Elastic Viscoplastic Self-consistent Research Articles

Evaluation of elastic–viscoplastic self-consistent polycrystal plasticity models for zirconium alloys

Our elastic viscoplastic self-consistent (EVPSC) model is improved by including thermal strain to allow study of the behavior of a Zircaloy-2 slab under moderately large strains. The approach of introducing thermal strain effect is similar to the one developed by Turner et al. (1995) and used by Xu et al. (2008a). Various self-consistent schemes (SCSs) of the EVPSC model are then evaluated in terms of the deformation behavior of the material under different uniaxial strain paths. The material parameters for the various models are determined by fitting experimental data from uniaxial tension and compression tests along the normal direction (ND) and from uniaxial tension tests along the rolling direction (RD). The quality of the various SCS predictions is assessed based on comparisons of macroscopic deformation behavior (stress–strain curves and R-values) and microscopic mechanical response (the evolution of lattice strains and texture coefficients) between the predicted and experimental data. It is revealed that the Affine and Meff=0.1 self-consistent models give much better performance than the Secant and Tangent models.

Stress and strain relaxation in magnesium AZ31 rolled plate: In-situ neutron measurement and elastic viscoplastic polycrystal modeling

Continuous mechanical tests with strain holds (stress relaxation) and with stress holds (strain relaxation) are performed simultaneously with in-situ neutron measurements to analyze the mechanisms of stress and strain relaxation in Mg AZ31 rolled plate. A dislocation activity based constitutive model, accounting for internal stress statistical distributions, is proposed and implemented into an elastic viscoplastic self-consistent (EVPSC) framework to simultaneously describe both stress and strain relaxation. The model captures the experimental data in terms of macroscopic stress strain curves, evolution of stress and strain during holding, as well as evolution of the internal elastic strains. Model results indicate that the magnitude of the stress relaxed during strain holding is dependent on both, the magnitude of the flow stress and the spread of the resolved shear stress distribution. The magnitude of strain accumulated during stress holding is, on the other hand, dependent on the magnitude of the hardening rate and on the spread of the resolved shear stress distribution. The internal elastic strains are directly correlated with the stress state, and hence the stress relaxation during strain holds has a greater influence on the lattice strains than strain relaxation during stress holds.

Mechanical behaviors of irradiated FCC polycrystals with nanotwins

In this paper, a theoretical model is proposed to characterize the mechanical behaviors of irradiated face-centered-cubic (FCC) polycrystals with nanotwins. At the grain level, the spatial-dependent interactions among twin boundaries (TBs), irradiation-induced defects and dislocations are considered in the crystal plasticity model. At the polycrystal level, the elastic-viscoplastic self-consistent (EVPSC) method is applied to bridge the property of microscopic individual grains to macroscopic mechanical behaviors of polycrystals with nanotwins. Applications of the proposed model to nanotwinned (nt) copper show that the numerical results match well with corresponding experimental data. It is found that: without irradiation, the mechanical properties of nt metals are closely related to the loading direction with respect to the TBs and the width of twin spacing. There exists a critical twin spacing for nt polycrystals: above which, the impediment of slip dislocations due to TBs leads to the hardening mechanism; below which, the slip of partial dislocations along the TB planes becomes dominant and leads to the softening mechanism. With irradiation, the irradiation-induced defects acting as obstacles could impede the movement of dislocations, which leads to irradiation hardening. However, TBs can effectively absorb irradiation-induced defects and reduce the defect density. Therefore, the irradiation hardening effect may be weakened due to the effects of TBs. The proposed model may offer an effective theoretical method to study the mechanical behaviors of irradiated polycrystals with nanotwins.

Analysis of Reversed Torsion of FCC Metals Using Polycrystal Plasticity Models

Large strain behavior of FCC polycrystals during reversed torsion are investigated through the special purpose finite element based on the classical Taylor model and the elastic-viscoplastic self-consistent (EVPSC) model with various Self-Consistent Schemes (SCSs). It is found that the response of both the fixed-end and free-end torsion is very sensitive to the constitutive models. The models are assessed through comparing their predictions to the corresponding experiments in terms of the stress and strain curves, the Swift effect and texture evolution. It is demonstrated that none of the models examined can precisely predict all the experimental results. However, more careful observation reveals that, among the models considered, the tangent model gives the worst overall performance. It is also demonstrated that the intensity of residual texture during reverse twisting is dependent on the amounts of pre-shear strain during forward twisting and the model used.

