In this paper, a multiscale investigation of fatigue crack initiation in shape memory alloys (SMAs) based on Transformation Induced Plasticity (TRIP) is presented. A mechanism for fatigue crack initiation during cyclic stress-induced phase transformation along with theoretical model is proposed. To validate the TRIP-based model, quasi-static tests at different ambient temperatures, 40∘C , 52∘C and 65∘C , and strain and stress controlled low-cycle fatigue tests at different frequencies ranging from 0.16 Hz to 5 Hz on pseudoelastic NiTi wires are carried out. The results show that, (i) TRIP appearing on phase transformation interfaces is the key factor that drives the fatigue crack initiation during cyclic stress-induced phase transformation in SMAs; (ii) maximum temperature during phase transformation is a relevant indicator to predict low-cycle fatigue of SMAs and, (iii) within the range of pseudoelasticity and below the plastic yield, low-cycle fatigue of SMAs is not directly correlated with the mechanical loads applied at macro-scale; in the sense that, if the maximum temperature reached during loading cycles is kept constant, the fatigue lifetime remains unchanged whatever the amplitude of the mechanical loading is. Based on the findings, a new criterion for pseudoelastic low-cycle fatigue of SMAs as well as fatigue-isolines diagram are proposed and validated experimentally.

This paper develops necessary preprocessors for image-based micromechanical analysis of polycrystalline-polyphase microstructures of Al alloys such as Al7075-T651. Starting from input data in the form of electron back scatter diffraction (EBSD) and scanning electron microscopy (SEM) maps of orthogonal surfaces of experimental specimens, the paper creates a robust methodology for generating 3D statistically equivalent virtual microstructures (3D-SEVMs) by 3D stereological projection of 2D statistical distribution and correlation functions using a genetic algorithm (GA)-based numerical algorithm. Validation studies of the SEVM reconstruction process by comparing with morphological and crystallographic distributions of grains and precipitates from the experiments. Next, microstructure-based statistically equivalent representative volume element (M-SERVE) that corresponds to the minimum sized SERVE for convergence of morphological or crystallographic distributions, are established using the Kolmogorov–Smirnov (KS) tests. Finally, property-based statistically equivalent RVE (P-SERVE), defined as the smallest SERVE for predicting response functions (both effective and local), are estimated by conducting crystal plasticity finite-element simulations. Convergence plots of material response functions are used to assess the P-SERVE. Comparison of M-SERVE and P-SERVE sizes are made to comprehend microstructure-property relations.

The interaction among solute atoms, local deformation velocity and viscoplasticity of host material plays a significant role in determining the stress evolution and concentration distribution in host material, especially in large-deformed electrode materials made from silicon and tin. In this work, a new viscoplastic model that describes diffusion-induced deformation is developed from the framework of the generation of defects due to the migration of solute atoms. The total flux in the diffusion equation is separated into two parts; one is the diffusion part due to the migration of solute atoms, and the other is the convection part due to the local deformation velocity in host material. Using the diffusion-convection equation, the theory of nonlinear continuum mechanics and the developed constitutive relationship, we analyze the Cauchy stress and viscoplastic deformation in a thin film Si-electrode on a “rigid” substrate numerically. The average Cauchy stress during lithiation and de-lithiation with the boundary flux of j0, 2j0 and 0.33j0 is calculated, and the numerical results reveal that the magnitude of compressive Cauchy stress in the thin film Si-electrode increases with the increase of the boundary flux. The numerical results are in good accord with the results from experimental study and the first principle simulation for the entire charging/discharging process.

A crystal plasticity finite element (CPFE) model is developed for pseudoelastic NiTi shape memory alloy (SMA). The model includes various inelastic mechanisms of deformation such as martensite transformation, dislocation glide in austenite phase and twinning in the martensite phase. This model is based on the finite deformation theory and predicts phase transformation, stress field and residual strain due to slip and twinning. Following the work of Anand and Gurtin (2003), the Helmholtz free energy is derived and further the thermodynamic driving forces for slip, twin and phase transformation are obtained by using Clausius-Duhem inequality. The developed constitutive model has been implemented within a user material subroutine interface VUMAT in ABAQUS™/Explicit. The activation of different inelasticity mechanisms at different temperatures and strains are first verified by performing various simulations of uniaxial tensile deformation. Then the model is calibrated and validated against the experimental stress-strain response of NiTi single crystal as reported in the literature. The single crystal constitutive model is extended for modeling the response of a polycrystal with both initial random and textured crystallographic orientations using Taylor scale transition technique. A series of simulations are performed on polycrystalline representative volume element (RVE) at various temperatures and strains. The effect of temperature and imposed strain on phase transformation and residual strain is investigated systematically. The residual strain increases due to slip in austenite phase and twinning in the martensite phases that are activated as temperature and imposed strain increase respectively. Further the uniaxial loading conditions are extended to multiaxial loading and the results are compared against the experimental data.

In this study, the cyclic mechanical characters of 316L stainless steel at elevated temperature are extensively investigated by the experimental and cyclic constitutive models. The experiments include the monotonic tensile tests with different loading rates and the low cycle fatigue tests considering the effect of strain amplitudes, strain rates and loading sequences. The evolution of cyclic stress amplitudes, hysteresis loops and elastic modulus under various loading conditions are comprehensively analyzed. The experimental results show that the 316L steel at elevated temperature performs a typical three-stage cyclic mechanical response, i.e., initial hardening, subsequent saturation and final accelerated softening. The cyclic softening in both stiffness and flow stress is mainly caused by the nucleation of micro-voids or micro-cracks, and the subsequent coalesce and propagation. Furthermore, although the nearly rate-independent mechanical behavior is observed at monotonic tensile and first several fatigue cycles due to the DSA effect, the cyclic hardening/softening behavior shows a significant strain-rate and loading history dependence. Finally, inspired by the experimental observations and analyses, a damage-coupled cyclic elastic-viscoplastic constitutive model involving strain-range, strain-rate and loading history dependence is proposed to predict the complex cyclic behaviors of the material at elevated temperature. A hardening factor is incorporated into the Chaboche kinematic hardening equations to model the kinematic-induced hardening behavior. And the plastic strain memory surface and the maximum plastic strain rate are introduced to model the strain-range, strain-rate and loading history dependence of cyclic behavior. The proposed model is proved to effectively describe the complex evolution of not only cyclic stress amplitude but also hysteresis loops for the 316L steel at elevated temperature.

The complicated constitutive behaviour of cast iron, involving a non-linear elastic regime, tension-compression stress asymmetry, varying elastic modulus and an inflection in the tension-to-compression hardening curve, is investigated using a micromechanical modelling approach. In this way, it is demonstrated that the abnormalities observed in the constitutive behaviour are qualitatively and quantitatively explained by the interaction behaviour between the matrix and graphite constituents. In initial tension, the absence of linearity is rationalised by the successive loss in load-carrying capacity of the graphite phase due to debonding, which in subsequent cycling, results in the opening and re-contact of the matrix-graphite interface. This effect is demonstrated to result in tension-compression asymmetry in stress and elastic modulus, as well as the inflection in tension-to-compression loading. The given model of explanation is validated by comparison to the experimentally acquired microscopic strain field in EN-GJV-400 at locations where stress concentrations are generated due to the matrix-graphite debonding, using high-resolution digital image correlation of scanning electron images.

