Finite element analysis of localization in FCC polycrystalline sheets under plane stress tension

Localization phenomena in thin sheets subjected to plane stress tension are investigated. The sheet is modelled as a polycrystalline aggregate, and a finite element analysis based on rate-dependent crystal plasticity is developed to simulate large strain behaviour. Accordingly, each material point in the specimen is considered to be a polycrystalline aggregate consisting of a large number of FCC grains. The Taylor model of crystal plasticity theory is assumed. This analysis accounts for initial textures as well as texture evolution during large plastic deformations. The numerical analysis incorporates certain parallel computing features. Simulations have been carried out for an aluminum sheet alloy, and the effects of various parameters on the formation and prediction of localized deformation (in the form of necking and/or in-plane shear bands) are examined.     

On the strain hardening and texture evolution in high manganese steels: Experiments and numerical investigation

We present a systematic investigation on the strain hardening and texture evolution in high manganese steels where twinning induced plasticity (TWIP) plays a significant role for the materials' plastic deformation. Motivated by the stress–strain behavior of typical TWIP steels with compositions of Fe, Mn, and C, we develop a mechanistic model to explain the strain-hardening in crystals where deformation twinning dominates the plastic deformation. The classical single crystal plasticity model accounting for both dislocation slip and deformation twinning are then employed to simulate the plastic deformation in polycrystalline TWIP steels. While only deformation twinning is activated for plasticity, the simulations with samples composed of voronoi grains cannot fully capture the texture evolution of the TWIP steel. By including both twinning deformation and dislocation slip, the model is able to capture both the stress–strain behaviors and the texture evolution in Fe–Mn–C TWIP steel in different boundary-value problems. Further analysis on the strain contributions by both mechanisms suggests that deformation twinning plays the dominant role at the initial stage of plasticity in TWIP steels, and dislocation slip becomes increasingly important at large strains.     

Crystal plasticity finite element modeling of mechanically induced martensitic transformation (MIMT) in metastable austenite

A new crystal plasticity model incorporating the mechanically induced martensitic transformation in metastable austenitic steel has been formulated and implemented into the finite element analysis. The kinetics of martensite transformation is modeled by taking into consideration of a nucleation-controlled phenomenon, where each potential martensitic variant based on Kurdjumov–Sachs (KS) relationship has different nucleation probability as a function of the interaction energy between externally applied stress and lattice deformation. Therefore, the transformed volume fractions are determined following selective variants given by the crystallographic orientation of austenitic matrix and applied stress in the frame of the crystal plasticity finite element. The developed finite element program is capable of considering the effect of volume change by the Bain deformation and the lattice-invariant shear during the martensitic transformation by effectively modifying the evolution of plastic deformation gradient of the conventional rate-dependent crystal plasticity finite element. The validation of the proposed model has been carried out by comparing with the experimentally measured data under simple loading conditions. Good agreements with the measurements for the stress–strain responses, transformed martensitic volume fractions and the influence of strain rate on the deformation behavior will enable the model to be promising for the future applications to the real forming process of the TRIP aided steel.     

Strain gradient crystal plasticity effects on flow localization

In metal grains one of the most important failure mechanisms involves shear band localization. As the band width is small, the deformations are affected by material length scales. To study localization in single grains a rate-dependent crystal plasticity formulation for finite strains is presented for metals described by the reformulated Fleck–Hutchinson strain gradient plasticity theory. The theory is implemented numerically within a finite element framework using slip rate increments and displacement increments as state variables. The formulation reduces to the classical crystal plasticity theory in the absence of strain gradients. The model is used to study the effect of an internal material length scale on the localization of plastic flow in shear bands in a single crystal under plane strain tension. It is shown that the mesh sensitivity is removed when using the nonlocal material model considered. Furthermore, it is illustrated how different hardening functions affect the formation of shear bands.     

