Polycrystal Plasticity Model Research Articles

Fatigue modelling in fretting contact with a crystal plasticity model

The damage mechanisms in fretting tests are wear and fatigue cracking. The gradients of the stress and strain fields are quite high under the contact, so that the typical associated lengths can be compared to grain size. Since the microstructure size is not negligible when compared to the length associated to the loadings, it seems reasonable to explicitly represent the grains in the computations. This is proposed in this paper: a polycrystal plasticity model is used for the case of a disk-plane contact with two bodies made of titanium alloy. The simulations corresponding to a material response fretting map are compared to fretting experiments. The fatigue prediction is made by means of the Dang Van high cycle fatigue parameter.

Predictions of forming limit diagrams using a rate-dependent polycrystal self-consistent plasticity model

In the sheet-metal forming industry, forming-limit strains have been a useful tool for quantifying metals formability. However, the experimental measurement of these strains is a difficult, time consuming and expensive process. It would be useful if strains calculated with a theoretical model could replace many of the experimental measurements. In this research, we analyze forming-limit strains of metals using a rate-dependent plasticity, polycrystal, self-consistent (VPSC) model in conjunction with the Marciniak–Kuczynski (M–K) approach. Previous researchers have studied forming limit diagrams (FLDs) based on the full-constraints Taylor model. This is the first time, to the authors’ knowledge, that the self-consistent approach has been introduced to simulate the polycrystal FLD behavior. Numerous microstructural factors characterizing the material have a strong influence on the FLD, so our model includes the effects of slip hardening, strain-rate sensitivity, anisotropy and initial texture. Finally, the calculation of the FLD with a more realistic scale transition successfully predicts some of the experimental tendencies that the Taylor model cannot reproduce for aluminum alloys AA6116-T4 and AA5182-O.

Multi-laminate plastic-strain organization for non-uniform TFA modeling of poly-crystal regularized plastic flow

A recently presented single plastic-potential, microstructure-based model of poly-crystal plasticity by the authors considers a globally regularized Schmid law (RSL) as the slip flow criterion of a homogeneous equivalent super-crystal. The homogenization scheme that is taken of affine type is specialized to the transformation field analysis (TFA) framework. The relevancy of the TFA here results from a description of intra-crystalline slip in terms of hierarchical multi-laminate (HML) structures that ensure the request of piece-wise homogeneous plasticity. This RSL–TFA–HML modeling has been shown efficient for heterogeneous intra-crystalline plastic slip in terms of overall stiffness estimates when laminates are parallel to slip planes or normal to slip directions. It is also suitable for twinning modes of crystal plasticity as stressed in this paper. The performed superposition of all possible HML plastic strain modes makes the TFA of the non-uniform (NTFA) and coupled type proposed by Michel and Suquet [Michel, J.C., Suquet, P., 2003. Non-uniform transformation field analysis. International Journal of Solids and Structures 40, 6937–6955; Michel, J.C., Suquet, P., 2004. Computational analysis of nonlinear composite structures using the non-uniform transformation field analysis. Computer Methods in Applied Mechanics and Engineering 193, 5477–5502]. In this new contribution, we investigate further our extension of this modeling to poly-crystals. It is interpreted as based on a description of the aggregate morphology in terms of the distribution of the crystallographic orientations of the grain boundary and sub-boundary facets, rather than in terms of a mean grain or domain shape. In its initial form, our extension amounted to assuming all these facets oriented either parallel to slip planes or normal to slip directions, what is proved convenient for large enough grains. In order to extend the relevancy of the modeling down to ultra-fine grains, we introduce a graded form of the modeling that is made grain size dependent from specifying the conditions for which the TFA accommodation hardening is negligible according to the range of the physical one. Some numerical stiffness comparisons from this graded RSL–TFA–HML modeling are provided.

