Viscoplastic Self-consistent Model Research Articles

Simulation of cold-rolled 2024 Al alloy thick plate based on visco-plastic self-consistent model

2024 Al has been used in various fields. However, most cold-rolled Al has poor strength and plasticity, so it needs a solution and aging treatment. The rolled reduction has an important influence on microstructure. For different rolled reductions, microstructure has different evolution rules even under the same solution and aging treatment. Therefore, different rolled reduction has a great influence on the subsequent treatment. In this paper, deform simulation analysis technique was used to study the changes of strain of 2024 Al alloy during rolling deformation, and visco-plastic self-consistent was used to study the texture evolution of 2024 Al alloy, which provided a new method for the study of deformation behavior and anisotropy during rolling.

A viscoplastic self-consistent analysis of tensile anisotropy and tension-compression asymmetry in rare-earth magnesium alloy

The anisotropy and tension-compression asymmetry of rare-earth magnesium (Mg-RE) alloys have attracted significant attention. In this study, the room-temperature tensile anisotropy and tension-compression asymmetry of the extruded Mg-8.5Gd-4.5Y-0.8Zn-0.4Zr alloy were investigated utilizing techniques such as optical microscopy (OM), electron backscatter diffraction (EBSD), and viscoplastic self-consistent (VPSC) modeling. Among the tensile samples, the T0 sample (with axis parallel to extrusion direction) exhibits the greatest tensile yield strength (TYS) of 270 MPa and ultimate tensile strength (UTS) of 336 MPa, the T45 sample (with axis inclined at a 45° angle to extrusion direction) and T90 sample (with axis perpendicular to extrusion direction) exhibit lower TYS and UTS. The C0 sample shows a slightly greater compressive yield strength (CYS) of 290 MPa. The ratio of TYS/CYS is approximately 1.07. This study significantly adjusts the VPSC hardening parameters through the Schmid factor of deformation mechanisms in Mg-RE alloy, particularly increasing the τ0 (critical resolved shear stress, CRSS) and τ1 values for basal <a> slip and {10-12} twinning. The ratios of CRSS for other deformation mechanisms to basal <a> slip are approximately as follows: CRSSTwin/CRSSBas = 2, CRSSPri/CRSSBas ≈ 2.7 and CRSSPyr/CRSSBas ≈ 3.3, while these ratios in traditional alloys are generally higher. The stress-strain curves and pole figures obtained from the modified VPSC model demonstrate excellent agreement with experimental results. According to the VPSC simulation results, the primary factor contributing to tensile anisotropy is the disparity in the activation levels of slip systems. The inclusion of rare-earth elements mitigates the tension-compression asymmetry by reducing the difference of CRSS between different deformation mechanisms.

Crystal Plasticity Modeling to Capture Microstructural Variations in Cold-Sprayed Materials

The high-velocity impact of powder particles in cold-spray additively manufactured (CSAM) parts creates intersplat boundaries with regions of high dislocation densities and sub-grain structures. Upon microstructure and mechanical characterization, CSAM Aluminum 6061 showed non-uniformity with spatial variation in the microstructure and mechanical properties, affecting the overall response of the additively manufactured parts. Post-processing treatments are conducted in as-printed samples to improve particle bonding, relieve residual stresses, and improve mechanical properties. In this work, we attempt to implement the effects of grain size and distribution of smaller grains along the intersplat boundaries using the grain size distribution function and powder size information to accurately predict the deformation response of cold-sprayed material using a mean-field viscoplastic self-consistent (VPSC) model. The incorporation of an intersplat boundary term in the VPSC model resulted in a stress–strain response closely matching the experimental findings, preventing the superficially high stresses observed due to Hall–Petch effects from ultra-fine-grain structures. Likewise, the results from the grain analysis showed the combined effects of grain size, orientation, and intersplat mechanisms that captured the stresses experienced and strain accommodated by individual grains.