Numerical study of the large strain behavior of extruded magnesium alloy AM30 tube by elastic viscoplastic self-consistent model

Abstract The anisotropic mechanical behaviors of the newly developed magnesium alloy AM30 are modeled by the elastic viscoplastic self-consistent (EVPSC) model. This is the first time to numerically study the mechanical behavior of AM30 based on EVPSC model. Three tests of uniaxial tension and compression along extrusion direction (ED) and ring hoop tension at temperature of 200 °C and strain rate of 0.1 s −1 are studied. It is found that extension twinning is an important deformation mechanism under both uniaxial compression along extrusion direction and ring hoop tension test. However the initial texture of the extruded AM30 tubes results in significantly different activities for these two tests. The twin volume fraction of extension twinning under ring hoop tension is less than that under uniaxial compression along extrusion direction. Numerical results are in good agreement with corresponding experimental results.

On twinning and anisotropy in rolled Mg alloy AZ31 under uniaxial compression

The mechanical anisotropy of hot-rolled Mg alloy AZ31 is investigated both experimentally and numerically. First, five different specimen orientations with tilt angles of α=0°, 30°, 45°, 60° and 90° between the normal direction and longitudinal specimen axis are used to experimentally study the mechanical anisotropy under uniaxial compression. Then, the Elastic Visco-Plastic Self-Consistent (EVPSC) model, with the recently developed Twinning and De-Twinning (TDT) description, is applied to simulate the uniaxial compression tests. It is demonstrated that accounting for the initial texture and calibrating the EVPSC-TDT model using in-plane uniaxial tension and compression along the rolling direction permits prediction of the strength anisotropy and strain hardening behavior along all the five orientations, for cases in which the contribution of twinning is dominated, negligible and intermediate.

Study of Lattice Strain Evolution in Stainless Steel Under Tension: The Role of Self‐Consistent Plasticity Model

The recently developed large strain elastic visco‐plastic self‐consistent (EVPSC) model, with various popular self‐consistent schemes including the Affine, Meff, Secant, and Tangent, is used to study the lattice strain evolution in a stainless steel under uniaxial tension. The material parameters for the various self‐consistent schemes are fitted to experimental stress and strain curve under uniaxial tension. An assessment of the predictive capability of the self‐consistent schemes is performed based on comparisons of the predicted lattice strain evolutions and in situ neutron diffraction measurements done on the same material. It is found that, among the self‐consistent schemes examined, the self‐consistent schemes with grain interaction stiffness halfway between those of the limiting Secant (stiff) and Tangent (compliant) approximations give the best results.

Numerical study of the effects of shear deformation and superimposed hydrostatic pressure on the formability of AZ31B sheet at room temperature

The effect of the shear deformation and the superimposed hydrostatic pressure on the formability of magnesium alloy sheet is simulated in terms of the forming limit diagram (FLD). The model employed is the elastic viscoplastic self-consistent (EVPSC) crystal plasticity model, which accounts for both slip and twinning systems as the deformation mechanisms. The conventional sheets have low formability at room temperature due to the strong basal texture developed by the rolling process. However differential speed rolling process develops relatively weak basal texture by introducing shear deformation. Therefore the formability of the sheets produced by differential speed rolling is enhanced. In terms of the superimposed hydrostatic pressure, it delays the onset of necking and therefore improves the formability of sheets. In addition, the effect of crystal elasticity on the formability of sheets is numerically studied.

Investigation of deformation dynamics in a wrought magnesium alloy

In the present research, the real-time in-situ neutron diffraction measurements under a continuous-loading condition and elastic–viscoplastic self-consistent (EVPSC) polycrystal modeling were employed to study the deformation dynamics and the effect of the deformation history on plastic deformation in a wrought magnesium alloy. The experimental results reveal that pre-deformation delays the activation of the tensile twinning during the subsequent compression, mainly resulting from the residual strains. Detwinning does not occur until the applied stress exceeds the tensile yield strength during the reverse loading. It is believed that the grain rotation plays an important role in the elastic region during the reverse loading. The EVPSC model, which has been recently updated by implementing the twinning and detwinning model, was employed to characterize the deformation mechanism during the strain-path changes. The simulation result predicts well the experimental observation from the real-time in-situ neutron diffraction measurements. The present study provides a new insight of the nature of deformation mechanisms in a hexagonal close-packed (HCP) structured polycrystalline wrought magnesium alloy, which has significant implications for future work on studying the deformation mechanisms of HCP-structured materials.

