Interpretation of the behavior of metals under large plastic shear deformations: comparison of macroscopic predictions to physically based predictions

A large plastic shear problem is analyzed by application of a macroscopic anisotropic plasticity model (Kuroda, M., 1997. Interpretation of the behavior of metals under large plastic shear deformations: a macroscopic approach. Int. J. Plasticity 13, 359–383), and the results are compared to predictions based on crystal plasticity with the Taylor assumption. It is found that these two different-scale models provide very similar predictions. The interpretations for such similarities are pursued in detail. The present macroscopic model reproduces quite well the change in orientation of anisotropy, which is directly predicted in the crystal plasticity analyses as a macroscopic manifestation of texture development. Consequently, the predictions for the rotation of the yield surface by the different-scale models become very similar. It is clearly shown that, in a macroscopic sense, the rotation of the anisotropic yield surface is a main cause of the axial effects in large plastic shear deformation.     

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.     

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.     

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.     

Incorporation of twinning into a crystal plasticity finite element model: Evolution of lattice strains and texture in Zircaloy-2

A crystal plasticity finite element code is developed to model lattice strains and texture evolution of HCP crystals. The code is implemented to model elastic and plastic deformation considering slip and twinning based plastic deformation. The model accounts for twinning reorientation and growth. Twinning, as well as slip, is considered to follow a rate dependent formulation. The results of the simulations are compared to previously published in situ neutron diffraction data. Experimental results of the evolution of the texture and lattice strains under uniaxial tension/compression loading along the rolling, transverse, and normal direction of a piece of rolled Zircaloy-2 are compared with model predictions. The rate dependent formulation introduced is capable of correctly capturing the influence of slip and twinning deformation on lattice strains as well as texture evolution.     

Modelling of texture evolution in metals accounting for lattice reorientation due to twinning

Twinning has been incorporated into a crystal plasticity model with the regularized Schmid law. In order to account for the appearance of twin-related orientations, a new probabilistic twin reorientation scheme that maintains the number of reoriented grains consistent with the accumulated deformation by twinning within the polycrystalline element, has been developed. A hardening rule describing slip–twin interactions has been also proposed. Model predictions concerning material response and texture evolution have been analyzed for fcc materials of low stacking fault energy.     

Finite element analysis of grain-by-grain deformation by crystal plasticity with couple stress

Rigid–plastic crystal plasticity with the rate-sensitive constitutive behavior of a slip system has been formulated within the framework of a two-dimensional finite element method to predict the grain-by-grain deformation of single- and polycrystalline FCC metals. For that purpose, individual grains are represented by several numbers of finite elements to describe the sub-grain deformation behavior, and couple stress has been introduced into the equilibrium equation to be able to describe the size effect as well as to prevent mesh-dependent predictions. A modified virtual work-rate principle with an approximate interface constraint has been suggested to use a C ⁰-continuous element in the finite element implementation, and the couple stress work-rate has been formulated on the basis of an assumed constitutive behavior. Simulated plane-strain compressions of a single crystal cube show that the shearing and the deformation load are closely related to the imbedded lattice orientation of the crystal grain, and that the sub-grain deformation and the load magnitude can be controlled by the couple stress hardening. It is also confirmed that almost the same predictions are obtained for different mesh systems by considering the couple stress hardening. Simulated plane-strain compressions of a bi-crystal show considerably curved grain-by-grain surface profiles after large reduction for several combinations of the imbedded lattice orientation. The high couple stress hardening predicted around grain boundaries is supposed to be related to the grain size effect. It is also supposed that consideration of couple stress is necessary to predict the sub-grain or the grain-by-grain deformation, and the couple stress hardening may be used to describe the state of microstructures in grain.     

Micromechanics of plastic deformation and phase transformation in a three-phase TRIP-assisted advanced high strength steel: Experiments and modeling

The micromechanics of plastic deformation and phase transformation in a three-phase advanced high strength steel are analyzed both experimentally and by microstructure-based simulations. The steel examined is a three-phase (ferrite, martensite and retained austenite) quenched and partitioned sheet steel with a tensile strength of ~980 MPa. The macroscopic flow behavior and the volume fraction of martensite resulting from the austenite–martensite transformation during deformation were measured. In addition, micropillar compression specimens were extracted from the individual ferrite grains and the martensite particles, and using a flat-punch nanoindenter, stress–strain curves were obtained. Finite element simulations idealize the microstructure as a composite that contains ferrite, martensite and retained austenite. All three phases are discretely modeled using appropriate crystal plasticity based constitutive relations. Material parameters for ferrite and martensite are determined by fitting numerical predictions to the micropillar data. The constitutive relation for retained austenite takes into account contributions to the strain rate from the austenite–martensite transformation, as well as slip in both the untransformed austenite and product martensite. Parameters for the retained austenite are then determined by fitting the predicted flow stress and transformed austenite volume fraction in a 3D microstructure to experimental measurements. Simulations are used to probe the role of the retained austenite in controlling the strain hardening behavior as well as internal stress and strain distributions in the microstructure.     