Referring to the existing experimental investigation, a meso-mechanical constitutive model is constructed to describe the deformation and failure of bulk metallic glass composites under the monotonic uniaxial tensile and compressive loading conditions. Firstly, a free volume based constitutive model considering the failure mechanisms of bulk metallic glass and a unified visco-plastic model are employed for the bulk metallic glass matrix and toughening phase, respectively. To effectively reflect the local failure occurring in the bulk metallic glass matrix of the composites, a new two-leveled homogenization method is developed by extending the traditional Mori-Tanaka’s method. Then, the algorithmic tangent operators for both of bulk metallic glass matrix and toughening phase are derived; the numerical integration algorithm of proposed model is also developed. Finally, the effectiveness of proposed model is validated by predicting the deformation and failure of bulk metallic glass composites under the monotonic tension and compression, respectively. Comparison of predicted results and corresponding experimental ones demonstrates that the proposed model can predict the deformation and local failure of bulk metallic glass composites well.

In this paper, a new constitutive model is proposed for the behavior of thermoplastic polymers under non-isothermal conditions. The model couples linear viscoelasticity, viscoplasticity and thermal effects. It is formulated within the framework of irreversible thermodynamics. The total strain is the sum of viscoelastic, viscoplastic and thermal strains. General hereditary integrals describe the thermo-viscoelastic response. The viscoplastic part accounts for both isotropic and kinematic hardenings. The stress-strain response and the material self-heating are predicted and compared to experimental data on Polyamide 66 (PA66) and Polypropylene (PP). Good agreement between the numerical simulations and experimental data was obtained for the two materials.

The effect of anisotropy and strain rate on the work hardening and fracture behavior of high manganese twinning induced plasticity (TWIP) steel was investigated. Uni-axial tensile tests in conjunction with digital image correlation were carried out to study the local deformation behavior and failure initiation. The influence of adiabatic heating on the mechanical behavior was studied by performing quasi-static and dynamic tensile tests with synchronous temperature and strain measurements. Interrupted micro tensile test samples were analyzed in the scanning electron microscope combined with the electron backscatter diffraction measurements to study the evolution of microstructure, twinning, and micro-cracking mechanisms. TWIP steel showed high strength of ≥1100 MPa in combination with excellent ductility of ≥45 %, but slight variation in yield strength and elongation values was observed when tested along rolling, transverse and shear (45∘) directions. The material exhibited excellent energy absorption capacity of above 55 kJ/kg at different strain rates. The serrations on the σ–ε curves was the main characteristic behavior of TWIP steel observed under quasi-static loading, which start to disappear with increasing ε˙ and vanishes completely under dynamic loading. Serrated flow behavior was caused due to dynamic strain aging (DSA), which include the dynamic interaction of solute atoms with dislocations and the Mn-C short-range ordering. The plastic instability caused due to DSA has led to inhomogeneous behavior in the form of nucleation and propagation of shear bands during deformation known as Portevin-Le Chatelier (PLC) effect. Temperature rise due to adiabatic heating at high ε˙ has led to increase of SFE, thereby resulting in a change of twinning behavior or the promotion of dislocation glide. Failure at macro-level occurred at the intersection of two shear bands close to the edge of the specimen with the negligible amount of strain localization. At the micro-level, cracks originated mainly at grain boundaries (GB) and triple junctions due to increased stress concentration caused by the intercepting deformation twins and the slip band extrusions at GB. Intergranular crack initiation and propagation instances were evident in the microstructure along with the rapid nucleation of minute voids. Even though few micro-cracks have appeared at lower strains, their growth was rather limited. Thus, TWIP steel exhibited enhanced resistance to damage resulting in superior ductility.

The mechanical response of hexagonal close-packed (HCP) materials are highly anisotropic due to the inherently asymmetric slip and twin systems in the HCP atomic structure. The slip and twin systems in the HCP atomic structure, i.e., slip/twin directions and planes, are not isotropic in terms of geometry. This inhomogeneous directionality produces various stress-strain responses along different loading directions. The question of which slip/twin systems are available in a specific HCP material has not been well understood and needs further experimental investigation. Since there was lack of experimental evidence that the pyramidal I slip is activated in single crystal magnesium, the pyramidal I slip has not been considered as the major slip mode in the computation research of single crystal magnesium. However, recent experimental and atomistic simulation works indicate that the pyramidal I slip is the dominant slip mode in the deformation of single crystal magnesium. Taking into account these recent findings on the pyramidal I slip in magnesium, this research aims to investigate the mechanical response of single crystal magnesium using the most number of slip/twin systems ever explored, including the pyramidal I slip system, tensile twin, compressive twin and etc. To quantify the contribution of each slip and twin system to overall deformation, i.e, the total shear strain amount, the plane strain compression experiment of single crystal magnesium performed by (Kelley and Hosford, 1967, 1968) is reproduced using crystal plasticity (CP) simulations. The computation scheme employed uses a standard crystal plasticity framework that takes into account the slip process and has an additional feature to implement the twinning process. Findings from the CP simulations indicate that the contribution of the pyramidal I slip mode to the overall shear strain in the deformation of single crystal magnesium is significant and comparable to that of the pyramidal II slip mode if their CRSS (Critical Resolved Shear Stress) are of similar magnitudes. The findings indicate as well that the pyramidal I slip mode will be dominant over pyramidal II in real experiments since the CRSS of pyramidal I has been reported to be smaller than that of pyramidal II by the recent experimental and atomistic simulation researches.

A numerical investigation of wedge indentation, with a nearly flat indenter, into a monazite (LaPO4) single crystal is carried out to obtain the asymptotic field solution associated with the moving contact point singularities. The crystal orientation is such that plane strain conditions prevail, under the assumption of small scale yielding, as out-of-plane deformations are eliminated due to out-of-plane mirror symmetry of the crystal, specimen and loading state. The plastic deformation in such a 2D study can be described in terms of effective in-plane slip systems comprised of crystallographic slip systems with equal and opposite out-of-plane deformation and rotation. The numerical simulations are conducted within a framework specialized for self-similar problems and adopts a visco-plastic single crystal material model. The detailed numerical investigation of the monazite single crystal reveals that the effective slip systems lead to a non-symmetric in-plane deformation field, which is consistent with the absence of in-plane mirror symmetries of the crystal. Interestingly, the non-symmetric deformation field results in one contact point singularity travelling at a greater speed than the other. The deformation near the moving contact point singularities are found to be divided into two angular sectors separated by a boundary of glide shear type. The slip rates on the individual systems reveal that one slip system dominates at both contact points, whereas the other slip system shows negligible activity. Thus, only one slip system gives rise to a discontinuity in the slip rate field.