基于晶体塑性理论研究铝材料高压高应变率下的强度特性

为了了解金属材料在极端加载下复杂动态响应过程中的多种机制和效应,重点针对Al材料在高压、高应变率加载下的塑性变形机制,在经典晶体塑性模型的基础上,对其中的非线性弹性、位错动力学和硬化形式进行改进,建立适用于高压、高应变率加载下的热弹-黏塑性晶体塑性模型。该模型可以较好地描述单晶铝和多晶铝材料屈服强度随压力的变化过程,相比宏观模型,用该模型还获得了多晶Al材料在冲击加载下的织构演化规律,揭示了织构择优取向行为和压力的关系。     

Investigating the limits of polycrystal plasticity modeling

A material model which describes the rate-dependent crystallographic slip of FCC metals has been implemented into a quasistatic, large deformation, nonlinear finite element code developed at Sandia National Laboratories. The resultant microstructure based elastic–plastic deformation model has successfully performed simulations of realistic looking 3-D polycrystalline microstructures generated using a Potts-model approach. These simulations have been as large as 50,000 elements composed of 200 randomly oriented grains. This type of model tracks grain orientation and predicts the evolution of sub-grains on an element by element basis during deformation of a polycrystal. Simulations using this model generate a large body of informative results, but they have shortcomings. This paper attempts to examine detailed results provided by large scale highly resolved polycrystal plasticity modeling through a series of analyses. The analyses are designed to isolate issues such as rate of texture evolution, the effect of mesh refinement and comparison with experimental data. Specific model limitations can be identified with lack of a characteristic length scale and oversimplified grain boundaries within the modeling framework.     

Microscale deformation of a tempered martensite ferritic steel: Modelling and experimental study of grain and sub-grain interactions

In this paper, a finite-element modelling framework is presented with explicit representation of polycrystalline microstructure for a tempered martensite ferritic steel. A miniature notched specimen was manufactured from P91 steel with a 20,000 h service history and tested at room temperature under three point bending. Deformation at the microscale is quantified by electron back scattered diffraction (EBSD) before and after mechanical loading. A representative volume element was developed, based on the initial EBSD scan, and a crystal plasticity model used to account for slip-based inelastic deformation in the material. The model showed excellent correlation with the experimental data when the relevant comparisons were made.     

Post-critical plastic deformation in incrementally nonlinear materials

The formation of multiple macroscopic shear bands is investigated as a mechanism of advanced plastic flow of polycrystalline metals. The overall deformation pattern and material characteristics are determined beyond the critical instant of ellipticity loss, without the need of introducing an internal length scale. This novel approach to the modelling of post-critical plastic deformation is based on the concept of a representative nonuniform solution in a homogeneous material. The indeterminacy of a post-critical representative solution is removed by eliminating unstable solution paths with the help of the energy criterion of path instability. It is shown that the use of micromechanically based, incrementally nonlinear corner theories of time-independent plasticity leads then to gradual concentration of post-critical plastic deformation. The volume fraction occupied by shear bands is found to have initially a well-defined, finite value insensitive to the mesh size in finite element calculations. Further deformation depends qualitatively on details of the constitutive law. In certain cases, the volume fraction of active bands decreases rapidly to zero, leading to material instability of dynamic type. However, for physically hardening materials with the yield-vertex effect, the localization volume typically remains finite over a considerable deformation range. At later stages of the plane strain simulation, differently aligned secondary bands are formed in a series of bifurcations.     

Study on the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy based on a new crystal plasticity constitutive model

In this paper, a crystal plasticity based constitutive model (Yu et al., 2013) is extended to describe the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy by considering the internal heat production. Two sources of internal heat productions are included in the proposed model, i.e., the mechanical dissipations of inelastic deformation and the transformation latent heat in the NiTi shape memory alloy. With an assumption of uniform temperature field in the alloy specimen, a simplified evolution law of temperature field is obtained by the first law of thermodynamics and the heat boundary conditions. An explicit scale-transition rule is adopted to extend the proposed single crystal model to the polycrystalline version. The capability of the extended polycrystalline model to describe the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy is verified by comparing the predictions with the corresponding experimental ones. The comparison demonstrates that the proposed constitutive model considering the internal heat production predicts the rate-dependent cyclic deformation of super-elastic NiTi shape memory alloy fairly well.     

A finite strain elastic-viscoplastic self-consistent model for polycrystalline materials

A large strain elastic-viscoplastic self-consistent (EVPSC) model for polycrystalline materials is developed. At single crystal level, both the rate sensitive slip and twinning are included as the plastic deformation mechanisms, while elastic anisotropy is accounted for in the elastic moduli. The transition from single crystal plasticity to polycrystal plasticity is based on a completely self-consistent approach. It is shown that the differences in the predicted stress-strain curves and texture evolutions based on the EVPSC and the viscoplastic self-consistent (VPSC) model proposed by Lebensohn and Tomé (1993) are negligible at large strains for monotonic loadings. For the deformations involving unloading and strain path changes, the EVPSC predicts a smooth elasto-plastic transition, while the VPSC model gives a discontinuous response due to lack of elastic deformation. It is also demonstrated that the EVPSC model can capture some important experimental features which cannot be simulated by using the VPSC model.     

