Viscoplastic Self-consistent Polycrystal Model Research Articles

Unveiling the self-annealing phenomenon and texture evolution in room-temperature-rolled Cu-Fe-P alloy sheets

The present study addresses the microstructural and texture evolution of Cu-Fe-P alloy sheets rolled at room temperature (RT). Cu-Fe-P specimens were subjected to 20, 40, 60, and 80% reduction ratios (RR) through room-temperature rolling (RTR). Nano-sized Fe2P precipitates were observed in the initial and deformed specimens. Continuous-rolling deformation causes strain hardening, whereas exposing severely deformed specimens to RT causes the self-annealing phenomenon. Deformed specimens to 60 and 80% RRs exhibited strain localizations (SLs) that formed only in Copper-type grains. In this study, a visco-plastic self-consistent (VPSC) polycrystal model was used to calculate the relative slip activity for major texture orientations. Copper-type grains showed the occurrence of predominant single-slip system which was the primary reason for the formation of SLs. Static recovery (SRV) and static recrystallization (SRX) were the main softening phenomena found in the RTR specimens. Both discontinuous SRX (DSRX) and continuous SRX (CSRX) were observed as the SRX phenomenon in RTR specimens. Major SRX grains were elongated in shape due to the combined effects of a higher orientation gradient (CSRX), to the larger SE differences between the matrix grains (restricted growth), and to a pinning effect by Fe2P particles. The as-received specimen showed weak plane-strain texture components at maxima around the S component ((123)<634>). As the RR increased, the volume fractions of Copper ((112)<111>), Brass ((110)<112>), and S components were likewise increased (except at 60% RR). The highest fraction of plane-strain components was observed for the RTR-80 specimen. The large number of SLs and the higher orientation gradient decreased the intensity of the plane-strain texture in the RTR-60 specimen, whereas a higher fraction of SRX in the RTR-80 specimen enhanced the plane-strain texture components. Time-dependent decay in the hardness values in the RTR specimens were attributed to SRV and SRX.

Evolution of microstructure and texture in the stir zone of commercially pure titanium during friction stir processing

The microstructure and texture in the stir zone (SZ) of friction-stir-processed (FSPed) commercially pure titanium (CP-Ti) were investigated via electron backscatter diffraction (EBSD), finite element analysis (FEA), and polycrystal modeling. The EBSD characterization elucidated the development of an equiaxed submicron grain microstructure across the SZ, which was induced by dynamic grain refinement and supported by a multi-faceted mechanism for dynamic recrystallization (DRX). FEA was used to theoretically explain the spatial and time dependence shown by the deformation history and to elucidate the distributions of temperature, strain, and strain rate that occur in CP-Ti during FSP. The deformation history results from FEA were further utilized as input for establishing a visco-plastic self-consistent (VPSC) polycrystal model that featured Zener-Hollomon parameter-dependent microscopic hardening and a DRX scheme to predict the texture evolution in FSPed material. The texture development in the SZ of FSPed material was highly dependent on the thermo-mechanical history of different zones of the FSPed CP-Ti. The combination of EBSD and VPSC modeling revealed a strong fiber texture in the SZ. Systems of prismatic and pyramidal <c+a> slip and compression twinning appear to be the dominant deformation modes in the SZ. In-plane shear components of the velocity gradients (L12 and L21) are mainly responsible for the crystal rotation about the normal direction in the SZ. On the other hand, normal and other shear components did not appear to alter the crystal rotation but did affect the texture intensity, spread and symmetry.

Modeling texture evolution during monotonic loading of Zn-Cu-Ti alloy sheet using the viscoplastic self-consistent polycrystal model

The aim of the present work is to simulate the macroscopic, anisotropic mechanical response and texture evolution of Zn-Cu-Ti alloy sheet under uniaxial tension and simple shear taking into account the grain fragmentation process due to continuous dynamic recrystallization (CDRX). The Visco-Plastic Self-Consistent (VPSC) model is applied using the affine linearization procedure, and the effect of CDRX on texture evolution is mimicked by empirically enforcing the continuity of the lattice rotation field between pairs of orientations randomly chosen. The proposed model is validated by tensile and shear tests at different loading directions; specimens were cut at 0°, 45°, and 90° with respect to the rolling direction. We show that the mechanical response and the texture evolution are adequately reproduced taking into account the effect of CDRX on the crystallographic orientations. In particular, the typical splitting of the basal poles predicted by VPSC simulations without the recrystallization effect when tensile loading is aligned to the transverse direction is avoided, in agreement with the experimental evidence. The proposed mechanics of short-range interaction can effectively mimic, in a very simple way, the effects of CDRX on the texture evolution of Zn-Cu-Ti alloy sheet under monotonic loadings.