152 結晶塑性モデルによるHCP金属の局所くびれ挙動解析(OS13.材料の組織・強度に関するマルチスケールアナリシス(5),オーガナイズドセッション)

152 結晶塑性モデルによるHCP金属の局所くびれ挙動解析(OS13.材料の組織・強度に関するマルチスケールアナリシス(5),オーガナイズドセッション)

$\Gamma$-Convergence of Power-Law Functionals, Variational Principles in $L^{\infty},$ and Applications

Two $\Gamma$-convergence results for a general class of power-law functionals are obtained in the setting of $\mathcal{A}$-quasiconvexity. New variational principles in $L^{\infty}$ are introduced, allowing for the description of the yield set in the context of a simplified model of polycrystal plasticity. A number of highly degenerate nonlinear partial differential equations arise as Aronsson equations associated with these variational principles.

Modeling Texture Evolution During Friction Stir Welding of Stainless Steel With Comparison to Experiments

Texture evolution during friction stir welding of stainless steel was investigated using a polycrystal plasticity model together with a three-dimensional, thermomechanically coupled, finite element formulation. The influence of frictional conditions with the tool pin and shoulder on the flow in the through-thickness direction was examined in terms of their impact on the evolving crystallographic texture. Trends in regard to the strengthening and weakening of the texture are discussed in relation to the relative magnitudes of the deformation rate and spin. Finally, the computed textures are compared to electron backscatter diffraction measurements and are discussed with respect to distributions along orientational fibers and the dominant texture components along the fibers.

The influence of a threshold stress for grain boundary sliding on constitutive response of polycrystalline Al during high temperature deformation

A continuum polycrystal plasticity model was used to estimate the influence of a threshold stress for grain boundary sliding on the relationship between macroscopic flow stress and strain rate for the aluminum alloy AA5083 when subjected to plane strain uniaxial tension at 450°C. Under these conditions, AA5083 deforms by dislocation glide at strain rates exceeding 0.001s−1, and by grain boundary sliding at lower strain rates. The stress–strain rate response can be approximated by ε˙=Aσn, where A and n depend on grain size and strain rate. We find that a threshold stress less or equal to 4MPa has only a small influence on flow stress and stress exponent n in the dislocation creep regime (a threshold stress of 2MPa increases n from 4.2 to 4.5), but substantially increases both flow stress and stress exponent in the grain boundary sliding regime (a threshold stress of 2MPa increases n from 1.5 to 2.7). In addition, when the threshold stress is included, our model predicts stress versus strain rate behavior that is in good agreement with experimental measurements reported by Kulas et al. [M.A. Kulas, W.P. Green, E.M. Taleff, P.E. Krajewski, T.R. McNelley, Metall. Mater. Trans. A 36 (2005) 1249].

Three-dimensional numerical simulations of multi-pass equal-channel angular pressing by a variation difference method and comparison with experiment

A variation-difference method (VDM) of solving continuum mechanics equations has been implemented for simulation of the equal-channel angular pressing (ECAP) process. Application of the developed DRAKON code (VNIIEF, Russia) for numerical study of multi-pass ECAP allowed processes of severe plastic deformation to be described in three-dimensional (3D) continuum approximation in the field of low strain rates and high-pressure levels in terms of contact interaction. The influence of ECAP processing parameters on stress–strain field distribution over the ECAP sample's cross-section is studied in 3D formulation. The model validation is performed by comparison of simulation results with various experimental data. Deformation histories provided by DRAKON were used together with a polycrystal plasticity model (viscoplastic self-consistent model) allowing simulation of texture evolution during ECAP with account to macro-parameters of the process. It is shown that the VDM-based model possesses good predictive capabilities for 3D simulation of severe plastic deformation processes involving strain-path changes.

