Viscoplastic Self-consistent Polycrystal Model Research Articles

Shear banding in sub-microcrystalline nickel at 4 K

A flat specimen of sub-microcrystalline nickel was tensile tested at 4K until fracture occurred and subsequently investigated by electron backscatter diffraction in a high resolution scanning electron microscope in order to deduce the local texture in the near crack area. Thus, two sets of intersecting fine slip markings observed on the surface (under ±55° with respect to the tensile axis) could be explained as a result of localized simple shear in the bulk material underneath the slip markings. The overall amount of shear in the region near the crack was estimated to be 1.25 based on texture simulations using the viscoplastic self-consistent polycrystal model.

Effect of the initial texture components of hot-rolled BH steel on the evolution of deformation texture and stored energy during the cold-rolling process

A visco-plastic self-consistent polycrystal model was used to investigate the effect of texture gradients through the thickness direction of hot-rolled bake-hardening steel on the evolution of deformation texture and stored energy during a cold-rolling process. The theoretical texture evolution was in good agreement with the experimental texture evolution, as measured using the electron back-scattering diffraction technique. The VPSC polycrystal model was also used to explain the individual contribution of major texture components to the evolution of deformation texture and stored energy during cold-rolling. The results demonstated that the biased bimodal distribution of stored energy in major texture components contributed to a distinct bimodal distribution of stored energy at the center and surface regions of cold-rolled BH steel.

Experimental and numerical investigations of yield surface, texture, and deformation mechanisms in AA5754 over low to high temperatures and strain rates

The effects of strain rate and temperature on the yield and flow stress of AA5754 sheets are presented under uniaxial (tension and compression), dynamic (tension), and simple shear loading conditions. The present study investigates the anisotropic behavior of AA5754 sheets through experiments performed in the rolling (RD), 45° to rolling (DD), and transverse to rolling (TD) directions at room and elevated temperatures. The experimental results show that the strain rate sensitivity varied from negative at room temperature to positive at elevated temperatures (>150°C), and the anisotropy was inversely proportional to the strain rate. Texture analysis was conducted on the specimens after uniaxial tension and simple shear deformation, using the neutron diffraction and electron back-scattered diffraction (EBSD) techniques. Rotation rate maps and orientation stability parameters, determined by the rate-sensitive model, were used to explain the kinematic stability of the initial texture components in AA5754 sheets during uniaxial tension and simple shear deformation. A visco-plastic self-consistent (VPSC) polycrystal model was used to simulate the evolution of the initial texture components in AA5754 sheets during uniaxial tension and simple shear deformation.

A constitutive model of twinning and detwinning for hexagonal close packed polycrystals

A new constitutive model to describe twinning and detwinning for polycrystalline materials with the hexagonal close packed (HCP) crystallographic structure is developed and implemented in the recently developed elastic viscoplastic self-consistent (EVPSC) polycrystal model. The new model is then applied to magnesium alloy Mg–3 Al–1 Zn (AZ31B) sheet under cyclic loadings and strain path changes. It is demonstrated that the new twinning model is able to capture key features associated with twinning and detwinning observed experimentally.

Study of limit strains for FCC and BCC sheet metal using polycrystal plasticity

In this research, we analyze forming-limit strains of FCC and BCC materials using a viscoplastic self-consistent polycrystal model (VPSC) in conjunction with the Marciniak–Kuczynski (MK) approach. In particular, our work is focused on the theoretical analysis and comparison between FCC and BCC crystal structures made by Inal et al. [Inal, K., Neale, K.W., Aboutajeddine, A., 2005. Forming limit comparison for FCC and BCC sheets, International Journal of Plasticity, 21, 1255–1266]. These authors performed their simulations based on a generalized Taylor-type polycrystal model (MK-FC), finding a remarkably low forming-limit curve for the FCC material and an extremely high forming-limit curve for the BCC material, in the biaxial stretching range. We verified that our predictions are similar to Inal’s results for both FCC and BCC materials when the MK-FC model is used. However, MK-VPSC calculations do not give such extreme values, and we believe that this theory predicts much more reliable results for both FCC and BCC crystallographic assumptions. We also found that localized necking depends on texture evolution in the vicinity of equi-biaxial stretching, through the sharpness of the predicted yield surface. Finally, it is shown that the MK-VPSC’s predictions are in good agreement with experimental data for AA5182-O and a DQ-type steel-sheet metal.