Viscoplastic Self-consistent Modeling of the Through-Thickness Texture of a Hot-Rolled Al-Mg-Si Plate

The through-thickness texture of an industrial hot-rolled Al-Mg-Si alloy plate is investigated both experimentally and numerically. The texture has been determined continuously from the plate center to the surface with large-scale electron backscatter diffraction scans. In accordance with literature results, a stable cube component and a strong brass component were found in the center, while the rotated cube component dominates the texture outside of the center region. A viscoplastic self-consistent polycrystal model including non-octahedral slip and grain shape evolution is shown to provide very good numerical predictions of the hot rolling texture. It captures the stability of the cube component and the gradients of the shear and brass component. However, it overestimates the intensity of the rotated cube component and wrongly predicts a stable goss component across the plate thickness. The calculation of deformation histories, which serve as boundary conditions for the polycrystal model, is presented and discussed.

Viscoplastic self-consistent polycrystal modeling of texture evolution of ultra-low carbon steel during cold rolling

The viscoplastic self-consistent (VPSC) polycrystal model, where each grain is regarded as an ellipsoidal inclusion interacting with a homogeneous effective medium represented by the polycrystal has long been successful in explaining the mechanical response and crystallographic texture development during plastic deformation. VPSC has especially been used to model low-symmetry materials such as Mg-alloys, uranium, etc, which could not be addressed by the conventional Taylor model. Although there are several reports on the modeling of steel that successfully reproduce its measured crystallographic texture at specific reductions, few studies have been carried out to reproduce the evolution of the intensity of texture fibers at various rolling reductions. In this study the texture evolution of body-centered-cubic ultra-low carbon steel during cold rolling was calculated using the VPSC model and compared with textures measured at 40%, 60%, 70%, 80% and 90% reduction. The deformation by cold rolling was accommodated by and slip systems interacting via a Voce hardening law. Addressing a wide range of rolling reductions poses a more severe test on the modeling. It is found that accounting for grain shape, grain interaction with the surroundings, and their evolution with strain, is critical for explaining the experimentally observed evolution of texture intensities. Specifically, the mechanisms of grain-neighbor co-rotation and the role played by the relative plastic stiffness of grain and surrounding medium were explored in this work. The predicted evolution of the main texture components, namely, α fiber (RD//) and γ fiber (ND//) was compared with experimental data measured by x-ray Schultz method, resulting in that the calculated texture evolution using the above models captures well the experimental results which show a gentle ODF intensity increase in the γ fiber and a strong ODF increase near components in the α fiber during cold rolling.

A new visco-plastic self-consistent formulation implicit in dislocation-based hardening within implicit finite elements: Application to high strain rate and impact deformation of tantalum

Modeling deformation processes of materials under high strain rate and impact conditions in which the strain rates vary spatiotemporally over several orders of magnitude is challenging, especially in terms of constitutive description. Visco-plastic power-law flow rule, commonly used within crystal plasticity constitutive models, usually introduces superfluous strain rate effects, entering numerically via the slip activation criterion, which result in artificially high flow stress predictions under high strain rate deformation conditions. This paper presents a novel, implicit finite element implementation of a visco-plastic self-consistent polycrystal model that is implicit in dislocation-based hardening with removed strain rate sensitivity introduced by the power-law flow rule. In the model, the strain rate dependence of the flow stress is defined solely by the rate sensitivity of Peierls stress and the evolution of dislocation density within the hardening law, enabling the prediction of high strain rate and impact deformation. As a result, the predicted flow stress is accurate in its magnitude. The physically based strain rate and temperature sensitive model also features, in addition to Schmid, the non-Schmid activation contribution for slip, which is necessary for understanding and modeling the plastic deformation of body-centered cubic metals. The model is calibrated to simulate the strain rate- and temperature-sensitive monotonic deformation of tantalum and is subsequently applied to a Taylor impact test of the same material. Since the impact simulation required remeshing and interpolation of state variables, the spherical linear interpolation algorithm in the space of quaternions is implemented to facilitate the interpolation of texture. Predictions of the simulation were found to compare favorably with experimental measurements of post-test geometrical changes and texture evolution. The implementation and insights from these predictions are presented and discussed in the paper.