This study proposes a modelling approach capable of capturing both the fatigue response and localisation of failure in cemented materials. This modelling approach takes advantage of Discrete Element Method (DEM) to reproduce the heterogeneous microstructure and crack development in cemented materials. In conjunction with this, a new constitutive model is developed to characterise the fatigue behaviour of the materials at the grain scale. The model formulation is based on coupling damage mechanics and plasticity theory and combining with a fatigue damage evolution law to describe the degrading response of cemented materials subjected to cyclic loading. The proposed model is employed to govern the explicit behaviours of DEM bonding contacts representing cement bridges between aggregates in the physical materials. The macro-behaviour is then obtained in DEM simulations as the collective response of all contacts and particles in the material domain. Through numerical experiments, the proposed modelling approach is shown to capture well the fatigue behaviour and cracking process in cemented materials subjected to cyclic loading. The microstructural effects on the fatigue response of the materials are naturally reproduced in simulations thanks to the discrete nature of DEM. These results demonstrate the capability of the proposed modelling approach as well as its potential to be a faithfully numerical technique for modelling and investigating fatigue damage in cemented materials.

On the basis of the order in which twinning occurs, twins are termed primary, secondary, and tertiary. In HCP materials, compression twins (CT) and extension twins (ET) are observed to form alternatively during sequential twinning. However, selections of twinning systems and variants are not yet fully understood. Both ET→CT→ET and CT→ET→CT sequences have been reported in literatures. Here we conduct a systematic and statistical study on the evolutions of twinning sequences and variants during cryogenic rolling of Ti. Both twinning sequences are observed in the same sample. Current statistical results indicate the selections of the twinning sequence and variants are governed by the following criteria: (1) the twinning sequence in an individual grain depends on its initial orientation; (2) the twin variant selection is mainly governed by the Schmid's law, although a few non-Schmid twins are observed along the short axis of the parent grains. These criteria are thought applicable to other HCP metallic materials.

This study develops an Orowan precipitate hardening equation applicable to twin propagation. It is derived from a series of two dimensional dislocation dynamics simulations of a twin tip impinging upon a line of obstacles. When the number of twinning dislocations present is low, the Orowan stress increases with the number of twinning dislocations in the twin. When the number of twinning dislocations is high, the trailing dislocations do not partake in the critical initial bypass event, instead, they multiply the stress on those leading dislocations that do. The result is that bypass takes place at lower stresses when more twinning dislocations are present. A double super dislocation model provides a good description of the phenomenon. It is seen that particle size exerts a stronger role than in the conventional Orowan hardening equation and that there exists a number of twinning dislocations for which the Orowan stress is greatest. For alloy design using non-shearable precipitates, the basic objective of decreasing the inter-particle spacing on the twin plane remains most efficacious.

A history dependent and physically-motivated Internal State Variable (ISV) constitutive model is presented that simultaneously accounts for the effects of static recrystallization, dynamic recrystallization, and grain size with respect to the mechanical behavior under different strain rates, temperatures, and pressures. A unique aspect of our ISV constitutive model is that grain size and recrystallized volume fraction can be directly included along with its associated rate of change under deformation and time in a coupled manner. The present ISV constitutive model was calibrated to several metals (oxygen-free high conductivity copper, AZ31 magnesium alloy, pure nickel, and 1010 low carbon steel) and geological materials (olivine and clinopyroxene). The model calibration shows good agreement with the experimental stress-strain behavior and average grain size data. Validation of the ISV constitutive model was accomplished by applying complex and history sensitive thermomechanical problems once the model was calibrated: i) sequential transitions of different loading conditions and ii) a multistage tubing process. The history dependence naturally provided by ISVs enabled the present model to effectively capture the complex boundary value problems with changing boundary conditions.

The stress-strain behavior of the aluminum alloy AA3103 subjected to single and double strain-path changes (SPCs) is studied experimentally. The experimental program includes compression-tension, tension-tension, rolling-tension and tension-rolling-tension tests. The considered AA3103 plate exhibits plastic anisotropy, a strong Bauschinger effect with hardening stagnation after strain reversal, cross-hardening and permanent softening after orthogonal SPCs in the tension-tension tests. However, when instead the orthogonal SPCs are obtained by rolling-tension tests, cross-softening is observed. The same behavior is seen in more complex tension-rolling-tension tests. Three state-of-the-art advanced plasticity models are used in an attempt to model the experimentally observed behavior. These models all account for plastic anisotropy and transient effects after SPCs, using a microstructure deviator tensor to describe a fading memory of the deformation history. While the models successfully describe the behavior after strain reversals, they fail to represent the behavior after orthogonal SPCs. It is concluded that the Schmitt angle, on which the current models depend, is not sufficient for a fundamental description of SPCs for the considered AA3103 alloy.

Plastic strain induced grain boundary migration (SIBM) is investigated by means of in-situ SEM experiments and AFM surface observations in the case of 4N pure aluminum. The study focuses on two polycrystalline samples obtained through different thermo-mechanical treatments that provide different initial (grain size and orientation) microstructures with different evolutions during heating. A total of 77 grain boundaries (GBs) were characterized from both samples. Evaluation of GB displacements was allowed by determining fixed points on initial and final EBSD maps and marks from thermal grooving along GB contours. Some sub-surface final examinations ensured the surface ones being pretty well representative of the bulk behavior. The GB displacements were related to their geometry and to their initially available migration driving force P , the two main contributions of which were estimated. The boundary curvature contribution Pc is estimated from SEM observations and the so-called "stored energy" contribution PΔρ (that results from the differential of dislocation densities Δρ across the boundary) is estimated using a crystal plasticity modeling within a homogenization scheme for aggregates validated on slip trace identifications from AFM observations. The resulting driving force P , related to the GB velocity V through the widely used law V=MP is compared with the observed displacement during a finite annealing time. Additional effects as thermal grooving and triple junction pinning or pulling are also discussed from complementary SEM and AFM observations of some typical GBs. Some evidences of GB out-of-plane displacements possibly contributing to the migration process are also commented. The quite extensive set of data regarding grain orientation, GB misorientation and curvature, intracrystalline slip activity and evolution during heating constitutes references for future comparisons with mesoscale simulations.

Direct comparisons between crystal plasticity simulations and experiments dedicated to test a sample containing a small number of grains (oligocrystal), instrumented using full field measurement techniques (DIC, grid method), have demonstrated their efficiency to reproduce the behavior of BCC and FCC metals at the grain scale. The extension of this approach to HCP metals, specifically for a grade 2 commercially pure titanium (CP-Ti) sample, is the objective of the present work. The influence of the critical resolved shear stress ratios on the numerical predictions of strain field and slip activity during uniaxial tension of the titanium oligocrystal was investigated. Simulation results were compared with their experimental counterparts, showing that a small variation of the critical resolved shear stress ratios identified by the authors in a previous study dedicated to grade 1 CP-Ti [Hama et al., Int. J. Plast., 91(2017), 77.] reproduced the experimental deformation behavior satisfactorily.