A dislocation density based crystal plasticity finite element model: Application to a two-phase polycrystalline HCP/BCC composites

We present a multiscale model for anisotropic, elasto-plastic, rate- and temperature-sensitive deformation of polycrystalline aggregates to large plastic strains. The model accounts for a dislocation-based hardening law for multiple slip modes and links a single-crystal to a polycrystalline response using a crystal plasticity finite element based homogenization. It is capable of predicting local stress and strain fields based on evolving microstructure including the explicit evolution of dislocation density and crystallographic grain reorientation. We apply the model to simulate monotonic mechanical response of a hexagonal close-packed metal, zirconium (Zr), and a body-centered cubic metal, niobium (Nb), and study the texture evolution and deformation mechanisms in a two-phase Zr/Nb layered composite under severe plastic deformation. The model predicts well the texture in both co-deforming phases to very large plastic strains. In addition, it offers insights into the active slip systems underlying texture evolution, indicating that the observed textures develop by a combination of prismatic, pyramidal, and anomalous basal slip in Zr and primarily {110}〈111〉 slip and secondly {112}〈111〉 slip in Nb.     

Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal

This is a study of plastic strain localization, surface roughening and of the origin of these phenomena in polycrystals. An oligocrystal aluminum sample with a single quasi-2D layer of coarse grains is plastically deformed under uniaxial tensile loading. During deformation, the history of strain localization, surface roughening, microstructure and in-grain fragmentation is carefully recorded. Using a crystal plasticity finite element model, corresponding high-resolution simulations are conducted. A series of comparisons identifying aspects of good and of less good match between model predictions and experiments is presented. The study suggests that the grain topology and microtexture have a significant influence on the origin of strain heterogeneity. Moreover, it suggests that the final surface roughening profiles are related both to the macro strain localization and to the intra-grain interaction. Finally slip lines observed on the surface of the samples are used to probe the activation of slip systems in detail. The study concludes with an assessment of the limitations of the crystal plasticity model.     

Assessment of crystal plasticity based calculation of the lattice spin of polycrystalline metals for FE implementation

When texture is incorporated in the finite element simulation of a metal forming process, much computer time can be saved by replacing continuous texture and corresponding yield locus updates by intermittent updates after strain intervals of e.g. 20%. The hypothesis that the evolution of the anisotropic properties of a polycrystalline material during such finite interval of plastic deformation can be modelled by just rotating the initial texture instead of continuously updating it by means of a polycrystal deformation model is tested in this work. Two spins for rotating the frame have been assessed: the classical rigid body spin and a crystal plasticity based “Mandel spin” (calculated from the rotated initial texture) which is the average of the spins of all the crystal lattices of the polycrystal. Each of these methods was used to study the evolution of the yield locus and the r-value distribution during the 20% strain interval. The results were compared to those obtained by simulating the texture evolution continuously using a polycrystal deformation model. When the texture was not updated during deformation, it was found that for most initial textures the Mandel spin does not perform better than the rigid body spin, except for some special initial textures for which the Mandel spin is much better. The latter ones are textures which are almost stable for the corresponding strain mode. When the texture was updated after each strain interval of e.g. 20% the Mandel spin performed much better than the rigid body spin.     

Modeling transients in the mechanical response of copper due to strain path changes

When copper is deformed to large strains its texture and microstructure change drastically, leading to plastic anisotropy and extended transients when it is reloaded along a different strain path. For predicting these transients, we develop a constitutive model for polycrystalline metals that incorporates texture and grain microstructure. The directional anisotropy in the single crystals is considered to be induced by variable latent hardening associated with cross-slip, cut-through of planar dislocation walls, and dislocation-based reversal mechanisms. These effects are introduced in a crystallographic hardening model which is, in turn, implemented into a polycrystal model. This approach successfully explains the flow response of OFHC Cu pre-loaded in tension (compression) and reloaded in tension (compression), and the response of OFHC Cu severely strained in shear by equal channel angular extrusion and subsequently compressed in each of the three orthogonal directions. This new theoretical framework applies to arbitrary strain path changes, and is fully anisotropic.     