Multiscale modelling of the response of Ti-6AI-4V sheets under explosive loading

The objectives of the current study are to develop a multiscale numerical modelling method to predict the plastic deformation of Ti-6Al-4V sheets under blast loading, validate the method with experiments and characterise, at room temperature, the impulsive mechanical behaviour of the alloy. The numerical modelling technique relates the microstructure of the alloy with its macroscopic behaviour taking into account anisotropic effects by combining the viscoplastic self-consistent polycrystal model (VPSC7c) with the Cazacu–Barlat orthotropic yield criterion (CPB06) as implemented in the finite element (FE) solver of LS-DYNA. Sheet specimens of two thicknesses are tested using an experimental setup which applies a planar blast load. High speed cameras and the digital image correlation (DIC) technique are used to measure the evolving strains in the specimens. In addition, an analytical model is used to calculate the maximum displacements. The obtained values are compared with the outcome of the tests and FE simulations.

Implementation of VPSC polycrystal model into rigid plastic finite element method and its application to Erichsen test of Mg alloy

A methodology on the multiscale simulation of metal forming processes is presented, which fully integrates the visco-plastic self-consistent (VPSC) polycrystal model into rigid plastic finite element method (FEM). To accurately predict the material behavior of a magnesium alloy from the microstructural level, the VPSC crystal plasticity model was used as a constitutive equation in this methodology. An optimization program VPSC-GA was developed in order to calculate the hardening parameters for each slip and twin mode of a single crystal from a couple of simple tension/compression tests. The existing constitutive equation for rigid plastic FEM is modified using the deviatoric stress components and the derivatives of them with respect to strain rate components. The stiffness matrix and the load vector were derived based on a new approach and implemented into DEFORMTM-3D via a user subroutine which handles stiffness matrix in elemental level. An application to the Erichsen tests of magnesium alloys was done and the stretch formability of two different Mg alloy sheets was analyzed using the results of both experiment and simulation.

Simulation of microtexture developments in the stir zone of friction stir-welded AZ31 Mg alloys

The evolution of the microtexture in the stir-zone (SZ) portion of AZ31 Mg alloys during friction stir welding (FSW) was investigated via microtexture analysis and polycrystal modeling. The microtexture distribution in as-welded specimens was characterized using electron backscatter diffraction (EBSD). EBSD analysis revealed that the FSW process induced the development of strong fiber textures in the SZ portion, and that the texture development was strongly dependent on the moving path of the material point with respect to the rotating pin. Three dimensional (3D) finite element analysis (FEA) was conducted to extract the thermo-mechanical history of the SZ portion of an AZ31 Mg alloy during the FSW process. In order to simulate the microtexture evolution in the SZ portion during the FSW process, the present study combined a visco-plastic self-consistent (VPSC) polycrystal model in which a dynamic recrystallization (DRX) scheme was implemented and 3D FEA. The thermo-mechanical history was gathered at a particular material point using 3D FEA and the unified microscopic hardening parameters were fitted with a Zener-Hollomon parameter and used as input data for the VPSC polycrystal model. The VPSC polycrystal model successfully predicted the development of strong and heterogeneous fiber textures in the SZ portion of a sample of AZ31 Mg alloy during the FSW process.

Modelling the plastic deformation of Ti6Al4V under dynamic loading

In this paper, a multiscale numerical method is presented with the aim to model the response of a Ti6Al4V sheet under explosive forming. The numerical modelling focuses on the accurate definition of the plastic deformation of the Ti6Al4V specimens based on the texture of the material. The viscoplastic self-consistent polycrystal model code (VPSC) is used as a link between macroscopic response and the underlying microstructure taking into account the viscoplastic deformation of the specimen. Comparison is made with experimental results. The Cazacu–Barlat (CB06) material model is used because of its capability to describe the yielding asymmetry between tension and compression and to take into account the anisotropic behaviour of the sheet. The study focuses on the evaluation of the material model parameters and on how these affect the structural response of the Ti6Al4V specimens under explosive loading.This paper is part of a Themed Issue on Euromech 570: Interface-dominated materials.