Analysis of texture evolution in magnesium during equal channel angular extrusion

Texture development in magnesium during equal channel angular extrusion (ECAE) with an angle of 90° between the intersecting channels has been studied. Textures were simulated using polycrystal plasticity models as well as determined experimentally for routes A, B c and C up to four passes. Based on a previous study on texture evolution during the simple shear of materials with hexagonal crystal structures [Beausir B, Tóth LS, Neale KW. Acta Mater 2007;2695:2705], the ideal orientations for ECAE of hexagonal metals were identified considering the shear to be at the 45° intersection plane of the two channels. Although dynamic recrystallization (DRX) was experimentally observed during the ECAE experiments, the polycrystal modeling using the viscoplastic self-consistent (VPSC) model was able to reproduce the experimental textures successfully. This was attributed to the fact that the textures were c-type fibers with their axis of rotation parallel to the c-axis, whereas the nucleation of grains during DRX takes place in positions simply rotated around the c-axis.

Grain size effects on the tensile properties and deformation mechanisms of a magnesium alloy, AZ31B, sheet

The grain size dependence of the tensile properties and the deformation mechanisms responsible for those properties are examined for Mg alloy, AZ31B, sheet. Specifically, the Hall–Petch effect and strain anisotropy ( r-value) are characterized experimentally, and interpreted using polycrystal plasticity modeling. {1 0 . 2} extension twins, {1 0 . 1} contraction twins, and so-called “double-twins” are observed via microscopy and diffraction-based techniques, and the amount of twinning is found to increase with increasing grain size. For the sheet texture and tensile loading condition examined, {1 0 . 2} extension twinning is not expected, yet the polycrystal plasticity model predicts the observed behavior, including this ‘anomalous’ tensile twinning. The analysis shows that the Hall–Petch strength dependence, of the polycrystal as a whole, is primarily determined by the grain size dependence of the strength of the prismatic slip systems.

Implementation of Twin Reorientation and Softening Schemes in a Polycrystal Plasticity Model for Mg Alloys

Uniaxial compression tests on hot-rolled AZ31 Mg alloy were carried out at a temperature of 300°C. In order to investigate work hardening and texture evolution during plastic deformation, cylindrical specimens were compressed to the rolling direction. Experimental investigation reveals that flow curves are strongly dependent on microstructure evolution such as deformation twinning and softening phenomenon. The occurrence of deformation twinning and softening phenomenon was revealed by the observation of microtexture using electron backscatter diffraction (EBSD). A visco-plastic self-consistent (VPSC) polycrystal model was used to simulate the work hardening, softening and texture evolution during the uniaxial compression. In order to calculate orientation of deformation twins, predominant twin reorientation (PTR) scheme was implemented into the polycrystal model. A softening scheme was also implemented in the polycrystal model to predict softening phenomenon and texture evolution after a peak stress.

Simulating Grain Growth in a Deformed Polycrystal by Coupled Finite-Element and Microstructure Evolution Modeling

The interplay between deformation and microstructure evolution can be strong and is the basis of a large majority of thermomechanical processing techniques for metals. We present simulations of this interplay, using a sharp-interface front tracking model for grain growth and a finite-element polycrystal plasticity model of deformation that includes anisotropic linear elasticity. The two approaches are iteratively coupled, so that grain growth affects the deformation behavior, and vice versa. Analyses of both purely elastic and of elastic-plastic materials are presented through coupled simulations of static loading of model polycrystalline microstructures. In the elastic case, stored elastic energies can reach relatively high values, and the mechanical driving force can locally exceed the curvature driving force, causing boundaries to assume noncompact (rippled) shapes. These large driving forces also serve to accelerate the grain growth process. In the elastic-plastic case, under relatively low strains, plasticity provides a stress relief mechanism that prohibits the generation of large stored elastic energies; thus, substantial deviations from compact interface morphologies were not observed, and growth kinetics did not accelerate substantially.