Study of a drawing-quality sheet steel. I: Stress/strain behaviors and Lankford coefficients by experiments and micromechanical simulations

The sheet-metal industry uses Lankford coefficients and the forming-limit curve, FLC, as standards for characterizing a sheet’s ability to be stretched and deep drawn. Investigators have recently made significant advances in computer codes that predict these measures of formability. However, complete experimental data sets that provide input properties and verification data for the simulations rarely exist for a single material. The current investigation focused on obtaining such data for a single drawing-quality steel sheet. Measurements intended for the calibration and initial verification of the simulation code include uniaxial-tension tests, through-thickness and plane-strain compression experiments, and quantitative texture – orientation distribution function – evaluations, while a comparison between measured and simulated Lankford coefficients, Part I, and an FLC, Part II, provide a rigorous verification of the computer simulations. In order to initially verify the simulations, we performed through-thickness and plane-strain compression measurements. A key experimental result was that the flow curve in free, through-thickness compression – an experiment that corresponds to biaxial stretching – lies 18% above the uniaxial tensile data. The plane-strain compression curve is another 11% above the free-compression stress/strain data. We measured the Lankford coefficients, as a function of angle to the rolling direction, for the same steel sheet, finding the maximum values in and at 90° to the rolling direction, 1.59 and 1.89 respectively. A minimum Lankford coefficient of 1.19 was measured at 45° to the rolling direction. For calibrating a rate-dependent visco-plastic self-consistent polycrystal model we needed only to measure the material’s initial texture and to fit power-law and saturation-hardening laws to our tensile data. This kept the set of adjustable parameters to a minimum. Without other adjustments to the model, we predicted the correct stress levels in the free and channel-die compression experiments as well as values of Lankford coefficients. These successes indicate that the polycrystal model should be capable of simulating the entire FLC, Part II.

Shear banding during cyclic deformation of sub-microcrystalline nickel

Sub-microcrystalline nickel produced by pulsed electrodeposition was investigated during cyclic deformation at high plastic strain amplitude. After a certain number of loading cycles the specimen developed a “macro” shear band at 45° with respect to the tensile axis, which acted as a crack initiator. Electron backscatter diffraction revealed that the shear band consists of relaxed grains elongated along the shear plane, showing a typical shear texture. The shear band texture was reproduced with the viscoplastic self-consistent polycrystal model using {1 1 1}〈1 1 0〉 slip systems.

An efficient constitutive model for room-temperature, low-rate plasticity of annealed Mg AZ31B sheet

Metals and alloys with hexagonal close packed (HCP) crystal structures can undergo twinning in addition to dislocation slip when loaded mechanically. The complexity of the plastic response and the limited extent of twinning are impediments to their room-temperature formability and thus their widespread adoption. In order to exploit the unusual deformation characteristics of twinning sheet materials in designing novel forming operations, a practical plane stress material model for finite element implementation was sought. Such a model, TWINLAW, has been constructed based on three phenomenological deformation modes for Mg AZ31B: S (slip), T (twinning), and U (untwinning). The modes correspond to three testing regimes: initial in-plane tension (from the annealed state), initial in-plane compression, and in-plane tension following compression, respectively. A von Mises yield surface with initial non-zero back stress was employed to account for plastic yielding asymmetry, with evolution according to a novel isotropic and nonlinear kinematic hardening model. Texture and its evolution were represented throughout deformation using a weighted discrete probability density function of c-axis orientations. The orientation of c-axes evolves with twinning or untwinning using explicit rules incorporated in the model. TWINLAW was implemented in Abaqus/Standard through UMAT with constitutive parameters obtained from in-plane tension/compression tests. Simulation of various tests showed good agreement with experiments, where available. Tests to assess the stability of the model for complex loading paths, for which no experimental results were available, have also been carried out. Comparison of computation times showed that TWINLAW is two orders of magnitude faster than a viscoplastic self-consistent polycrystal model incorporating twinning, but an order of magnitude slower than a conventional continuum model with isotropic hardening. TWINLAW reproduces all of the standard and special features of Mg deformation in terms of slip, twinning, and untwinning, for a range of strain states and transitions among such states, but has not been verified for multi-cycle strain paths.

Plastic flow anisotropy of pure zirconium after severe plastic deformation at room temperature

The present work investigates the plastic flow anisotropy of zirconium following one pass of equal-channel angular extrusion (ECAE) at room temperature in a 90° die. Samples were oriented with their strong basal pole texture either aligned with or perpendicular to the extrusion direction prior to processing, which leads to two significantly different starting textures. After ECAE, the samples were compressed to 30% along one of three sample directions. A visco-plastic self-consistent polycrystal model was used to determine the mechanisms responsible for the observed anisotropy. Using the same single-crystal material parameters, the model reasonably predicts texture evolution and the post-compression stress–strain response. We found that basal slip is crucial in reproducing the experimental results, and twinning makes an important contribution. These findings are noteworthy because basal slip is not active in zirconium at room temperature, and grain size reductions associated with ECAE are expected to suppress deformation twinning.