The local stress and strain are analysed in a heterogeneous microstructure induced by compression of aluminium rings under nearly full sticking conditions. This analysis is based on characterization of mechanical behaviour and microstructure applying three complementary techniques covering multiple length scales: microhardness, electron microscopy (electron backscatter diffraction) and finite element modelling. The findings are underpinned by applying those techniques in an analysis of a homogeneous microstructure induced by compression of hot-extruded aluminium cylinders. The local stress and strain are estimated at 14 different positions in two rings representing large variations in strain. A comparison with the stress and strain in the homogeneously compressed cylinders related to the average spacing between deformation induced low and high angle boundaries, validates the characterization techniques and supports a hypothesis that the microstructure of local regions in a heterogeneous structure evolve in accordance with universal principles and mechanisms established for the evolution of the deformation microstructure of polycrystalline metals.

In this work, the crack tip fields in the neighborhood of a stationary mode I crack in a hardening Cu single crystal, under tensile load was investigated. A modified boundary layer (MBL) simulation was performed with the implementation of Bassani and Wu (1991) hardening model while taking into account the crystal elastic anisotropy. The effect of latent hardening ratio (LHR) on the stress and strain fields was studied by considering three different values of LHR, q, viz. diagonal hardening (q=0 ) and latent hardening (q=1,1.4 ). In addition, the effect of crack tip constraint representing different test specimens and load conditions was examined with the inclusion of T-stress through the imposed displacement boundary condition. Important observations from this work include the suppression of kink band, presence of elastic sectors, and the occurrence of triple slip near the crack tip. The increase of T-stress suppressed the plastic strain accumulation and showed a decrease in the number of triple slip sectors near the crack tip. Whereas, the increase in q made the triple slip regions slightly prominent with wider angular spread for non-negative T. But, for negative T case, rise in q caused a suppression in the angular spread of triple slip regions. Also, the implementation of T-stress allowed for a correlation between full 3D and 2D plane strain simulations in the analysis of crack tip fields for hardening single crystals. The present study offers a comprehensive investigation of the effect of crack tip constraint and latent hardening ratio on the crack tip fields for hardening FCC single crystals.

A serrated flow, which occurs in a material undergoing mechanical deformation, is a complex process of great engineering significance. Here statistical, dynamical, and multifractal modeling and analyses were performed on the stress-time series to characterize and model the stress-drop behavior of an Al0.5CoCrCuFeNi high-entropy alloy (HEA). Results indicate that the spatiotemporal dynamics of the serrated flow is affected by changes in the strain rate and test temperature. The sample entropy, in general, was found to be the highest in the samples tested at 500oC. The higher complexity in the serrated flow at this temperature appeared to be associated with the stress-drop behavior that had intermediate values in terms of the maximum stress drop, the multifractality of the data set, and the histogram distributions. Moreover, the sample entropy was the lowest for the samples tested at 600oC. The lower complexity values were associated with a wider multifractal spectrum and a less uniform and sparser distribution of the stress-drop magnitudes. In terms of the serration types, Type-C serrations were related to the lowest complexity values, highest multifractal spectra, and higher probability of exhibiting larger stress drops. Conversely, Type-A and B serrations were associated with the higher complexity, smaller spectra, and lower probability of higher stress drops. Furthermore, the body-centered-cubic (BCC) structure and the fully-ordered L12 nano-particles were found to emerge in the samples at 600oC and are thought to be linked with the decreased spatiotemporal correlations in the stress-drop behavior.

The thermodynamic dislocation theory developed for non-uniform plastic deformations is used for the analysis of twisted copper wires. With a small set of physical parameters, assumed to be independent of strain rate and temperature, we can simulate the torque-twist curves that match the experimental ones of Liu et al. [2012]. It is shown that the size effect results from the nucleation and pile-up of excess dislocations.

The microstructure of dislocations can be accessed by the total density of dislocations or the density of geometrically necessary dislocations (GND). The total dislocation density determines the flow strength of a crystal, which, in the case of high dislocation contents, is a quantity very difficult to measure accurately. On the other hand, related to crystal rotations, the GND densities are conveniently measured from electron diffraction experiments or calculated via simulations. Here, a novel and modern approach is proposed to understand the microstructures of dislocations based on deep learning, which estimates the total density of dislocations from a given density of GND distributions. In this method, the convolutional neural networks (ConvNets) are applied to extract the hidden information in the GND distribution maps to understand the microstructures of dislocations. It is demonstrated that the pre-trained ConvNets can be used to predict the distribution of total dislocation density from a small GND density map. Moreover, this technique is further developed to post-process real EBSD images for α-Fe to estimate the average total dislocation density, which corresponds to stress increments from a Taylor hardening assumption that is in good agreement with experimental values. Compared with previous methods involving much effort to track individual dislocations or other quantities, the present machine learning method is quick and convenient to use.

In engineering applications, various types of defects inevitably exist in materials which would critically affect their properties. By introducing an edge dislocation into the model of single-crystal iron, the plasticity and α→ ε phase transition in iron under shock loading have been investigated by means of non-equilibrium molecular dynamics (NEMD) simulations with a modified analytic embedded-atom model potential. Plastic slip is clearly observed in our work, which is induced by the initial edge dislocation under shock loading. The activated slip systems are considered as {110}<111> at the nucleation stage of dislocation generation, and then a self-adaptive transformation process occurs, which results in transforming the activated slip systems from {110}<111> into {112}<111>. The α→ ε phase transition only occurs after the activation of dislocation slip, which indicates there is a strong connection between plasticity and the phase transition. The process of this plasticity-controlled phase transition is illustrated. By calculating the resolved shear stress along the shuffle plane of the shocked crystal iron at different moments, the mechanism of the plasticity-controlled phase transition is deeply discussed. Our findings could contribute to the better understanding of the behaviors of iron or iron-based alloy under high pressure conditions.

The widespread use of magnesium alloys in applications that require high specific strength and stiffness has been hindered by its relatively low ductility. The hexagonal close-packed crystalline structure of magnesium alloys causes strong anisotropy in the mechanical response, which is reasonably well understood; however, the failure behavior is more complex. It is not clear whether the plastic anisotropy or the existence of second phase particles control failure, and to date, more attention has been given to the former than the latter. In this work, a series of high-rate tension experiments were performed on thin foil specimens of hot rolled magnesium alloy AZ31B using a miniaturized tensile Kolsky bar along an array of angles in the normal-rolling plane at strain rates of nominally 104s−1 . These experiments are compared with a set of finite element computations employing crystal plasticity and direct numerical simulation of void-nucleating second phase particles measured using micro-CT. Simulations are used to quantify the relative role that plastic anisotropy and second phase particle morphology play in dictating the failure response of rolled magnesium. Results indicate that plastic anisotropy dictates the way that voids grow and coalesce, and that in some cases, the pronounced plastic anisotropy of magnesium increases, rather than decreases, the maximum strain to failure. In all cases, the large second phase particles in rolled magnesium AZ31B greatly reduce the maximum failure strain as compared with an equivalent volume fraction of randomly distributed spherical particles. Additionally, it is shown that simulations lacking a proper description of orientation-dependent plastic anisotropy and particle morphology do not correlate well with measured failure behavior.