A finite deformation theory of strain gradient plasticity

Plastic deformation exhibits strong size dependence at the micron scale, as observed in micro-torsion, bending, and indentation experiments. Classical plasticity theories, which possess no internal material lengths, cannot explain this size dependence. Based on dislocation mechanics, strain gradient plasticity theories have been developed for micron-scale applications. These theories, however, have been limited to infinitesimal deformation, even though the micro-scale experiments involve rather large strains and rotations. In this paper, we propose a finite deformation theory of strain gradient plasticity. The kinematics relations (including strain gradients), equilibrium equations, and constitutive laws are expressed in the reference configuration. The finite deformation strain gradient theory is used to model micro-indentation with results agreeing very well with the experimental data. We show that the finite deformation effect is not very significant for modeling micro-indentation experiments.     

Forming simulation of aluminum sheets using an anisotropic yield function coupled with crystal plasticity theory

This paper describes the application of a coupled crystal plasticity based microstructural model with an anisotropic yield criterion to compute a 3D yield surface of a textured aluminum sheet (continuous cast AA5754 aluminum sheet). Both the in-plane and out-of-plane deformation characteristics of the sheet material have been generated from the measured initial texture and the uniaxial tensile curve along the rolling direction of the sheet by employing a rate-dependent crystal plasticity model. It is shown that the stress–strain curves and R-value distribution in all orientations of the sheet surface can be modeled accurately by crystal plasticity if a “finite element per grain” unit cell model is used that accounts for non-uniform deformation as well as grain interactions. In particular, the polycrystal calculation using the Bassani and Wu (1991) single crystal hardening law and experimental electron backscatter data as input has been shown to be accurate enough to substitute experimental data by crystal plasticity data for calibration of macroscopic yield functions. The macroscopic anisotropic yield criterion CPB06ex2 (Plunkett et al., 2008) has been calibrated using the results of the polycrystal calculations and the experimental data from mechanical tests. The coupled model is validated by comparing its predictions with the anisotropy in the experimental yield stress ratio and strain ratios at 15% tensile deformation. The biaxial section of the 3D yield surface calculated directly by crystal plasticity model and that predicted by the phenomenological model calibrated with experimental and crystal plasticity data are also compared. The good agreement shows the strength of the approach. Although in this paper, the Plunkett et al. (2008) yield function is used, the proposed methodology is general and can be applied to any yield function. The results presented here represent a robust demonstration of implementing microscale crystal plasticity simulation with measured texture data and hardening laws in macroscale yield criterion simulations in an accurate manner.     

Dislocation-mediated strain hardening in tungsten: Thermo-mechanical plasticity theory and experimental validation

A self-consistent thermo-mechanical model to study the strain-hardening behavior of polycrystalline tungsten was developed and validated by a dedicated experimental route. Dislocation–dislocation multiplication and storage, as well dislocation-grain boundary (GB) pinning were the major mechanisms underlying the evolution of plastic deformation, thus providing a link between the strain hardening behavior and material's microstructure. The microstructure of the polycrystalline tungsten samples has been thoroughly investigated by scanning and electron microscopy. The model was applied to compute stress–strain loading curves of commercial tungsten grades, in the as-received and as-annealed states, in the temperature range of 500–1000 °C. Fitting the model to the independent experimental results obtained using a single crystal and as-received polycrystalline tungsten, the model demonstrated its capability to predict the deformation behavior of as-annealed samples in a wide temperature range and applied strain. The relevance of the dislocation-mediated plasticity mechanisms used in the model have been validated using transmission electron microscopy examination of the samples deformed up to different amounts of strain. On the basis of the experimental validation, the limitations of the model are determined and discussed.     

Texture gradient simulations for extrusion and reversible rolling of FCC metals

A texture simulation method is described for some complex plane strain deformation paths during hot shaping of FCC metals. The method employs both finite element calculations and a polycrystal plasticity model based on the Relaxed-Constraints (RC) Taylor hypothesis and a viscoplastic constitutive law. We have considered the {111}<110> slip systems and the {100}, {110}, {112} <110> non-octahedral slip systems. The finite element codes simulate the strain paths of material flow during a shaping process. The local velocity gradients, expressed in the macroscopic reference coordinates, are rewritten in the local flow line coordinates using a kinematic analysis for steady-state flow. Secondly, for the different deformation paths, the RC polycrystal plasticity model is used to numerically simulate the local deformation texture evolutions as a function of depth. Texture simulations are carried out for two deformation processes combining hot compression and shear: extrusion and reversible rolling. For extrusion, the simulated pole figures and ODFs show the typical texture variations through the thickness of an extruded 6082 aluminium alloys, i.e. (β-fibre in the centre and a TD rotated copper component near the surface. It is shown that hot reversible rolling should develop a strong pure shear texture {001}<110> near the surface.