Through-process simulation of texture and properties during the thermomechanical processing of aluminium sheets

Computer-based alloy and process development requires the integration of models for simulating the evolution of microstructure, microchemistry and crystallographic texture into process models of the thermomechanical production of Al sheet. In this paper, a softening model simulating the progress of recovery and recrystallization and the following texture changes is linked to deformation and microchemistry models. The possibility of such coupled simulations is illustrated by way of the thermomechanical processing of Al–Mn–Mg AA 3104 can stock. In particular, the impact of inter-stand recrystallization between the tandem hot rolling passes as well as recrystallization during coil cooling (“self-annealing”) on the resulting hot strip and final gauge textures are explored. Finally, the predicted textures are input into a polycrystal–plasticity model to simulate anisotropic properties (earing behaviour) of the sheets. Thus, it is possible to link the materials properties at final gauge to the decisive steps of deformation and recrystallization along the thermomechanical process chain.

A polycrystalline model for the description of ratchetting: Effect of intergranular and intragranular hardening

In this work, numerical simulations for predicting uni- and multi-axial ratchetting behaviors are carried out, using a polycrystal plasticity model. In this multi-scale modeling, the single crystal behavior is based on crystallographic slip (intragranular scale), whereas the polycrystal behavior is obtained from an explicit transition rule to calculate the local stresses and strains (intergranular scale). A systematic study is performed to show the effect of intergranular and intragranular hardening on the ratchetting behavior. For illustrative purposes, two examples are presented: the model is applied to simulate the experimental results from the literature for a 316 austenitic stainless steel and for a 1026 carbon steel. It was demonstrated that the polycrystalline model was successful in describing the inelastic behavior of the two considered materials adequately.

Deformation of (Mg,Fe)SiO 3 Post-Perovskite and D'' Anisotropy

Polycrystalline (Mg(0.9),Fe(0.1))SiO3 post-perovskite was plastically deformed in the diamond anvil cell between 145 and 157 gigapascals. The lattice-preferred orientations obtained in the sample suggest that slip on planes near (100) and (110) dominate plastic deformation under these conditions. Assuming similar behavior at lower mantle conditions, we simulated plastic strains and the contribution of post-perovskite to anisotropy in the D'' region at the Earth core-mantle boundary using numerical convection and viscoplastic polycrystal plasticity models. We find a significant depth dependence of the anisotropy that only develops near and beyond the turning point of a downwelling slab. Our calculated anisotropies are strongly dependent on the choice of elastic moduli and remain hard to reconcile with seismic observations.

Heterogeneous crystal and poly-crystal plasticity modeling from a transformation field analysis within a regularized Schmid law

The regularized Schmid law (RSL) has recently been proposed as a plastic flow criterion for poly-crystals under the crude assumptions of either uniform stress or uniform strain. We first reconsider this law for application to heterogeneous intra-crystalline plasticity, with reference to a Homogeneous Equivalent Super-Crystal. We then extend the modeling to poly-crystals with the goal to account for both stress and strain heterogeneities within as well as between grains. The transformation field analysis (TFA) is used as the homogenization procedure. This TFA is known to be accurate for materials that can be described as assemblies of plastically homogeneous domains. Otherwise, the estimates of the material effective behavior that result from its application are too stiff. Because stress and strain fields are almost everywhere uniform in laminates, we consider crystal slip organizations into multi-laminate structures. It is demonstrated that laminate layers either parallel to slip planes or normal to slip directions do not contribute to the over-stiffness due to the TFA. Thus, hierarchical multi-laminate (HML) structures are introduced where the successive laminate orientations are taken parallel to the crystal slip planes. It is shown that a conveniently weighted superposition of all the possible plane hierarchies cancels out most of the undesirable TFA contributions to the overall stiffness estimates. A relevant extension to poly-crystal plasticity of this (RSL-TFA-HML) modeling is presented.