The metals with gradient nanostructures possess exceptionally superior mechanical properties. Here, the gradient-nanotwinned 304 stainless steel wires are fabricated by surface mechanical attrition treatment (SMAT) with a range of process time. The quasi-static tensile tests and dynamic compressive tests are conducted to examine the constitutive response of gradient-nanotwinned 304 stainless steels under different loadings. The experimental measurements show that under static and dynamic loadings, their mechanical properties are closely related to the SMAT process time. With an increase in the process time, their yield strength is improved, while their ductility is weakened. Furthermore, a theoretical model is proposed to describe the static and dynamic constitutive relation of gradient nanotwinned 304 stainless steels. The micromechanical model of nanotwinned composite is developed to characterize the constitutive relation of the material with nanograins embedded in nanotwinned matrix in depth. For the constitutive relations of each phase in nanotwinned composite structure, the athermal behaviors of dislocations are only considered in describing the flow stress under the static loadings. The size-dependent athermal flow stress and rate-dependent thermal flow stress are both involved under the dynamic loadings. The theoretical simulations demonstrated that the mechanical response of gradient-nanotwinned 304 stainless steels under different loadings can be successfully characterized by the presented model. A good agreement is obtained between the numerical results and experimental measurements. Furthermore, the mechanical properties of gradient-nanotwinned 304 stainless steels are forecasted for the various distribution of twin spacing along the depth. The results in this work are helpful for optimizing the static and dynamic mechanical performance of the gradient-nanostructured metallic materials through controlling microstructural size and distribution.

This paper deals with continuous description of elasto-plastic materials with lattice defects such as dislocations and disclinations, and grain boundaries. The behaviour of crystalline solids containing defects is described by non-local fields that are smooth over an interatomic length scale and at times of micro-seconds. The dislocation and disclination densities are appropriate measures of incompatibilities of the plastic distortion and of the plastic connection relative to plastic distortion, respectively. The grain boundaries will be simulated in terms of an array of disclination dipoles. The heterogeneous initial disclinations are a source of dislocations. These lattice defects, stress, strain and the displacement vector will be provided by solving initial and boundary value problems in elasto-plastic bodies, which involve dissipative evolution equations for plastic distortion and disclination tensor. The numerical procedure and corresponding algorithms to solve the variational formulation of the initial and boundary value problems are provided. The results of numerical simulations are analyzed and a number of graphs illustrate the elasto-plastic behaviour of the sheet when a shear stress is applied on one of its edge.

This paper proposes a grain fragmentation modeling approach that couples continuum dislocation dynamics analysis with a crystal-plasticity framework. The proposed model investigates the microstructural features of FCC metals subjected to severe plastic deformation (SPD) processes. Several aspects of the deformation process were considered in this model, including texture evolution, statistically stored dislocations (SSDs) and geometrically necessary dislocations (GNDs) densities evolution, and grains fragmentation and its effect on the overall mechanical response. The proposed model was applied to a reference volume element (RVE) in which the grains are distributed and assigned an initial position. Within the model, each grain has the ability to split into 1024 new smaller grains, which subsequently leads to strain hardening and grain refinement. The latter was modeled by accounting for the grain-grain interaction, for which the concept of the GNDs is incorporated into the mean free path of the dislocations. GNDs were assumed to be induced by grain boundaries that restrict the free deformation of a grain and result in an increase of stresses leading to the grain size reduction. Our grain fragmentation hypothesis was based on the Tóth et al. (2010) lattice curvature assumption [Tóth, L.S., Estrin, Y., Lapovok, R., Gu, C., 2010. A model of grain fragmentation based on lattice curvature. Acta Mater. 58, 1782–1794]. The grain refinement procedure was triggered when the misorientation threshold between subgrains was exceeded. The model parameters were calibrated using torsion tests of pure copper material. The simulation results give reliable predictions of the crystallographic texture, the evolution of dislocation density, and the final grain size based on available experimental data.

To explore the interactive influence of the deformation stress state and material microstructural grain size on the fracture behaviour in micro-scaled deformation, a series of micro-scale copper specimens of various geometrical dimensions and microstructural grain sizes are prepared and deformed to achieve various stress states represented by stress-related variables, such as the normalised third deviatoric stress invariant and the stress triaxiality. The speckle pattern method of continuous tracking is used to investigate the mechanical responses of materials in various deformation stress states and material microstructures, and a finite-element simulation of each deformation is conducted with the combined surface layer and grain boundary strengthening constitutive model, which considers the contributions of the surface grain, grain interior and grain boundary in representing the grain and geometry sizes. The interactive effects of the normalised third invariant, stress triaxiality and microstructural grain size on the fracture strain are identified and established by accounting for the correlation between the results of simulation and those of physical experimentation. Their influences on the fracture mechanism, mode and behaviour are further explored. The results reveal that greater stress decreases the fracture strain in the tensile deformation of round bar and cylindrical compression and increases the fracture strain in sheet shear and tensile deformations. The larger grain size generates fewer micro-voids, more uneven grain distribution and severer localisation deformation, which accelerates failure. Furthermore, stress triaxiality and the normalised third invariant at a low stress triaxiality are decreased with the increase of grain size, which in turn affects the occurrence of fracture. These effects coexist and compete with each other. In view of these influences, a larger grain size and a higher stress state inhibit the occurrence of fracture for sheet specimens with fracture modes from shear-dominant to dimple-dominant; in contrast, a smaller grain size and a lower stress state inhibit the occurrence of fracture in other cases.

High-resolution crystal plasticity-finite element method (CPFEM) simulations are performed to provide new reference values of the Taylor factor M and the isotropic yield surface exponent a for high stacking fault energy face-centred-cubic (FCC) polycrystalline metals with random orientations. The visco-plastic Taylor factor with strain rate sensitivity M˜ is introduced and linearly extrapolated to its zero strain rate sensitivity limit to give the new reference value of M. The linear extrapolation technique is also employed to define the new reference value of a . The obtained new reference values are 2.7 and 6.9, for M and a , respectively, which are much smaller than the reference values currently used for FCC materials based on full constraint (FC) Taylor model calculations, i.e. 3.07 for M and 8 for a. Other state-of-the-art Taylor-type models, e.g. ALamel, ALamel with the type III relaxation (ALamel-T3) and the visco-plastic self-consistent (VPSC) models, can also give values for M and a much smaller than the FC-Taylor calculations. The performance of the CPFEM and these state-of-art Taylor-type models in terms of resolving deformation and stress fields within the aggregate can only be assessed in a statistical manner since all are statistical aggregate models. Selected statistical distributions are analysed for all models, by means of local deviations of the velocity gradient tensor, of the plastic deformation-rate tensor and of the stress tensor etc., for uniaxial tensile deformation. The ALamel models are found to provide similar statistics as CPFEM, whereas the VPSC model results are qualitatively different. The intra-grain analysis for CPFEM demonstrates that the intra-grain interactions are as much important as the local interactions at the grain boundaries.

