Viscoplastic Self-consistent Crystal Plasticity Model Research Articles

Modelling-assisted description of anisotropic edge failure in magnesium sheet alloy under mixed-mode loading

An uncoupled fracture criterion based on a simple damage indicator computed using a mean-field crystal plasticity framework is proposed and applied to predict failure of an AZ31 sheet originating from the edges. The damage indicator quantifies the contribution of strain components along the axes of orthotropy leading to material failure. The model is calibrated by uniaxial tension tests. The damage indicator is validated for various mixed-mode deformation histories realized by modified Arcan tests in various loading configurations. The loading history of respective fracture sites obtained from DIC analyses is directly employed to a visco-plastic self-consistent crystal plasticity model to obtain the stress responses. The results indicate that the damage indicator requires – beside the strain history – an input of stress triaxiality, by which an improved predictive accuracy can be achieved. This effect is quantified for various loading scenarios, in which cracks are initiated near or at the edge of the sample.

Effect of temperature on the selection of deformation modes in Zircaloy-4

The effect of deformation temperature (77, 298 and 573 K) on the evolution of slip and twinning modes in Zircaloy-4 was studied. Samples of Zircaloy-4 were uniaxially compressed to different strains at a nominal strain rate of 10−3 s−1. The compression direction was chosen so as to activate twinning. Microstructural examination was carried out using electron backscatter diffraction to relate the evolution of microstructure and texture to the micro-mechanics and work-hardening behaviour. In conjunction with experiments a visco-plastic self-consistent crystal plasticity model was used to determine the evolution of deformation modes. Extensive twinning was observed at all the test temperatures. Twinning activity at 298 and 573 K was comparable, but was lower than that at 77 K. A strong basal texture parallel to the compressive direction was found at 298 and 573 K. The VPSC model predicted well the texture evolution at 298 and 573 K. The basal texture developed at 77 K was found to have partially reoriented back to the initial texture due to secondary twinning. Prism slip was the dominant deformation mode with secondary slip becoming more active at higher temperatures.

Transition of dynamic recrystallization mechanisms of as-cast AZ31 Mg alloys during hot compression

This study investigates the transition of dynamic recrystallization (DRX) mechanisms of as-cast AZ31 Mg alloys during hot compression. It is experimentally revealed that the transition between the twin-induced dynamic recrystallization (TDRX) and the grain boundary bulging dynamic recrystallization (GBBDRX) depends on the local strain accumulation and grain size. Based on the secondary twinning growth controlled by the grain size and stresses, a theoretical DRX transition criterion is built. Subsequently, two cooperating DRX schemes are implemented into the viscoplastic self-consistent crystal plasticity model to simulate the evolution of slip and twinning activity, textures and stress-strain relationships influenced by the double DRX mechanisms and the transition. The results show: (1) For as-cast Mg alloys with coarse grains, the TDRX is common at low-strain stage, and is the key to continuing plastic deformation. The smaller twin-walled grains that inherit the c-axis orientation of the parent twins can weaken the deformation basal texture, enhancing basal slip activity and reducing the extension twinning activity; (2) The GBBDRX that can decrease local dislocation density replaces the TDRX if the post-saturation state of secondary twinning is achieved by the applied stress together with local stress within refined grains. The dominant GBBDRX mechanism strengthens the basal texture by limiting pyramidal slip. The activities of basal and prismatic slip are reduced and enhanced by the GBBDRX, respectively; (3) The TDRX leads to a dramatic decrease of strain-hardening rate, and the transition between the two successive DRX mechanisms switches the decrease of the hardening rate to flow softening. Furthermore, some control schemes of DRX transition are proposed according to the transition criterion.

A crystal plasticity model for describing the anisotropic hardening behavior of steel sheets during strain-path changes

In the present study, a viscoplastic self-consistent crystal plasticity model (VPSC-RGBV), which accounts for various microstructural features, including the accumulation and annihilation of dislocations due to slip activity and latent hardening originated from interactions between gliding dislocations on different slip planes, is described. The simulation results of the VPSC-RGBV model are compared with those of a macro-mechanical distortional plasticity model, the so-called homogeneous anisotropic hardening (HAH), and experimental data pertaining to metals undergoing complex loading histories. The differences between the simulated and experimental results under non-proportional loading, including 1) the stress-strain curve, 2) instantaneous r-value after strain-path change, and 3) yield surface evolution, are discussed. Finally, potential improvements are suggested for VPSC-RGBV model.

Forming limits of dual phase steels using crystal plasticity in conjunction with MK approach

A viscoplastic self-consistent crystal plasticity model was used to describe the mechanical behavior of two dual phase steel samples DP780 and DP1000. Mechanical anisotropy of these alloys was observed in uniaxial tests conducted along various directions. Additionally, X-ray diffraction was conducted to obtain the averaged crystallographic texture of ferrite and martensite. The hardening parameters were identified by fitting with the flow stress-strain curve obtained from bulge tests. The model-predicted and experimental flow-stress curves and R-values were compared in order to estimate the adequacy of the crystal plasticity model to describe the anisotropic behavior of the dual-phase steel samples. Furthermore, the crystal plasticity model, in conjunction with the Marciniak-Kuczynski approach, was used to predict forming limit diagram. The predictive accuracy was estimated by comparing with the experimental forming limit strains obtained through Nakazima tests. It turned out that several assumptions made in the current study led to somewhat poorer predictive accuracy in comparison with the previous reports, which implies that certain improvements in the model application are required for successful and valid model applications.