Length changes and texture prediction during free end torsion test of copper bars with FEM and remeshing techniques

FEM numerical simulations of the experimental free end torsion tests [Toth, L.S., Jonas, J.J., Daniel, D., Bailey, J.A., 1992. Texture development and length changes in copper bars subjected to free end torsion. Textures Microstruct. 19, 245–262] of copper cylindrical bars were analysed in the present study. The self-made Finite Element (FE) code LAGAMINE was used to compute numerical prediction of the Swift effect, i.e. the lengthening of the cylinder during the torsion. The material behaviour was represented by an interpolation law [Habraken, A.M., Duchêne, L., 2004. Anisotropic elasto-plastic finite element analysis using a stress–strain interpolation method based on a polycrystalline model. Int. J. Plasticity 20 (8–9), 1525–1560] linked with a Taylor polycrystal plasticity model either based on a strain rate insensitive or a visco-plastic crystal plasticity model. The influence of texture evolution was analysed. A torsion dedicated remeshing technique was developed to allow very large strain simulations. Predicted axial lengthening and predicted textures were compared to experimental measurements. A good agreement was obtained for shear strain up to 2.0. The Swift effect related angular shift of the pole figure maxima from symmetrical orientations was reproduced correctly.

Investigation on cold-drawn gold bonding wire with serial and reverse-direction drawing

Gold bonding wires have been manufactured through multiple drawing steps with serial and reverse-direction drawing. The texture and microstructure of the gold bonding wires were characterized with X-ray diffraction and EBSD and compared with the predictions of finite element (FE) simulation. Initial 〈1 0 0〉 fiber decreases during drawing and is replaced by 〈1 1 1〉 fiber. The 〈1 0 0〉 oriented grains are concentrated in the center and surface regions, whereas the 〈1 1 1〉 oriented grains are located throughout the cross-section of the wire. Regions near the surface often exhibit the complex textures. A simplified forward and backward drawing process was modeled by FE analysis with ABAQUS/Standard™. The simple two-step drawing process results in severe variation in shear strain under the surface and displays the opposite behavior in the shear components of the deformation gradient. The texture evolution was predicted using the deformation gradient calculated in the FE simulations together with a model of polycrystal plasticity. The 〈1 1 1〉 and 〈1 0 0〉 fibers are predicted to develop in the center part of the wire where homogeneous deformation occurs. The regions near the surface that experience repeated shear strain exhibit complex textures that deviate from the standard 〈1 1 1〉 and 〈1 0 0〉 fibers. The {1 1 2}〈1 1 0〉 and {1 1 1}〈1 1 2〉 components are prevalent in the higher shear strain regions. The variations of the anisotropic elastic directional moduli with position were also calculated.

Characterization of deformation textures in pure copper processed by equal channel angular extrusion via route A

Texture evolution in pure copper processed by equal channel angular extrusion (ECAE) for up to eight passes via route A is investigated. The experimental textures develop very closely along ideal orientations and fibers derived from those for simple shear torsion by a rotation about the flow plane normal, and show a continuous strengthening of the B θ / B ¯ θ components with increasing pass number. Such tendencies are satisfactorily predicted by polycrystal plasticity models. The polycrystal simulations also reveal that, despite significant changes of entry textures and strain path in multiple passes, the deformation in each pass is large enough to re-orient grains to the ideal fibers such that shear-type ECAE textures can be re-established. It is suggested that the rotation of the local (or simple shear) reference system from the laboratory (or ECAE) reference system needs to be taken into account in ECAE texture analyses.

Modeling lower mantle anisotropy development in a subducting slab

A model is presented that simulates anisotropy development in a subducting slab from the upper–lower mantle boundary (661 km) to the core–mantle boundary (2891 km). Two phases are considered: orthorhombic MgSiO 3-perovskite and cubic magnesiowuestite (Mg,Fe)O. Single crystal elastic properties at mantle conditions are obtained from existing density functional theory calculations and quasiharmonic approximation. It is assumed that deformation is accommodated by slip. A polycrystal plasticity model predicts strong texture development for perovskite and weaker texture for magnesiowuestite. When averaging single crystal elastic properties with the orientation distribution this results for both phases in weak P-wave anisotropy and shear wave splitting in the upper part of the lower mantle but pronounced anisotropy near the core–mantle boundary (up to 4% for V p and 7% for V s). The anisotropy pattern is complex and asymmetric and local heterogeneity is expected. These predictions are consistent with seismic observations.