Examining the microtexture evolution in a hole-edge punched into 780 MPa grade hot-rolled steel

The deformation behavior in the hole-edge of 780MPa grade hot-rolled steel during the punching process was investigated via microstructure characterization and computational simulation. Microstructure characterization was conducted to observe the edges of punched holes through the thickness direction, and electron back-scattered diffraction (EBSD) was used to analyze the heterogeneity of the deformation. Finite element analysis (FEA) that could account for a ductile fracture criterion was conducted to simulate the deformation and fracture behaviors of 780MPa grade hot-rolled steel during the punching process. Calculation of rotation rate fields at the edges of the punched holes during the punching process revealed that metastable orientations in Euler space were confined to specific orientation groups. Rotation-rate fields effectively explained the stability of the initial texture components in the hole-edge region during the punching process. A visco-plastic self-consistent (VPSC) polycrystal model was used to calculate the microtexture evolution in the hole-edge region during the punching process. FEA revealed that the heterogeneous effective strain was closely related to the heterogeneity of the Kernel average misorientation (KAM) distribution in the hole-edge region. A simulation of the deformation microtexture evolution in the hole-edge region using a VPSC model was in good agreement with the experimental results.

A multiscale simulation framework of the accumulative roll bonding process accounting for texture evolution

The accumulative roll bonding process is one of the most prominent severe plastic deformation processes for obtaining sheet materials with ultra-fine-grained microstructures and high strength. The properties of such sheets differ significantly from those of conventionally rolled sheets. It is hence desirable to have a simulation framework that can accurately predict the material properties, including the evolving texture and anisotropy during processing. Here, we propose such a framework for multiple pass rolling using explicit finite elements and embedding the visco-plastic self-consistent (VPSC) polycrystal texture model for the material response. To facilitate multiple pass rolling, we propose a novel solution mapping scheme that transfers the material state from the deformed finite element mesh to a new one. Additionally, we implement a two-level parallelization scheme – with decomposition of the FE domain using message passing interface (MPI) and thread based parallelization of the material response using openMP – to ensure reduced simulation times. The predictive capabilities of the proposed framework are demonstrated by simulating the accumulative roll bonding of aluminum alloy AA5754 sheets. The simulations validate the working of the solution mapping scheme, and clearly show the development of a through thickness gradient of texture and anisotropy in the roll-bonded sheet after two passes.

Combined effects of anisotropy and tension–compression asymmetry on the torsional response of AZ31 Mg

In this paper it is demonstrated that only by accounting for the combined effects of anisotropy and tension–compression asymmetry at polycrystal level, it is possible to explain and accurately predict the room-temperature torsional response of a strongly textured AZ31 Mg material. This is shown by using two modeling frameworks, namely: a viscoplastic self-consistent (VPSC) polycrystal model, and a macroscopic plasticity model based on an yield criterion, developed by Cazacu et al. (2006), that accounts for both orthotropy and tension–compression asymmetry in plastic flow. It is shown that unlike Hill’s (1948) criterion, the latter macroscopic criterion quantitatively predicts the experimental results, namely: that the sample with axial direction along the rolling direction contracts, while the sample with axial direction along the normal direction elongates. Moreover, it is demonstrated that these experimentally observed axial strain effects can be quantitatively predicted with the VPSC polycrystal model, only if both slip and twinning are considered operational at single crystal level. On the other hand, if it is assumed that the plastic deformation is fully accommodated by crystallographic slip, the axial strains predicted by VPSC are very close with that predicted with Hill (1948) criterion, which largely underestimates the measured axial strain in the rolling direction, and predicts zero axial strain in the normal direction.

Mechanical responses and deformation mechanisms of an AZ31 Mg alloy sheet under dynamic and simple shear deformations

The mechanical responses and deformation mechanisms of AZ31 Mg alloy sheets were studied under dynamic (tension and compression) and simple shear deformations along different in-plane loading directions. This paper is a continuation of the author’s previous manuscript (Khan et al., 2011) on the quasi-static responses and texture evolution of AZ31 Mg alloy sheets. The strain-hardening rate (dσ/dε) of specimens under in-plane dynamic compression at room temperature showed a strong strain-rate dependency when deformation entered the dynamic region. The electron back-scattered diffraction (EBSD) technique was used to conduct texture analysis on each specimen after simple shear deformation under a quasi-static load (100s−1) at 150°C and after dynamic compression under a strain rate of 1500s−1 at RT and 150°C. Loading direction during simple shear deformation did not significantly affect either the texture evolution or the twinning evolution. Deformation temperature during dynamic compression affected both the texture evolution and the twinning evolution only slightly, but it significantly affected the kernel average misorientation (KAM) distribution in deformed grains. A visco-plastic self-consistent (VPSC) polycrystal model was successfully used to simulate the mechanical responses and the evolution of the initial texture in an AZ31 Mg alloy sheet during simple shear deformation and dynamic compression.

