B microstructure) as shown in (a) and (b). It was considered that the heterogeneous microstructure was formed due to the difficulty of heat treatment because the storage buffer had large wall thickness (=40.5 mm).In order to investigate the microscopic hardness, Vickers hardness testing was performed for each microstructure. The measurement load was 0.01 kgf and the holding time was 30 s shows the results of the Vickers hardness tests. The average hardness of the W microstructure and the B microstructure were HV270 and HV331 respectively. Although the detail mechanism which caused such difference had not been clarified, it was presumed that the B microstructure was more susceptible to hydrogen embrittlement because the hardness of the B microstructure was higher than that of the W microstructure. shows the representative variation in BFS during 115 MPa hydrogen gas exposure. The symbol of Kapp means the initial applied stress intensity factor by bolt-loading. The crack initiation and the crack arrest were clearly determined from the change in BFS. The fact that the stop of the crack propagation is confirmed is critically important to determine threshold values. shows plots of Kappvs. incubation time. Although the incubation time varied greatly even at the same Kapp, the incubation time had a tendency to increase as Kapp decreased. The crack initiation threshold for the constant displacement test was 65 MPa m1/2. This value met the following small-scale yielding (SSY) and plane-strain validity criteria required in ASTM E1681-03 shows the relationship between crack arrest thresholds and Kapp. The crack arrest thresholds which met Eq. were 44.3 MPa m1/2 and 44.5 MPa m1/2. Some results which did not meet Eq. were slightly higher than those values, but all the crack arrest thresholds were much smaller than the crack initiation threshold (= 65 MPa m1/2) under constant displacement test. According to ASTM E1681-03 shows the typical example of relationship between load and time duration (P-t curve) for stepwise rising load tests in 115 MPa hydrogen gas at Kpre-crack of 10 MPa m1/2. The load dropped at 11.6 kN and the crack initiation threshold was 35.9 MPa m1/2. When Kpre-crack was 27.7 MPa m1/2, the crack initiation threshold was 33.1 MPa m1/2. According to ISO 11114-4 method B shows the P-t curve for a monotonic rising load test in 115 MPa hydrogen gas at Kpre-crack of 10 MPa m1/2. The load dropped at 11.4 kN and the crack initiation threshold was 35.3 MPa m1/2. The crack initiation threshold at Kpre-crack of 27.7 MPa m1/2 was 41.1 MPa m1/2. In terms of the crack initiation thresholds, there were little difference between the stepwise rising load tests and the monotonic rising load tests. A monotonic rising load test was also performed in 35 MPa hydrogen gas. The crack initiation threshold was 52.4 MPa m1/2. All the crack initiation thresholds satisfied Eq. summarizes the results from the constant displacement tests and the rising load tests. shows the comparison of the crack arrest thresholds and the crack initiation thresholds. The crack arrest thresholds from the constant displacement tests were roughly coincident with the crack initiation thresholds from the rising load tests in 35 MPa and 115 MPa hydrogen gas although the crack arrest thresholds were slightly higher than the crack initiation thresholds in 115 MPa hydrogen gas. Wada et al. . In this study, the crack arrest thresholds which satisfied Eq. were used to compare with the crack initiation thresholds but Nibur et al. used smaller WOL specimens with W and B equal to 56.9 mm and 22.2 mm respectively, which did not satisfy Eq. . Since it is known that specimen sizes strongly affect fracture toughness, the cause of the difference could be due to specimen sizes although Nibur et al. confirmed from FEM analysis and experiments that the crack arrest threshold was not dependent on a/W. Second one is due to different test method for each rising load test. Nibur et al. conducted the rising displacement tests in accordance with ASTM E1820-09 . In this study, the values of σ0.2 and σUTS were 772 MPa and 948 MPa respectively, but the microscopic hardness varied with the inhomogeneous microstructures as shown in , i.e., the Vickers hardness of W microstructure and B microstructure were HV270 and HV331 respectively. Kondo et al. Threshold stress intensity factor for hydrogen-assisted cracking, KIH, of JIS-SCM435 low alloy steel (Cr-Mo steel) used as stationary storage buffer of a hydrogen refuelling station has been examined from constant-displacement and rising load tests in 35 MPa and 115 MPa hydrogen. The obtained results are as follows:Crack growth monitoring technique using back face strain gauges was established to detect crack initiation and crack arrest under constant displacement test during high-pressure hydrogen gas exposure.The crack initiation thresholds in the constant displacement tests were much higher than the crack arrest thresholds. The crack arrest threshold shall be used to determine appropriate value for KIH rather than the crack initiation threshold in the constant displacement test.The crack arrest thresholds from the constant displacement tests were roughly coincident with the crack initiation thresholds from the rising displacement tests as far as small-scale yielding and plane strain criteria were satisfied. Both test methods of the constant-displacement and the rising-load tests were suitable to determine appropriate value for KIH.Natural convection from a circular cylinder in confined Bingham plastic fluidsHeat transfer by laminar natural convection to Bingham plastic fluids from a heated horizontal circular cylinder in a square cavity has been investigated numerically. The governing partial differential equations describing the fluid flow and heat transfer have been solved (using the finite-element based COMSOL solver) over wide ranges of the pertinent dimensionless parameters, namely, Rayleigh number (103⩽Ra⩽105), Prandtl number (1⩽Pr⩽500) and Bingham number (0⩽Bn⩽Bnmax) for a range of values of the ratio of the cylinder diameter to the size of the square cavity, 0.125⩽B⩽0.5. The detailed flow and temperature fields in the proximity of the heated cylinder are visualized in terms of the streamline and isotherm profiles, respectively. These also facilitate the delineation of the yielded and unyielded regions formed in different parts of the cavity. Further insights are provided in terms of the distribution of the local Nusselt number along the cylinder surface together with its average value. It is found that the average Nusselt number decreases with the increasing Bingham number up to a limiting value of the Bingham number (Bnmax) beyond which the average Nusselt number attains its asymptotic value, close to the pure conduction limit due to the virtually unyielding nature of the fluid. Furthermore, the influence of the aspect ratio, B, on the maximum Bingham number (Bnmax) and the resulting average Nusselt number has been explored extensively. It is found that as the size of the cavity increases with respect to the cylinder diameter, i.e., decreasing value of B, the both maximum Bingham number and average Nusselt number increase. On the other hand, Nusselt number shows a very weak dependence on the Prandtl number beyond that included in the definition of the Rayleigh number.Bingham number (≡τ0μBdgβΔT), dimensionlesspressure drag coefficient, dimensionlesspressure coefficient on the surface of cylinder, defined as 2(ph-p0)/ρcVr2Grashof number (≡ρc2gβΔTd3μB2), dimensionlessthermal conductivity of fluid, W m−1