Deformation behavior of solid-solution-strengthened Mg–9 wt.% Al alloy: In situ neutron diffraction and elastic–viscoplastic self-consistent modeling

In situ neutron diffraction and elastic–viscoplastic self-consistent (EVPSC) modeling have been employed to understand the deformation mechanisms of the loading–unloading process under uniaxial tension in a solid-solution-strengthened extruded Mg–9 wt.% Al alloy. The initial texture measured by neutron diffraction shows that the {00.2} basal planes in most grains are tilted around 20–30° from the extrusion axis, indicating that basal slip should be easily activated in a majority of grains under tension. Non-linear stress–strain responses are observed during unloading and reloading after the material is fully plastically deformed under tension. In situ neutron diffraction measurements have also demonstrated the non-linear behavior of lattice strains during unloading and reloading, revealing that load redistribution continuously occurs between soft and hard grain orientations. The predicted macroscopic stress–strain curve and the lattice strain evolution by the EVPSC model are in good agreement with the experimental data. The EVPSC model provides the relative activities of the available slip and twinning modes, as well as the elastic and plastic strains of the various grain families. It is suggested that the non-linear phenomena in the macroscopic stress–strain responses and microscopic lattice strains during unloading and reloading are due to plastic deformation by the operation of basal 〈a〉 slip in the soft grain orientations (e.g. {10.1}, {11.2} and {10.2} grain families).

Modeling inelastic behavior of magnesium alloys during cyclic loading–unloading

The inelastic behavior presenting in magnesium alloys during cyclic loading–unloading have been investigated through the finite strain elastic viscoplastic self-consistent (EVPSC) model for polycrystals (EVPSC-TDT), which has been updated by implementing the twinning and de-twinning (TDT) model. Corresponding to the existing experiments of extruded bars of Mg alloys, we constructed the extruded bars of magnesium alloys with different initial textures in our simulations to study the effects of initial textures and deformation processes (tension and compression) on inelastic behavior during cyclic loading and unloading. Taking the advantage of numerical modeling, the evolution of the instantaneous gradients, the activity of the deformation mechanisms and the evolution of twin volume fraction are characterized to interpret the inelastic behavior. We found that the alternation of deformation mechanisms corresponds to the inelastic behavior; in particular, the inelastic behavior becomes more pronounced when twinning and de-twinning are activated. Thus, a strong extrusion texture reduces the hysteresis loops of the loading–unloading cycle under uniaxial tension, while magnifies the inelastic behavior under uniaxial compression, because twinning and de-twinning are more active for extrude bars with the strong extrusion texture under compression. The simulated results are in agreement with the available experimental observations.

Studying the effect of stress relaxation and creep on lattice strain evolution of stainless steel under tension

Due to relatively long associated count times, in situ strain measurements using neutron diffraction requires periodic interruption of the test to collect the diffraction data by holding either the stress or the strain constant. As a consequence, stress relaxation or strain creep induced by the interrupts is inevitable, especially at loads which are close to the flow stress of the material. An in situ neutron diffraction technique, which consists in performing the diffraction measurements using continuous event-mode data collection while conducting the mechanical loading monotonically with a very slow loading rate, is proposed here to avoid the effects associated with interrupts. The lattice strains in stainless steel under uniaxial tension are measured using the three techniques, and the experimental results are compared to study the effect of stress relaxation and strain creep on the lattice strain measurements. The experimental results are simulated using both the elastic viscoplastic self-consistent (EVPSC) model and the elastic plastic self-consistent (EPSC) model. Both the EVPSC and EPSC models give reasonable predictions for all the three tests, with EVPSC having the added advantage over EPSC that it allows us to address the relaxation and creep effects in the interrupted tests.

ON THE LARGE STRAIN TORSION OF HCP POLYCRYSTALS

The large strain torsion of polycrystalline materials with the hexagonal close packed (HCP) crystallographic structure is numerically studied by using a special purpose finite element. All simulations are based on the recently developed large strain elastic visco-plastic self-consistent (EVPSC) model for polycrystalline materials. For the first time, the effect of twinning on the large strain torsion is assessed in the present study. It is found that the response of the large strain torsion of HCP polycrystals is very sensitive to the initial texture and texture evolution. Numerical results indicate that excluding texture evolution dramatically reduces the development of the second-order axial strain under free-end torsion, or the axial force under fixed-end torsion. It is also numerically demonstrated that twinning has a significant influence on the large strain torsion of HCP polycrystals. For the magnesium alloy AZ31 extruded bar, the predicted results are in good qualitative agreement with experimental observations.