PREDICTION OF EARING IN TEXTURED ALUMINIUM SHEETS BASED ON CRYSTAL PLASTICITY

The phenomenon of earing is investigated in the present study based on the theory of crystal plasticity with the dynamic explicit finite element program developed. Firstly texture analysis is carried out of rolled aluminium alloy Al5052 by means of X-ray technique. Then from the texture coefficients an analytical expression for the orientation distribution function (ODF) is derived making use of the computer algebraic language Mathematica4.0, which makes it easier to discretize the ODF into a series of Eulerian angles representing the distribution of lattices and further the preferred orientation (texture) of crystals of the original sheets. For the polycrystal model, the material is described using crystal plasticity where each material point in grains with each grain modelled as an FCC crystal with 12 distinct slip systems. The modified Taylor theory of crystal plasticity is used and only the initial texture is taken into consideration during large plastic deformation. Numerical simulation of earing has been performed for an aluminium sheet with texture and one with crystals exhibiting random distribution to demonstrate the effect of texture of materials on their plastic anisotropy and formability. Project supported by the National Natural Science Foundation of China (No. 59875025).     

Crystallographic plasticity in fretting of Ti–6AL–4V

The deformation occurring under fretting conditions occurs over length scales of the same order as the grain size. Consequently, the crystallographic orientation of the grains plays a significant role in the deformation response. The cyclic deformation response in the region experiencing fretting predicted by a crystal plasticity model is compared to prediction of an initially isotropic J₂ cyclic plasticity theory with nonlinear kinematic hardening. The crystal plasticity model provides enhanced understanding of the fretting fatigue process, especially with regard to the shakedown and ratchetting limits.     

Modeling texture evolution in equal channel angular extrusion using crystal plasticity finite element models

A new approach to modeling crystallographic texture evolution in Equal Channel Angular Extrusion (ECAE) is presented in this paper. The proposed approach utilizes an elastic–viscoplastic single crystal constitutive model implemented in a finite element framework. A representative volume element of the polycrystal is subjected to boundary conditions that simulate the approximate deformation history experienced by different regions of the sample (at different through-thickness depths) in both Route A and Route C processing. The proposed approach aims to capture the influence of the complex interactions that ensue among the constituent individual crystals of a polycrystal in controlling the texture evolution in the sample, while capturing the boundary conditions inherent to ECAE deformation. The predictions from the proposed approach are compared against previously reported experimental measurements in ECAE of copper. It is observed that the proposed approach provides significantly better agreement with the measurements when compared against previously reported model predictions.     

Deformation texture prediction: from the Taylor model to the advanced Lamel model

The paper reports on a recent effort to develop a statistical (or Monte-Carlo) model for quantitative deformation texture prediction which is yet fast enough for implementation in every Gauss point of an FE simulation of a metal-forming process. The principles of Taylor-type models for the prediction of deformation textures of polycrystalline materials are reminded. This includes the full-constraints Taylor theory (every grain of a polycrystal undergoes the same plastic deformation), classical Relaxed Constraints Taylor theory (one or two of the components of the local velocity gradient tensor need not be the same for all grains) and multi-grain models (LAMEL model; mentioning of GIA model). The primal–dual structure of the equations relating strain rates with slip rates, and those relating stresses and resolved shear stresses on slip systems, is made clear. It is then possible to describe the basic philosophy and the mathematical implementation of a new model, called “advanced Lamel model” (ALAMEL). This model is more generally applicable than the previously developed LAMEL model, which is only valid for rolling. Both take interactions between neighbouring grains into account. Finally, quantitative comparisons are given between experimentally observed rolling textures and the predictions of the new model, as well as of other models: full-constraints and relaxed constraints Taylor, LAMEL, GIA, visco-plastic self-consistent and crystal plasticity finite element (CPFEM) models. This was done for IF steel (one thickness reduction) and for two aluminium alloys: AA1200 (five thickness reductions) and AA5182 (one thickness reduction). It was found that for AA1200, the new model is on average the best; for the two other cases, it is among the best models, but the LAMEL or CPFEM models are better. These results suggest that in spite of all simplifications, the ALAMEL model captures (and identifies) the domination mechanisms controlling the development of deformation textures in cubic metals.     

Polycrystal constraint and grain subdivision

Typically, intergranular constraint relations of various sorts are introduced to improve the accuracy of prediction of texture evolution and macroscale stress–strain behavior of metallic polycrystals within the context of simple polycrystal averaging schemes. This paper examines the capability of a 3-D polycrystal plasticity theory (Kocks, U.F., Kallend, J.S., Wank, H.-R., Rollett, A.D. and Wright, S.I. (1994), popLA, Preferred Orientation Package—Los Alamos. LANL LA-CC-89-18), based on the Taylor assumption of uniform deformation among grains, to predict texture evolution and stress–strain behavior for complex finite deformation loading paths of OFHC Cu. Compression, shear and sequences of deformation path are considered. It is shown that the evolution of texture is too rapid and that the intensity of peaks is more pronounced than for experimentally measured pole figures. Comparisons of both stress–strain behavior and texture evolution are made with experiments, with and without the inclusion of latent hardening effects. It is argued that grain subdivision processes accommodate intergranular kinematical constraints, leading to the notion of a generalized Taylor constraint that considers the distribution of subgrain orientations. The subdivision process is assumed to follow the experimentally observed refinement of low energy dislocation structures associated with geometrically necessary dislocations. A modification of the kinematical structure of crystal plasticity is proposed based on generation of geometrically necessary dislocations that accommodate a fraction of the plastic stretch and rotation at the scale of a grain.     