K−1local pressure on the surface of cylinder, PaRayleigh number ≡ρc2cpgβΔTd3μBk, dimensionlessvelocity component in x-direction, dimensionlessvelocity component in y-direction, dimensionlessvelocity component in z-direction, dimensionlessWithin the framework of time-independent fluid behavior, yield-stress fluids display solid-like (unyielded) and fluid-like (yielded) regions in different parts of a given flow configuration depending upon the prevailing stress levels vis-a-vis the value of the yield stress of the fluid. Whether the true yield stress exists or not has been (and continues to be) a matter of intense discussion in the literature In contrast, the corresponding body of knowledge on heat transfer in such systems is very limited indeed, even in duct flows In particular, the coupled momentum and energy equations have been solved numerically for laminar natural convection from a heated circular cylinder submerged in quiescent Bingham plastic media in a square duct over the following ranges of conditions: Rayleigh number (103⩽Ra⩽105), Prandtl number (1⩽Pr⩽500), Bingham number (0⩽Bn⩽Bnmax) and the ratio of the cylinder diameter to the size of the square enclosure (0.125⩽B⩽0.5). The paper is concluded by presenting comparisons with the previous studies in the limiting cases of Newtonian fluid (Bn

= 0) and/or free convection without the heated circular cylinder placed at the axis of the enclosure filled with a Bingham fluid.Consider a horizontal circular cylinder of diameter d (infinitely long in z-direction) whose surface is maintained at a constant temperature, Th, and it is positioned collinearly in a square duct of side length L and the intervening annular region is filled with a Bingham plastic fluid. The four walls of the confining duct are maintained at a constant temperature Tc(<Th), as shown schematically in . In order to delineate the role of geometry, the value of B

= (d/L) was varied in the range 0.125⩽B⩽0.5. Due to the existing temperature difference between the wall and the cylinder, the density of the fluid will be minimum near the cylinder and it will increase gradually away from the cylinder ultimately reaching the value ρc corresponding to the wall temperature Tc. This, in turn, sets up a buoyancy induced flow leading to heat transfer by free (or natural) convection from the cylinder to the fluid or vice versa depending upon the direction of the imposed temperature difference in the system in a given application. Over the range of conditions spanned here, the resulting flow field is considered to be laminar, steady, two-dimensional and incompressible (except for the body force term in the y-momentum equation). The other thermo-physical properties of the fluid (thermal conductivity, k, heat capacity, cp, Bingham viscosity, μB and yield stress τ0) are assumed to be independent of temperature except for the density term in the body force term in the y-momentum equation. Since the maximum temperature difference (ΔT

=

Th

−

Tc) imposed here never exceeded 5 K, it is thus justified to use the physical properties of the fluid at the mean film temperature of (Th

+

Tc)/2. The variation of the fluid density with temperature is treated by the well known Boussinesq approximation as:where ρc is the fluid density at the reference temperature Tc and β is the coefficient of thermal expansion at a constant temperature defined as:Under these assumptions, the coupled governing equations for fluid flow and heat transfer can be written in their dimensionless form as follows:∂(VxVx)∂x+∂(VxVy)∂y=-∂p∂x+PrRa∂τxx∂x+∂τyx∂y∂(VyVx)∂x+∂(VyVy)∂y=-∂p∂y+θ+PrRa∂τxy∂x+∂τyy∂yNote that the viscous dissipation contribution in the energy equation has been assumed to be negligible. Evidently, due to the buoyancy induced flow, there is a strong coupling between the velocity and temperature fields and hence one needs to solve the energy and momentum equations simultaneously together with an appropriate constitutive equation for the fluid rheological behavior and boundary conditions.For a Bingham plastic fluid, the extra stress tensor in simple shear may be written as follows:Naturally, the discontinuity inherent in this equation poses enormous difficulties in attempting numerical solution of the governing equations. In the present study, this difficulty is circumvented by employing the regularization scheme due to Papanastasiou where m is the regularization parameter. In the limit of m