In this paper, an infinitesimal-strain based FFT formulation is extended to account for deformation twinning in hexagonal close-packed (HCP) materials. A model called the Complex Voxel (CV) model is developed that includes twinning as pseudo-slip and accounts for interaction between parent grains and corresponding twin variants by assuming a Taylor-type approximation at the voxel level. The macroscopic deformation behaviour of Magnesium alloy AZ31, a representative HCP material, is simulated in three different loading directions. Detailed analysis of twinning dominated deformation reveals that: (a) Global Schmid factors indicate twin variant selection and the rate of twin growth; (b) Basal slip is the dominant active slip system during the twin nucleation and twin growth stages; (c) A comparison of numerical results of the present study with the published experimental and numerical studies indicate that the evolution of local stress states in parent grains and corresponding twin variants depend on their orientation with respect to the loading direction and/or the neighbouring grains. Further, the need of immediate experimental evidence to assist assumptions made during modelling deformation twinning is discussed.

Interfaces can act as dislocation obstacles, sinks or dislocation sources and, therefore, influence strongly the mechanical properties of metals. To consider these effects at high temperature creep, a three-dimensional gradient crystal plasticity model is introduced. The interaction between dislocations and the fiber-matrix interface is included by an interface flow rule, which accounts for the gradient stresses and the normal component of the Cauchy stress on the interface. Motivated by the interface-enriched generalized finite element method (IGFEM), continuous shape functions allowing for weak discontinuities are introduced. These shape functions are used to evaluate the interface flow rule at sharp interfaces and are validated by comparing numerical simulation results of a laminate for single slip with an analytical solution. To investigate the slip transfer/activation at the interface, the directionally solidified NiAl-9Mo composite is modeled as regular fibrous microstructure. The simulated creep curves agree well with experimentally measured ones. It is found that the stress dependency of the interface flow rule is necessary to reproduce the well known composite's Norton behavior. The simulations reveal that the creep behavior of the composite is mainly controlled by the fibers and the interface properties. Finally, the specific shape of the creep curve could be explained.

In diffuse-interface (phase field) models of polycrystalline solids, the grain boundaries naturally possess a narrow region of finite thickness. A Ginzburg-Landau type kinetic equation for plastic deformation of a solid is derived that combines crystal plasticity and J2 plasticity. Within such a framework for a polycrystal the grain interior can be defined by crystal plasticity, and the grain boundary region can be assigned J2 type plasticity. The two are connected smoothly. This allows the modeling framework to accommodate grain boundary sliding (GBS), an important deformation mechanism for creep. The relaxation of elastic modulus of a polycrystalline solid and the power-law creep (both accommodated by GBS) are studied by 2D and 3D simulations, respectively, and the results are compared to the 2D finite-element simulations of Ghahremani and Crossman-Ashby. A strong grain shape dependence and orientation dependence (for non-equiaxed grains) of the GBS effect are predicted by this model.

Recent Electron Backscatter Diffraction (EBSD) experiments have revealed the emergence of heterogeneous dislocation microstructures forming under a wedge indenter in fcc crystals, where micro-meter dislocation patterns challenge the predictions of traditional models of plasticity. In order to explain the formation of these features and develop a relationship between the force-displacement curve and the dislocation substructure, we present here a model of wedge indentation based on the continuum theory of dislocations. The model accounts for large deformation kinematics through the multiplicative split of the deformation gradient tensor, where the incompatible plastic component of deformation results from the flux of dislocations on different and interacting slips systems. Constitutive equations for dislocation fluxes are determined from a dissipative variational principle. As a result, each dislocation density satisfies an initial-boundary value problem with convective-diffusive character, which is coupled to the macroscopic stress and displacement fields governing the deformation process. Solution to the self-consistent continuum formulation is found using the finite element method. Computer simulations mimic the experimental conditions of wedge micro-indentation experiments into Ni single-crystals used by Kysar et al. (2010a). A comparison of overall dislocation density distribution and macroscopic mechanical response shows good overall agreement with the experimental results in terms of the detailed features of dislocation patterns and lattice rotations as well as the macroscopic force-displacement response.

A phenomenological damage model is proposed to account for the strain rate dependency of the damaging processes at high temperature. Mechanical softening during tertiary creep and monotonic tension are modeled by an isotropic scalar internal variable D, whose evolution is described using a rate damage law dD/dt=⋯ governed by visco-plasticity and accounting for the enhancement by stress triaxiality. A novel rate sensitive damage threshold is introduced in order to reproduce the rate dependency of the onset of damaging processes. Damage evolution is coupled with the visco-plasticity model developed by the same authors for single crystal superalloys and accounting for microstructural evolution (like γ' -rafting and coarsening) in Desmorat et al. (2017). The curves presented in this article are identified at 1050 °C for the Ni base single crystal superalloy CMSX-4 but the proposed rate sensitive threshold modeling can be applied to other alloys showing a rate sensitive damage onset, as for example the single crystal superalloys MC2 but also the polycristalline aggregate AD 730™.

Combined three-dimensional plastic flow and strain-induced phase transformation (PT) in boron nitride (BN) under high pressure and large shear in a rotational diamond anvil cell (rotational DAC or RDAC) are investigated. Geometrically nonlinear frameworks including finite elastic, transformational, and plastic deformations and finite element method (FEM) are utilized. Quantitative information is obtained on the evolutions of the stress tensor, plastic strain, volume fraction of phases in the entire sample, and slip-cohesion transitions, all during torsion under a fixed compressive load in RDAC. The effects of the applied compressive stress and the sample radius on PT and plastic flow are discussed. In comparison with DAC, the same amount of the high-pressure phase can be obtained at a much lower pressure in RDAC, which reduces the required force and the risk of diamond fracture. Also, RDAC has a potential to complete PT during torsion under pressure close to the minimum possible. A quasi-homogeneous pressure can be obtained in a transforming sample in RDAC under a proper choice of properties and parameters of a gasket. A number of experimental phenomena, including the pressure self-multiplication and quasi-homogeneous pressures in DAC and RDAC, are reproduced and interpreted. The simulation results provide a significant insight into coupled PTs and plastic flow in material in RDAC, and are important for the optimum design of experiments and the extraction of material parameters for PT, as well as for the optimization and control of PTs by the variation of various parameters.

A coordinate change of conjugate twin boundaries in Ni-Mn-Sn single crystals is studied with scanning electron microscopy. During mechanical training, the so-called orthogonal shear process initiates variant reorientation leading to the replacement of the main with conjugate type I twin boundaries. The experimental data demonstrate that highly organized redistribution of adjacent variants, in the neighboring areas, is then critical for the removal of conjugation boundaries by coordinated secondary twinning. In addition, a more complex variant reorientation mechanism is uncovered and it is found to allow for transitioning between non-conjugate twin systems. The proposed mechanism appears consistent with the orientation relationship between austenite and martensite, which is controlled by a shear deformation and martensite crystallography leading to an equal distribution of martensitic variants. This contribution complements the existing theory of martensite crystallography providing direct evidence for the general nature of the orthogonal shear process as a first step in variant reorganization during mechanical training of martensite.