Accurate simulation of texture evolution and mechanical response of cubic and hexagonal structural alloys using self-consistent polycrystal plastic method

Simulating the evolution of microstructures and the mechanical response of alloys with cubic and hcp structures is crucial for the industrial manufacturing of key alloy components. In this work, a modified Voce (ME-Voce) model is proposed, based on the extended Voce hardening model, to depict the variations of hardening rate with cumulative shear strain. Also, an orientation-dependent weight that describes the neighboring grain-induced ‘drag’ effect is evaluated. These improvements are numerically implemented in a standard viscoplastic self-consistent (VPSC) model. The ME-Voce parameters are determined through multi-parameter optimization using Matlab software. The influences of grain shape and neighboring grains on the hot deformation behavior of alloys are investigated. The proposed ME-Voce model is validated through hot compression experiments of alloys with cubic and hcp structures. The results show the VPSC embedded in the ME-Voce can reasonably predict the mechanical response under different deformation conditions. This enhances the predictive capability of the VPSC model and provides more options for crystal plasticity simulation of alloys with different crystal structures.

Suppressed Plastic Anisotropy via Sigma-Phase Precipitation in CoCrFeMnNi High-Entropy Alloys.

The effect of sigma-phase precipitation on plastic anisotropy of the equiatomic CoCrFeMnNi high-entropy alloy was investigated. Annealing at 700 °C after cold-rolling leads to the formation of the Cr-rich σ phase with a fraction of 2.7%. It is experimentally found that the planar anisotropy (∆r = -0.16) of the CoCrFeMnNi alloy annealed at 700 °C is two times lower than that of the alloy annealed at 800 °C (∆r = -0.35). This observation was further supported by measuring the earing profile of cup specimens after the deep drawing process. The plastic strain ratio, normal anisotropy, and planar anisotropy were also predicted using the visco-plastic self-consistent model. The results indirectly indicated that the reduction of plastic anisotropy in alloy annealed at 700 °C can be attributed to the formation of the σ phase.

Tailoring the formability and planar anisotropy of Al-Mg-Si-Cu-Zn alloys via cross hot rolling and two-stage cold rolling

Al-Mg-Si-(Cu) alloys have shown great potential in responding to the growing demand for automotive lightweight, but the limited formability and high planar anisotropy have always hindered their application. The present study designs a novel method for simultaneously improving the formability and planar anisotropy of Al-Mg-Si-Cu-Zn alloys by coupling cross hot rolling and two-stage cold rolling. The results have shown that the multi-scale distribution of secondary particles and strong Brass{011}<112> and S{123}<634> texture are induced by the designed cross hot rolling process, which weakens the recrystallization texture after solution treatment, especially Cube{001}<100> orientation. Meanwhile, the designed two-stage cold rolling process (intermediate cold rolling process with high reduction + final cold rolling process with low reduction) promotes the precipitation of unstable precipitates (Mg2Si and Q phase), and inhibits the formation of Copper{112}<111> orientation, which further weakens the recrystallization texture and results in the dispersion distribution of recrystallization texture. Accordingly, the formability and planar anisotropy of the Al-Mg-Si-Cu-Zn alloy are simultaneously improved without strength loss by coupling the designed cross hot rolling with two-stage cold rolling, and the influence mechanism of texture on r value has been analyzed by Visco-Plastic Self-Consistent (VPSC) model.

Effects of extrusion die cavity on the texture components and the associated mechanical properties for ZK60 magnesium alloy

This work managed the extrusion strain path by designing various extrusion die cavities, successfully realizing the texture modification for the ZK60 magnesium alloy. The mechanisms involving the texture dependence on the extrusion die cavity as well as their effects on the mechanical properties were emphatically investigated. Results showed that dynamic recrystallization refined the grain size and improved the microstructure homogeneity in the three extrusion specimens, but did not produce too large microstructure differences. By comparison, significant texture differences developed owing to the various extrusion die cavities, which here were mainly reflected in the strong or weak texture components for the c-axes//TD and the c-axes//ND. Such texture differences started from the deformation texture instead of the recrystallization texture whose roles only consisted in dispersing the texture component and reducing the texture intensity. The results from the finite element analysis and the visco-plastic self-consistent model indicated that, in order to accommodate the different strain components induced by the extrusion die cavities, slip systems or tension twinning were activated differently, and this was the critical reason causing the above texture differences. One modified Hall-Petch relationship was adopted to analyze the conjoint effects of grain refinement and texture variation on the yield stress. Additionally, the quantitative results about deformation mechanism activation fractions demonstrated that the texture variations influenced the competition relationships between the twinning induced deformation and the slip dominant deformation, and the former generally produced the lower yield stress and the increasing stage of strain hardening rate, while the latter produced the higher yield stress and the continuous decline of strain hardening rate.