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.

Tension-compression asymmetry of a rolled Mg-Y-Nd alloy

In this work, tension and compression deformation behaviors of rolled and aged Mg-Y-Nd alloys were investigated. The microstructure evolution and plastic deformation mechanism during tension and compression were analyzed by combined use of electron backscatter diffraction and a visco-plastic self-consistent crystal plasticity model. The results show that both rolled and aged Mg-Y-Nd sheets show an extremely low yield asymmetry. Elimination of yield asymmetry can be ascribed to the tilted basal texture and suppression of {10-12} twinning. The rolled sheet has almost no yield asymmetry, however exhibits a remarkable strain-hardening behavior asymmetry. Compressed sample shows lower initial strain hardening rate and keeps higher strain hardening rate at the later stage compared with tension. The strain-hardening asymmetry can be aggravated by aging at 280 C. It is considered the limited amount of twins in compression plays the critical role in the strain hardening asymmetry. Finally, the relevant mechanism was analyzed and discussed.

Evolution of microstructure and texture in commercial pure aluminum subjected to high pressure torsion processing

Commercially pure aluminum was chosen as a model face-centered cubic material for a detailed investigation of microstructural and textural evolution during processing by high pressure torsion. Severe grain refinement was observed as the average grain size decreased from ~85μm to ~1.22μm at an equivalent strain of ɛ=99. It is observed that at early stages of deformation an accumulation of dislocations inside grains occurs. More straining results in an increase of misorientation and eventually gives rise to fragmentation of parent grains to new smaller grains. A near saturation of grain refinement is observed after a strain of ɛ=15. Kernel average misorienation maps suggest the occurrence of a weak recovery process at relatively large strains, resulting in annihilation of dislocations inside the grains. The texture results show that a simple shear type texture develops during deformation, although it is a relatively weak texture due to the nature of simple shear strain mode and the occurrence of grain fragmentation. The full constraint Taylor model and the viscoplastic self-consistent crystal plasticity model were employed to reproduce the experimental textures at relatively large strains. It is shown that the Taylor model leads to a better agreement between simulated and experimental data. It is observed that a satisfactory simulation of the texture evolution at severe strain amplitudes cannot be obtained with models that ignore the effect of grain fragmentation.

Texture-based forming limit prediction for Mg sheet alloys ZE10 and AZ31

A viscoplastic self-consistent crystal plasticity model was employed to study the formability of two magnesium sheet alloys, i.e., AZ31 and ZE10 at 200 °C. The flow stress-strain curves obtained by uniaxial tension tests at various strain rates and the crystallographic texture obtained from X-ray diffraction were used to calibrate the model. The crystal plasticity model was incorporated with the Marciniak–Kuczyński model in order to address the forming limits of the magnesium sheets. A good agreement of the model predictions with the experimental data obtained by Nakajima tests was achieved. The model was further studied to quantify the effects of the sample orientation with respect to laboratory axes, the amount of pre-strain applied to the sheet prior to forming, and the initial crystallographic texture. The resulting forming limit diagrams demonstrate the optimal choice of sample orientation and crystallographic texture that can lead to a significant improvement in forming limit strains.

A Microstructure-Sensitive Model for Simulating the Impact Response of a High-Manganese Austenitic Steel

Microstructurally informed macroscopic impact response of a high-manganese austenitic steel was modeled through incorporation of the viscoplastic self-consistent (VPSC) crystal plasticity model into the ansys ls-dyna nonlinear explicit finite-element (FE) frame. Voce hardening flow rule, capable of modeling plastic anisotropy in microstructures, was utilized in the VPSC crystal plasticity model to predict the micromechanical response of the material, which was calibrated based on experimentally measured quasi-static uniaxial tensile deformation response and initially measured textures. Specifically, hiring calibrated Voce parameters in VPSC, a modified material response was predicted employing local velocity gradient tensors obtained from the initial FE analyses as a new boundary condition for loading state. The updated micromechanical response of the material was then integrated into the macroscale material model by calibrating the Johnson–Cook (JC) constitutive relationship and the corresponding damage parameters. Consequently, we demonstrate the role of geometrically necessary multi-axial stress state for proper modeling of the impact response of polycrystalline metals and validate the presented approach by experimentally and numerically analyzing the deformation response of the Hadfield steel (HS) under impact loading.