In this paper, the so-called “β rule” is used to simulate the anisotropic behaviour of directionally solidified superalloys. First, the “mean-field” model is extended to the general case of heterogeneous local elasticity. Two other models also designed using the “self-consistent” framework are applied to make comparisons, either with the assumption of a purely elastic accommodation of grains (Kröner-Weng model) or the translated field theory. As a reference, full-field simulations using a representative volume element (RVE) and a crystal plasticity finite element model (CPFEM) are carried out. Results show that the β rule is able to predict the overall response of the material for various cases such as one-dimensional or two-dimensional cyclic loading with or without a mean stress. Otherwise, local estimations are studied for both mean-field and full-field models. The local responses of the β rule are consistent when they are compared to those of CPFE simulations.

Proper finite element modelling of elastoplastic behavior under cyclic and multiaxial loading requires the consideration of nonlinear kinematic hardening. Popular models available for nonlinear kinematic hardening are based on multiple additive backstresses, whose evolution include a dynamic recovery term and follow the Armstrong-Frederick proposal; among them, the Ohno-Wang models. Whereas the small strain theory and its numerical implementation are satisfying, large strain extensions are more controversial, specially regarding the mathematical treatment of flow kinematics and the numerical implementation. In this work we present a new approach for modelling nonlinear kinematic hardening at large strains, reproducing the Ohno-Wang model at small strains without explicitly employing the backstress concept. The formulation uses only the classical Kröner-Lee multiplicative decomposition. It avoids the Lion decomposition and it is fully hyperelastic, employing only elastic variables both in the elastic and hardening parts, as well as in the flow equations. The theory has no restriction on the form of stored energies or in the amount of elastic strains so it can be used in soft materials, and it is weak-invariant and volume-preserving by construction. Furthermore, it has the same additive structure of classical small strain algorithms. Geometrical mapping tensors are systematically employed to account for large strain kinematics whereas the iterative algorithmic part is identical to the small strains model, which is recovered bypassing the geometrical mappings. The modelling of visco-hyperelastoplasticity is also straightforward by combining the present theory with finite nonlinear viscoelasticity formulations based on the same framework previously developed by our group.

The large strain fracture of non-linear complex solids concerns a wide range of applications, such as material forming, food oral processing, surgical instrumental penetration as well as more recently, the design of biodegradable composites for packaging and bio-medical use. Although computer simulations is a powerful technology towards understanding and designing such processes, modelling ductile fracture in soft natural composites imposes a new challenge, particularly when the fracture patterns cannot be pre-defined. Here we bring to light new information on these aspects of benefit to the multidisciplinary community, by characterising and modelling the deformation and fracture of short cellulose fibre starch extruded composites. Hyperviscoelastic-Mullins damage laws show merits in modelling such complex systems. Yet they are inferior to a viscoplastic-damage law able to capture exactly their highly non-linear, rate dependent and pressure dependent pseudo-plastic stress-strain response. It also predicts fracture based on experimental toughness values without pre-specifying the crack path in a Finite Element (FE) model, displaying superiority over the conventional cohesive zone approach. Yet, despite using a toughness parameter to drive crack propagation, spurious mesh dependency is still observed while other previously unreported sources of error imposed by the finite element aspect ratio are also highlighted. The latter is rectified by developing a novel numerical strategy for calculating the characteristic element length used in the damage computations. Inherent mesh dependency is however not resolved, suggesting that non-local damage models may be essential to model this newly investigated class of natural composites.

Utilizing a non-equilibrium thermodynamic setting that involves two temperatures, we present a model for ductile and brittle damage. The thermodynamic system consists of two interacting subsystems– configurational and kinetic-vibrational. While the kinetic-vibrational subsystem describes fast degrees-of-freedom (DOFs) of ordinary thermal vibration, the configurational subsystem includes the slower DOFs pertaining to a slew of configurational rearrangements that characterize elasto-visco-plasticity and damage, e.g. dislocation motion, lattice stretching, void nucleation, void growth and micro-crack formation. Following statistical mechanics, an expression for the entropy of a plastically deforming metal with growing voids and micro-cracks is derived. Subsequent application of the first and second laws of thermodynamics, suitably modified for the two-temperature system, yields coupled evolution rules for dislocation density, void volume fraction, micro-crack density etc. A modified flow rule for dilatant plasticity and evolution equations for the two temperatures are also derived. When the two subsystems are strongly coupled, we show that a splitting of energy and entropy is feasible and that the notion of two temperatures conforms with such splitting. We conduct numerical experiments on both brittle and ductile damage to assess the predictive features of the model and validate the results against available experimental evidence. Finally, a generalized fluctuation relation is put forth for deformations with extremely high strain rates. This leads to an entirely new procedure for constitutive closure, providing valuable insights into the emergent pseudo-inertial aspects of the evolving thermodynamic states.

Nanolayered metallic composites usually deform via a transition from homogeneous deformation to major shear banding with decreasing layer thickness, and thus the improvement of strength often sacrifices the plasticity of materials. Here, we show two methods to promote brittle-to-ductile transition in nanolayered Ag/Nb pillars. Intrinsically, while keeping the pillar diameter constant, the reduction of layer thickness can increase the strength of multilayers and suppress shear induced failure. Extrinsically, for a constant layer thickness, decreasing the diameter of pillar suppresses shear bands and promotes more uniform plastic deformation. Furthermore, the critical layer thickness at peak strength of multilayers increases monotonically with decreasing pillar diameter. Interface structures evolve from amorphous layer to coherent interface with reduction of layer thickness. Homogeneous co-deformation mediated by heterogeneous interfaces and columnar grain boundaries promotes a unique work hardening behavior. This study indicates that a combination of intrinsic and extrinsic size effect may enable the accomplishment of high strength and uniform deformation simultaneously.

In this paper, a unified multi-mechanism continuum viscoplastic damage model is proposed to simulate the thermomechanical behavior of high-Cr steels at elevated temperatures. To represent the effects of material degradation under external loads, a total damage tensor is incorporated, which is composed of the low-cycle fatigue damage, the creep damage and the ductile damage. Within the small strain framework, the model is established through a thermodynamically consistent approach. First, some kinematic assumptions are proposed and the concept of effective stress is adopted. Then, based on a state potential with proper constitutive form, the constitutive equations can be derived from the second law of thermodynamics. By further considering the postulate of maximum dissipation, a Lagrangian functional is constructed through a regularization scheme. The stationary points of the Lagrangian functional yield the evolution equations of the dissipative variables. For the isotropic damage case, the damage tensor can be represented by a scalar damage variable and the constitutive evolution equations in the model can be simplified. To be prepared for practical applications, numerical integration algorithms are proposed to solve the constitutive evolution equations, and the material parameters in the model are identified based on the experimental data. To demonstrate the efficiency of the current model, it is applied to simulate the thermomechanical response of high-Cr steels under different loading conditions. The simulation results can fit the experimental data at a quantitative level and the damage mechanisms under the different loading conditions can be revealed. Besides that, the model is further modified to take into account the microcracks closure effect of the ductile damage. The current model would be helpful for the safety design and lifetime evaluation of high-Cr steel components in practical applications.