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.     

A theoretical investigation of the influence of dislocation sheets on evolution of yield surfaces in single-phase B.C.C. polycrystals

Accurate and reliable predictions of yield surfaces and their evolution with deformation require a better physical representation of the important sources of anisotropy in the material. Until recently, the most physical approach employed in the current literature has been the use of polycrystalline deformation models, where it is assumed that crystallographic texture is the main contributor to the overall anisotropy. However, recent studies have revealed that the grain-scale mesostructural features (e.g. cell-block boundaries) may have a large impact on the anisotropic stress-strain behaviour, as evidenced during strain-path change tests (e.g. cross effect, Bauschinger effect).In previous papers, the authors formulated an extension of the Taylor-type crystal plasticity model by incorporating some details of the grain-scale mesostructural features. The main purpose of this paper is to study the evolution of yield surfaces in single-phase b.c.c. polycrystals during deformation and strain-path changes using this extended crystal plasticity model. It is demonstrated that the contribution of the grain-scale substructure in these metals on yield loci is comparable in magnitude to the effects caused by the differences in texture. Furthermore, it is shown that the shape of yield loci cannot be predicted accurately by the traditional polycrystalline deformation model with equal slip hardening. The trends predicted by the extended crystal plasticity model are in much better agreement with the experimental evidence reported in the literature than those represented in classical treatments by isotropic and kinematic hardening.     

FeCrAl合金材料织构对其宏观力学本构关系的影响研究

FeCrAl合金具有优良的高温抗氧化性和耐辐照性能,是事故容错核燃料包壳的重要候选材料.其在加工过程和热处理过程中易形成a纤维织构(//RD)和γ纤维织构(//ND),会影响材料的宏观力学性能与深加工成形能力.该研究针对具有不同织构的多晶FeCrAl合金,建立了代表性体元模型,使用晶体塑性有限元方法,在ABAQUS/Explicit中模拟材料单轴加载下的宏观应力应变曲线,分析不同织构对FeCrAl合金宏观力学本构关系的影响.计算结果表明,对于具有a织构、γ织构和晶粒无择优取向的材料,在轧向上的应力应变曲线差异较小.γ织构会引起材料强烈的各向异性,在轧面法向上的屈服强度远高于轧向和横向上的屈服强度,这是因为晶粒的方向平行于加载方向,滑移系难以启动.提高γ纤维织构的比例,将增大轧面法向上的屈服强度.该研究可以为优化FeCrAl合金材料织构、加工条件和材料力学性能提供参考.     

FeCrAl合金材料织构对其宏观力学本构关系的影响研究

FeCrAl合金具有优良的高温抗氧化性和耐辐照性能,是事故容错核燃料包壳的重要候选材料. 其在加工过程和热处理过程中易形成α纤维织构（<110>//RD）和γ纤维织构（<111>//ND）,会影响材料的宏观力学性能与深加工成形能力. 本研究针对具有不同织构的多晶FeCrAl合金,建立了代表性体元模型, 使用晶体塑性有限元方法,在ABAQUS/Explicit中模拟材料单轴加载下的宏观应力应变曲线,分析不同织构对FeCrAl合金宏观力学本构关系的影响. 计算结果表明,对于具有α织构、γ织构和晶粒无择优取向的材料,在轧向上的应力应变曲线差异较小. γ织构会引起材料强烈的各向异性,在轧面法向上的屈服强度远高于轧向和横向上的屈服强度,这是因为晶粒的<111>方向平行于加载方向,滑移系难以启动. 提高γ纤维织构的比例,将增大轧面法向上的屈服强度. 本研究可以为优化FeCrAl合金材料织构、加工条件和材料力学性能提供参考.     

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.     

A simplified “polycrystalline” model for viscoplastic and damage finite element analyses

In the framework of classical polycrystalline models, drastic reductions of the numbers of slip systems and of “grains” are proposed. With a number of “grains” representing the texture of the material smaller than 10, good results are obtained either for initially isotropic fcc steel or anisotropic hcp zirconium alloy, with some predictive capacity despite the partial loss of physical relevance. Finite element analyses CPU times are not significantly increased as compared to advanced macroscopic models. Novel extensions of the polycrystalline model are developed for intergranular creep or void growth damage. This methodology increases the field of application of the polycrystalline approach in plastic anisotropy, cyclic plasticity, plastic instability and fracture, and in corresponding industrial problems.