Evolution of the deformation texture and yield locus shape in an AZ31 Mg alloy sheet under uniaxial loading

A visco-plastic self-consistent (VPSC) polycrystal model was employed to simulate the evolution of yield locus shape in a polycrystalline AZ31 Mg alloy sheet under uniaxial loading. Macroscopic velocity gradients were imposed to calculate a full yield locus on the two-dimensional projection of a stress potential. The directions of the plastic strain rate vector were evaluated for various loading directions at the four quadrants of yield locus. The change of yield locus shape during plastic deformation was explained by texture evolution and the variation in the relative activity of each deformation mode. The validity of the polycrystal model for simulation of yield locus in a polycrystalline AZ31 Mg alloy sheet was demonstrated through the comparison of simulated deformation texture and R-value, which is a differential property of yield locus, with the experimental results.

Effect of reduction ratio on annealing texture and r-value directionality for a cold-rolled Al–5% Mg alloy

The evolution of the macrotexture and r-value directionality of cold-rolled Al–5% Mg alloys during annealing at various temperatures was investigated to seek an optimum annealing condition to improve the formability of TRBs. The change of volume fractions for the typical texture components of Al–5% Mg alloys was calculated using a misorientation approach in 3-D Euler space. A visco-plastic self-consistent (VPSC) polycrystal model was used to predict r-value directionality of the cold-rolled and annealed Al–5% Mg alloys. The electron backscatter diffraction (EBSD) technique was used to investigate a rapid change of the initial deformation texture in the specimen deformed by a reduction of 9% during annealing. The results showed that an optimum annealing temperature for achieving the low planar anisotropy was strongly dependent on the rolling reduction ratio.

Simulation of strain-softening behaviors in an AZ31 Mg alloy showing distinct twin-induced reorientation before a peak stress

To investigate strain-softening behavior during plastic deformation of an AZ31 Mg alloy, cylindrical specimens were compressed in a rolling direction at 300 °C. Experimental evidence revealed that an inhomogeneous microstructure evolved due to the softening behavior associated with deformation at elevated temperatures. The large grains that reoriented as a result of deformation twinning were free of dynamic recrystallization (DRX). Fine grains nucleated at grain boundaries of grains were deformed by a slip-dominated mechanism, which accommodated the external strain. A visco-plastic self-consistent (VPSC) polycrystal model was used to simulate softening of the flow stress curve and texture evolution during uniaxial compression. A softening scheme was implemented in the polycrystal model to predict the softening phenomenon and texture evolution after the peak stress. The original VPSC model was modified to simulate texture evolution in an AZ31 Mg alloy that exhibited twin-dominated deformation before the peak stress.

디프도로잉 시 DP강의 집합조직 및 이방성 거동 모사

A visco-plastic self-consistent (VPSC) polycrystal model has been applied to simulate texture simulation and anisotropic properties of DP steels during deep drawing process. In order to evaluate the strain path during deep drawing, a steady state was assumed in the flange part of deep drawn cup. The final stable orientations were strongly dependent on the initial location in the blank. The evolution of anisotropy of DP steel sheets has been demonstrated through comparison of plastic strain rate vector at the different plastic strain levels.

Simulation of Texture Evolution during Hot Rolling Deformation in FCC Materials

The evolution of hot rolling texture in FCC materials has been simulated numerically using a visco-plastic self-consistent (VPSC) polycrystal model. A finite element (FE) analysis with ABAQUS/StandardTM was conducted to evaluate the deformation gradients during hot rolling deformation. In order to capture crystallographic rotation during hot rolling deformation, an octahedral slip system was considered in a microscopic hardening model. The FE analysis with the VPSC polycrystal simulations successfully predicted the inhomogeneous texture development through the thickness direction in the hot-rolled Al-5wt%Mg alloy sheets.

Tension–compression asymmetry in severely deformed pure copper

In this work, we investigate the tension–compression asymmetry in the flow response of pure copper, severely deformed by a single pass of equal channel angular extrusion (ECAE), and tested afterwards in tension and compression along three orthogonal directions. The tension and compression responses differ in flow stress, hardening rate and transient behavior. The asymmetry in tension and compression responses depends on the direction of straining. Predictions from a microstructurally based hardening law implemented in a viscoplastic self-consistent polycrystal model demonstrate that the tension–compression asymmetry and its anisotropy arise not only from crystallographic texture but also from the directional substructure induced by the severe pre-straining. Slip activity differs in each grain and in each axial test, depending on its crystallographic orientation, orientation relationship with the previously generated substructure and pre-strain history. Asymmetry occurs because tension and compression represent two different types of strain path changes. Consequently, macroscopic deformation is a reflection of the type of strain path change represented by the post-ECAE axial test.