It is important to investigate the constitutive behavior of high density polyethylene (HDPE) under cyclic loading since it is widely used for industrial applications. However, there are only a few preliminary investigations on the constitutive behavior of HDPE under cyclic loading. This work aims at investigating the deformation mechanism, developing the constitutive model especially for the cyclic-loading behavior, and proposing an efficient approach for model calibration. Firstly, the deformation mechanism was successfully explored by conducting a special designed relaxation-unloading test by which the time-independent elastic-plastic behavior was decoupled from the time-dependent overall deformation behavior. Then, a nonlinear elastic-viscoplastic constitutive model was developed based on the parallel rheological framework (PRF) composed of an elastic-plastic network in parallel with multiple nonlinear viscoelastic networks. Finally, an approach was proposed to calibrate the constitutive model by means of relaxation-unloading tests and material parameter optimizations. The agreement between the prediction and the test data successfully demonstrated that the model could be used to precisely simulate the constitutive behavior of HDPE under static, quasi-static and dynamic cyclic loading. The developed constitutive model is beneficial to the long-term durability evaluation of HDPE. The methodology for exploring the deformation mechanism and calibrating the constitutive model may also be applicable to other polymers.

Dislocation dynamics simulation is used to investigate the effect of grain size and grain shape on the flow stress in model copper grains. We consider grains of 1.25 – 10 μm size, three orientations (<135>, <100> and <111>) and three shapes (cube, plate and needles). Two types of periodic aggregates with one or four grains are simulated to investigate different dislocation flux at grain boundaries. It is shown that in all cases the flow stress varies linearly with the inverse of the square root of the grain size, with a proportionality factor varying strongly with the grain orientation and shape. Simulation results are discussed in the light of other simulation results and experimental observations. Finally, a simple model is proposed to account for the grain shape influence on the grain size effect.

Overcoming the trade-off between strength and ductility in metallic materials is a grand challenge. Recently, materials with a gradient nano-grained (GNG) surface layer adhering to a ductile coarse-grained (CG) substrate have been proposed to overcome this long-standing dilemma. Constitutive modeling and simulation are crucial to understand the deformation mechanisms controlling the strength and ductility in GNG/CG materials, and to enable theory to guide microstructure optimization for upscaling. Here, we develop a dislocation mechanism based size-dependent crystal plasticity model, where multiple dislocation evolution mechanisms are considered. Furthermore, damage evolution and mechanically driven grain growth during the deformation of GNG/CG materials are incorporated into the constitutive model to study the role of microstructure gradient in the overall plastic response. The developed size-dependent constitutive model was implemented within a finite-strain crystal plasticity finite element framework, and used to predict the tensile mechanical behavior of GNG/CG copper, including yield stress, strain-hardening and ductility with a highly simplified geometrical representation of the microstructure. The simulations reveal some of the underlying deformation mechanisms controlling ductility and strengthening in terms of the spatial distribution and temporal evolution of microstructure and damage. The model was also used to demonstrate optimization of strength and ductility of GNG/CG copper. By manipulating the thickness of the GNG layer and the grain size of the CG substrate, the strength increase is associated with a loss of ductility showing the same linear inverse relationship observed experimentally for GNG/CG copper, which demonstrates the improvement over the typical nonlinear trade-off between strength and ductility.

The constitutive behavior of a hexagonal close-packed (HCP) polycrystalline ZEK100 magnesium alloy was investigated using combined high energy X-ray diffraction (HEXRD) from a synchrotron source and crystal plasticity modeling approach. The in-situ tensile test data coupled with the HEXRD enabled the tracking of the lattice strain evolution during deformation. The microscopic behavior represented by lattice strain and the macroscopic behavior represented by stress-strain curves were then used together as objective function to estimate the critical resolved shear stress (CRSS) and hardening parameters of available slip and deformation twin systems in the ZEK100 alloy. An enhanced predominant twinning reorientation (ePTR) scheme was proposed in the current work, and the ePTR parameters were determined for the first time by the use of basal plane peak intensity along loading direction measured from HEXRD. Two crystal plasticity models, the computationally efficient elastic-plastic self-consistent (EPSC) and crystal plasticity finite element (CPFE) models, were developed incorporating the deformation twinning for the HCP-structured metals. The determined constitutive parameters were further validated by comparing the predicted deformation texture with the measured one. The work provides a useful and computationally-efficient modeling scheme to understand the slip/twin induced deformation behaviors of the ZEK100 alloy in micro- and macro-scales.

In this work, quasi-in situ tensile unloading and electron backscatter diffraction (EBSD)-based slip trace analysis were applied to study the room-temperature deformation behaviour of Ti-22Al-25Nb alloys with three different microstructures and the plastic deformation mechanism of the B2, α2, and O phases. In addition, the interaction model of the three phases was presented. The results showed obvious B2 slip deformation in the necking region of the B2+α2 microstructure and the B2 texture+α2 samples. The cracks expanded along the regions with low grain boundary density, and the fracture mode was transgranular fracture. The B2 texture improved the harmony and uniformity of the slip deformation between different grains, obviously improving ductility. Owing to the obstruction of the O phase to the B2 phase slip, the B2+O+α2 sample generated an obvious deformation strengthening effect, had no necking phenomenon, and it was also transgranular fracture. The B2 phase slip deformation mode included single system, double system, tri-system, and cross slips. The B2 phase induced a small number of the α2 phases to experience basal slip ((0001) [11-20]) and cracking. The O phase had two deformation modes: (001) plane slip and twin that had (021) as a twinning plane. Two of the 24 slip systems of the B2 phase {110} <111> and {112} <111> can induce an O phase (001) plane slip, 12 systems whose <111> slip direction formed a 54.7° angle with the (001) plane can induce an O phase twin, and other 10 systems cannot induce O phase deformation.

An equivalence is assumed between a microstructural length scale related to dislocation density and the constitutive length scale parameter in phenomenological strain gradient plasticity. An evolution law is formed on an incremental basis for the constitutive length scale parameter. Specific evolution equations are established through interpretations of the relation between changes in dislocation densities and increments in plastic strain and strain gradient. The length scale evolution has been implemented in a 2D-plane strain finite element method (FEM) code, which has been used to study a beam in pure bending. The main effect of the length scale evolution on the response of the beam is a decreased strain hardening, which in cases of small beam thicknesses even leads to a strain softening behavior. An intense plastic strain gradient may develop close to the neutral axis and can be interpreted as a pile-up of dislocations. The effects of the length scale evolution on the mechanical fields are compared with respect to the choice of length evolution equation.τ=αμbρ

A series of stress relaxation experiments were performed on samples of rolled Zircaloy-2 plate. In situ synchrotron x-ray diffraction was used to observe changes in interatomic lattice spacing during both deformation and relaxation. The concepts of strain rate sensitivity and activation volume are extended from the macroscopic to the microscopic scale using the results of the diffraction analysis. The technique outlined in this paper allows for the precise measurement of thermally activated properties at the level of subsets of grains sharing similar crystal orientations relative to the loading direction. Self-consistent modelling results are used to connect the observed strain rate sensitivity of these grain families with the rate sensitivities of the various active slip systems in zirconium alloys. The results show that the dependence of strain rate sensitivity on crystal orientation occurs primarily due to the differing strain rate sensitivities of the individual slip systems, which ultimately determines the macroscopic value.