Mechanical behavior and texture prediction of Ti-6Al-4V based on elastic viscoplastic self-consistent modelling

The goal of this study is to apply an elastic viscoplastic self-consistent crystal plasticity model to predict the texture evolution in a Ti-6Al-4V alloy which has a (mainly) hexagonal crystal structure. The model under consideration is an extension of the viscoplastic self-consistent model proposed by Lebensohn and Tome [1993] which has been adapted to account for elasticity and has been integrated with a new algorithm, making it more computationally efficient within an implicit FE scheme. The flow behavior of Ti-6Al-4V is strongly dependent on strain rate and temperature. To estimate the model parameters, the flow behavior of quasi-static experiments is used. A temperature sensitivity term has been introduced to correct the effects of temperature increase during the dynamic experiments. In order to have a meaningful rate sensitivity exponent, a value is calculated based on valid experimental data, rather than choosing an arbitrary large numerical value. In this way the behavior of Ti-6Al-4V is captured at different strain rates. Predictions of the model are compared to experimental data.

Modelling the plastic anisotropy of aluminum alloy 3103 sheets by polycrystal plasticity

The plastic anisotropy of AA3103 sheets in the cold-rolled condition (H18 temper) and in the fully annealed condition (O temper) was studied experimentally and numerically in this work. The microstructure and texture of the two materials were characterized and the anisotropic plastic behaviour was measured by in-plane uniaxial tension tests along every 15° from the rolling direction to the transverse direction of the sheet. Five polycrystal plasticity models, namely the full-constraint Taylor model, the Alamel model, the Alamel type III model, the visco-plastic self-consistent crystal plasticity model and the crystal plasticity finite element method (CPFEM), were employed to predict the plastic anisotropy in the plane of the sheet. Experimentally observed grain shapes were taken into consideration. In addition, a hybrid modelling method was employed where the advanced yield function Yld2004-18p was calibrated to stress points provided by CPFEM simulations along 89 in-plane strain-paths. This provided a close approximation to in-plane CPFEM predictions and is one convenient way to include the influence of realistic grain morphology on the plastic anisotropy. Based on comparisons between the experimental and the predicted results, the hybrid modelling method is considered as the most accurate way of describing the plastic anisotropy. The Alamel type III and Alamel models are also recommended as accurate and time-efficient models for predicting the plastic anisotropy of the AA3103 sheets in H18 and O tempers.

Crystal-Plasticity Simulation of the Evolution of the Matt Surface in Pack Rolling of Aluminium Foil

Aluminium foil is rolled double-layered during the final rolling pass. When the sheets are later separated, the inside surface is dull and the outside surface is shiny. The matt inner side is characterized by significant surface corrugations which are believed to be a precursor for the initiation of fracture upon a subsequent forming operation. Therefore, understanding of the development of the matt side of Al foil will help to control and, eventually, improve the properties of Al foil. It was the goal of the present study to correlate the development of the matt side with the spatial arrangement of the crystallographic orientations of the foil rolling texture. This approach builds on a recent project to correlate the phenomenon of roping in AA 6xxx alloy sheet for car body applications to the occurrence of band-like clusters of grains with similar crystallographic orientation. Large-scale orientation maps obtained by electron back-scattered diffraction (EBSD) were input into a visco-plastic self-consistent crystal-plasticity model to analyse the strain anisotropy caused by the spatial distribution of the various rolling texture components. The new model is applied to several Al foils with different characteristics of the matt side.

Crystal plasticity analysis of constitutive behavior of 5754 aluminum sheet deformed along bi-linear strain paths

Sheet specimens of aluminum alloy 5754 were deformed along a series of bi-linear, equal-biaxial and uniaxial, strain paths while simultaneously measuring stress–strain behavior. The Visco-Plastic Self-Consistent crystal plasticity model, which incorporates texture evolution, was used to simulate the flow stress and hardening behavior based in part on the measured crystallographic texture before deformation. The predicted crystallographic texture qualitatively captures the texture measured in the experiments. Including latent hardening of multiple slip planes allowed the model to explain the decrease in flow stress when changing from equal-biaxial to uniaxial deformation. However, the model captures neither the details of the drop in flow stress nor the magnitude of the plastic hardening after the change in deformation mode. This is likely due to room temperature recovery between the two segments of testing.

Analysis of Slip Behavior in a Single Shear Lap Lead-Free Solder Joint During Simple Shear at 25°C and 0.1/s

The relative activity of the potential slip systems in Sn is examined by comparing an experiment of a single shear lap deformation with simulations using the viscoplastic self-consistent crystal plasticity model developed by Lebensohn and Tome. In a single shear lap specimen made using eutectic Sn-Ag solder on copper pull tabs, the initially polished side was characterized using orientation mapping before and after 0.8 shear deformation at 25°C at a shear strain rate of 0.1/s. The critical resolved shear stress of potential slip systems and the rate sensitivity was altered by trial and error until good agreement between experimentally observed and computed texture was obtained. This result indicated that slip on {101) and {211) planes is much more difficult to activate than on other slip systems for the grain orientations present in this sample. This particular sample showed much activity on the {010)〈101] slip system, but the activation of this slip system may be related to the initial dominant orientation in the specimen. This result is compared with literature and related experiments on ball grid arrays in a companion paper in this volume that show similar trends. As lead-free solder joints are commonly single crystals or multicrystals, this particular result is not indicative of lead-free solder joints as a whole, but must be interpreted in the context of a larger data set.