Texture Evolution during Uniaxial Compression of Hot-Rolled AZ31 Mg Alloy

Uniaxial compression tests on hot-rolled AZ31 Mg alloy were carried out at 200°C. In order to investigate the evolution of texture during plastic deformation, cylindrical specimens were compressed to the rolling and normal directions. Experimental investigation reveals that work hardening and texture evolution are strongly dependent on the loading direction. The occurrence of deformation twinning 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 texture evolution during the uniaxial compression. The texture evolution induced by crystallographic slip and deformation twinning can be explained by the relative activity of each deformation modes.

Modeling the temperature dependent effect of twinning on the behavior of magnesium alloy AZ31B sheet

Uniaxial compression test data were obtained from magnesium alloy AZ31B sheet material tested along three sample directions (rolling, transverse and normal direction) over the temperature range T = 22–250 °C. The yield point during in-plane compression is insensitive to temperature, up to 200 °C, suggesting that athermal mechanisms are responsible for yielding. The in-plane compression samples exhibit very low r-values, which provides another signature of significant twinning activity in magnesium sheet, in addition to the characteristic sigmoidal strain hardening curve. By varying the critical resolved shear strengths (CRSS) and hardening behaviors of the deformation mechanisms, it is possible to model the changes in the flow stress profile, the strain anisotropy, and texture evolution using a viscoplastic self-consistent polycrystal model. Notably, the CRSS values for basal slip were observed to be constant, while that of twinning increased slightly, and the CRSS values of thermally activated slip modes, i.e., prismatic and pyramidal 〈 c + a〉 slip, decrease over the temperature range investigated. Because deformation twinning is observed to be significantly active over the entire temperature range, and the ductility improves markedly as the temperature is increased, it is concluded that twinning is not intrinsically detrimental to the ductility. However, the poor ductility during in-plane compression at the lower temperatures appears to be connected with the twinning reorientation since there is a very limited ability to accommodate c-axis compression.

Evolution of crystallographic texture during equal channel angular extrusion of copper: The role of material variables

The evolution of crystallographic texture during equal channel angular extrusion (ECAE) using route A has been investigated experimentally as well as by simulations for three types of materials: pure, commercially pure, and impure (cast) copper. The ECAE texture of copper can be compared with simple shear textures. However, there are deviations in terms of location of the respective components. These differences can be nearly reproduced using a recent flow line approach for ECAE deformation (L.S. Toth, R. Arruffat-Massion, L. Germain, S.C. Baik, and S. Suwas: Acta Mater., 2004, Vol. 52, pp. 1885-98) with the help of the viscoplastic self-consistent polycrystal model. The main texture components common to all three materials are $A_1_E$ and $B_E/\overline{B}_E$; the latter ones are significantly stronger in the cast material. The effect of further deformation on texture modification depends on material variables, such as purity, initial microstructure, and texture.

Analysis of substructure evolution during simple shear of polycrystals by means of a combined viscoplastic self-consistent and disclination modeling approach

Microstructure development during severe plastic deformation by simple shear is modeled using a disclination model for substructure formation incorporated into the viscoplastic self-consistent (VPSC) polycrystal model. The strain incompatibilities between a homogeneous effective medium and a grain calculated by the VPSC model are assumed to result in an accumulation of disclinations at junctions of the grain. These disclinations are then relaxed by the growth of low-angle dislocation boundaries from the junctions. These boundaries split the grain into smaller, misoriented volumes which with further deformation can lead to its subdivision into new grains. The evolution of misorientation angles between the newly formed grains and the parent with applied straining agrees reasonably well with experimental misorientation angle distributions for geometrically necessary boundaries. Accounting for subgrain boundaries and grain subdivision results in textures after large strains that are more diffuse and lower in intensity than those predicted using standard VPSC modeling.

Prediction of spring-back behavior in high strength low carbon steel sheets

The spring-back of polycrystalline materials has been predicted numerically using the elastic and visco-plastic crystal plasticity models. The anisotropic plane strain moduli for texture components typical in high strength steel sheets and low carbon high strength steel sheets were calculated with the upper–lower bounds and elastic self-consistent model. The yield stresses of polycrystalline materials were calculated with the visco-plastic self-consistent polycrystal model. The influence of texture components on the spring-back was analyzed in detail. The elastic and visco-plastic self-consistent models were also used to evaluate magnitude and directionality of the spring-back angle of high strength low carbon steel sheets subjected to plane strain bending.