A constitutive model of twin nucleation, propagation and growth in magnesium crystals

A new constitutive model to describe twin nucleation, propagation and growth for magnesium crystals is developed and implemented in the recently developed Elastic Viscoplastic Self-Consistent polycrystal model. The new model explicitly takes into account the stress relaxation associated with twin nucleation. It is demonstrated that the new twinning model is able to capture key macroscopic features associated with twin nucleation, propagation and growth observed experimentally.

Effect of microstructural features on the planar anisotropy of the R-value in Cu-added bake-hardenable steels

Abstract This study was focused on investigating the effect that microstructural features have on the planar anisotropy of the plastic strain ratio ( R -value) in Cu-added bake-hardenable (BH) steel. Ti–Nb-added BH steel was used for a comparison of microstructural features and their effects on the planar anisotropy of an R -value. Quantitative and qualitative analyses of the precipitates for two hot-rolled BH steels were conducted via TEM. An EBSD technique was used to analyze the evolution of the microtexture in consecutive manufacturing processes of hot-rolling, cold-rolling and annealing. Microstructural features in cold-rolled specimens were explained in terms of the type of deformed grains. The stored energy distribution that developed in subgrains was used to explain the relatively high planar anisotropy of the R -value for Cu-added BH steel. A visco-plastic self-consistent (VPSC) polycrystal model was employed to calculate the planar anisotropy of the R -value for annealed BH steels.

Unexpected brass-type texture in rolling of ultrafine-grained copper

Performing large-strain rolling of initially ultrafine-grained copper obtained by eight passes in equal-channel angular pressing, a brass-type – rather than a copper-type – texture was achieved. Clearly, the deformation mechanism is different in ultrafine-grained materials for subsequent rolling. Using the viscoplastic self-consistent polycrystal model, we find that the deformation mechanism is associated with the activation of partial {1 1 1} 〈1 1 −2〉 slip and with a reduced quantity of geometrically necessary dislocations that lead to near Taylor polycrystal deformation conditions in ultrafine-grained copper.

Influence of deformation temperature on texture evolution in HPT deformed NiAl

NiAl is an intermetallic compound with a brittle-to-ductile transition temperature at about 300°C and ambient pressure. At standard conditions, it is very difficult to deform, but fracture stress and fracture strain are increased under high hydrostatic pressure. On account of this, deformation at low temperatures is only possible at high hydrostatic pressure, as for instance used in high pressure torsion. In order to study the influence of temperature on texture evolution, small discs of polycrystalline NiAl were deformed by high pressure torsion at temperatures ranging from room temperature to 500°C. At room temperature, a typical shear texture of body centred cubic metals is found, while at 500°C a strong oblique cube component dominates. These textures can be well simulated with the viscoplastic self-consistent polycrystal deformation model using the primary and secondary slip systems activated at low and high temperatures. The oblique cube component is a dynamic recrystallization component.

A hierarchical multi-scale model for hexagonal materials taking into account texture evolution during forming simulation

Due to the absence of sufficient number of slip systems in hexagonal close packed (hcp) metals to accommodate arbitrary plastic deformation, mechanical twinning occupies an important role in the mechanical behavior of these metals. Twinning causes a significant and abrupt change in the orientation of crystals, whilst simultaneously affecting the hardening and plastic flow behavior of the material considerably. Modeling of forming processes of hexagonal close packed metals thus requires accounting for the evolution of texture and texture induced anisotropy, especially due to twinning. Additionally, the computational framework for the simulation of forming processes must be reliable and efficient in order to guarantee results in realistic time frames. In the present work, a phenomenological constitutive model consisting of an anisotropic yield function, associate flow rule and isotropic hardening, is coupled with the viscoplastic self-consistent polycrystal model in order to capture the slip and twinning activity, texture evolution and the evolving anisotropy during plastic deformation of hcp materials, similar to a hierarchical multi-scale modeling framework proposed by Van Houtte et al. [41] for cubic metals. To account for texture evolution during plastic deformation, the parameters involved in the anisotropic yield function are regularly updated based on mechanical test data obtained from the polycrystal model at the micro-scale. The parameter update is performed at discrete steps instead of every increment. The developed model is applied to describe the behaviors of pure zirconium at liquid nitrogen temperature. The results of the numerical simulations were found to be good agreement with experimental results, and at acceptable computation time.

Reprint of: 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.