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 lattice strains in magnesium alloy AZ31 based on a large strain elastic-viscoplastic self-consistent polycrystal model

The recently developed large strain elastic visco-plastic self-consistent (EVPSC) model, which incorporates both slip and twinning deformation mechanisms, is used to study the lattice strain evolution in extruded magnesium alloy AZ31 under uniaxial tension and compression. The results are compared against in-situ neutron diffraction measurements done on the same alloy. For the first time, the effects of stress relaxation and strain creep on lattice strain measurements in respectively displacement controlled and load controlled in-situ tests are numerically assessed. It is found that the stress relaxation has a significant effect on the lattice strain measurements. It is also observed that although the creep does not significantly affect the trend of the lattice strain evolution, a better agreement with the experiments is found if creep is included in the simulations.

On crystal plasticity formability analysis for magnesium alloy sheets

Sheet metal formability is assessed in terms of the Forming Limit Diagram (FLD) for magnesium alloys with Hexagonal Close Packed (HCP) crystallographic structure. All simulations are based on the recently developed elastic–visco-plastic self-consistent (EVPSC) model and the classical Taylor model, in conjunction with the M–K approach. The role of crystal plasticity models and the effects of basal texture on formability of magnesium alloy AZ31B sheet are studied numerically. It is observed that formability in HCP polycrystalline materials is very sensitive to the intensity of the basal texture. The path-dependency of formability is examined based on different non-proportional loading histories, which are combinations of two linear strain paths. It is found that while the FLD in strain space is very sensitive to strain path changes, the Forming Limit Stress Diagram (FLSD) in stress space is much less path-dependent. It is suggested that the FLSD is much more favourable than the FLD in representing forming limits in the numerical simulation of sheet metal forming processes. The numerical results are found to be in good qualitative agreement with experimental observations.

Effects of basal texture on mechanical behaviour of magnesium alloy AZ31B sheet

The effect of the basal texture on the mechanical behaviour of AZ31B magnesium alloy sheet is studied numerically using a recently developed Elastic Visco-Plastic Self-consistent (EVPSC) model, in which both slip and twinning contribute to plastic deformation. We simulate uniaxial tension within the sheet plane using starting textures having the basal poles tilted at varying degrees from the normal direction. It is found that increasing the tilt angle increases the uniform strain, but decreases the 0.2% proof strength and the R-value. The effect of texture on sheet metal forming is further assessed by calculating the limit strain under in-plane plane strain tension. It is demonstrated that the limit strain increases dramatically with decreasing intensity of the basal texture. The numerical results are found to be in good qualitative agreement with experimental observations.

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

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

Creep-fatigue crack propagation behavior in a surface cracked plate: Nonaka, I. Kitagawa, M., Kaneko, H., Sato, T., Sato, T., Watashi, K. and Asada, Y. Nucl Eng Des (Mar. 1993) 139 (3), 293–298

Sheet metal formability is assessed in terms of the Forming Limit Diagram (FLD) for magnesium alloys with Hexagonal Close Packed (HCP) crystallographic structure. All simulations are based on the recently developed elastic–visco-plastic self-consistent (EVPSC) model and the classical Taylor model, in conjunction with the M–K approach. The role of crystal plasticity models and the effects of basal texture on formability of magnesium alloy AZ31B sheet are studied numerically. It is observed that formability in HCP polycrystalline materials is very sensitive to the intensity of the basal texture. The path-dependency of formability is examined based on different non-proportional loading histories, which are combinations of two linear strain paths. It is found that while the FLD in strain space is very sensitive to strain path changes, the Forming Limit Stress Diagram (FLSD) in stress space is much less path-dependent. It is suggested that the FLSD is much more favourable than the FLD in representing forming limits in the numerical simulation of sheet metal forming processes. The numerical results are found to be in good qualitative agreement with experimental observations.

The effect of crack wake characteristics on fatigue crack closure. I. A. crack Wave removal study: Mirzaei, M. and Provan, J.W. Theor Appl Fract Mech (Apr. 1993) 18 (3), 179–183

Sheet metal formability is assessed in terms of the Forming Limit Diagram (FLD) for magnesium alloys with Hexagonal Close Packed (HCP) crystallographic structure. All simulations are based on the recently developed elastic–visco-plastic self-consistent (EVPSC) model and the classical Taylor model, in conjunction with the M–K approach. The role of crystal plasticity models and the effects of basal texture on formability of magnesium alloy AZ31B sheet are studied numerically. It is observed that formability in HCP polycrystalline materials is very sensitive to the intensity of the basal texture. The path-dependency of formability is examined based on different non-proportional loading histories, which are combinations of two linear strain paths. It is found that while the FLD in strain space is very sensitive to strain path changes, the Forming Limit Stress Diagram (FLSD) in stress space is much less path-dependent. It is suggested that the FLSD is much more favourable than the FLD in representing forming limits in the numerical simulation of sheet metal forming processes. The numerical results are found to be in good qualitative agreement with experimental observations.