Effects of primary α grains on rolling reductions and deformation modes in Zr alloys: Experiments and modeling

Microstructure and texture evolution of β-quenched Zr-xNb-0.4Mo (x = 0, 0.4, 0.6 and 1.0 wt %) alloys during the cold rolling process were systematically investigated. The Zr-xNb-0.4Mo alloys exhibit the area fractions of the martensitic structure are 33.2%, 69.4%, 100% and 100% with an increase in Nb content. Under the same rolling gap (1.2 mm), the rolling reductions are 24%, 28%, 29.7% and 30%, respectively. To understand the reason for the gradual increase of rolling reductions until approximately 30%, a visco-plastic self-consistent (VPSC) model was employed to predict the texture evolution and relative activity of different deformation modes. The variation of average Schmid factors (SFs) and the variation of the relative activity of different deformation modes before and after cold rolling were calculated and compared. With the increase of Nb content, a similar variation law between the variation of average SF and the variation of relative activity was found. The basal <a> slip in Zr-0.4Nb-0.4Mo alloy is difficult to activate due to the initial texture of Zr-0.4Nb-0.4Mo alloy. Pyramid <c+a> slip can accommodate the strain along the normal direction (ND), which is beneficial to the high plasticity of Zr alloys during cold rolling. By comparing the variation of average SF of pyramid <c+a> slip, it is found that the larger rolling reductions of Zr-0.6Nb-0.4Mo alloy and Zr-1.0Nb-0.4Mo alloys can be attributed to the activation of pyramid <c+a> slip. The existence of primary α grains can decrease the average SF and inhibit the activation of pyramid <c+a> slip. The cold rolling can make the martensite plates crushed and refined, but not to the primary α grains.

Measuring texture-component-dependent stress of CuZn39Pb2 by neutron diffraction

Understanding the micromechanical behavior of polycrystalline material is pivotal for regulating its mechanical performance and widening its application. Taking advantage of its non-destructive nature, the neutron diffraction technique has been widely applied to investigate the micromechanical behaviors, usually at the resolution of grains sharing the same diffraction plane. This work employs a newly developed technic of the texture-component-dependent (TCD) in-situ neutron diffraction method to obtain the full strain/stress tensor of a textured CuZnPb alloy at the resolution of individual crystallographic orientation. The variation of the internal stresses and lattice strains over the grains that share the same diffraction plane has been successfully captured by the TCD method. According to the results of in situ neutron diffraction, Copper ({-1–1–2}<-1–11>) possesses the highest lattice stress while Cube ({010}<100>) and Goss ({110}<001>) bear the lowest stress of 370 MPa. In parallel, the micromechanical response of the texture components is modeled by the elastic visco-plastic self-consistent (EVPSC) model. The simulated results are in reasonable agreement with the corresponding experiments in loading direction, while the lateral stress exhibits some deviation. By crystal plasticity finite element modeling, the deviation is related to the neighbor grain which affect more significantly the lateral stress than the material parameters. The full tensor of stress within the individual crystallographic orientation measured by TCD method gives more insight into the crystal plasticity modeling.

Ductility enhancement by activating non-basal slip in Mg alloys with micro-Mn

The effect of micro-Mn addition on the microstructure and mechanical properties of Mg alloys was analyzed. Electron back scattered diffraction, slip traces analysis, transmission electron microscopy and visco-plastic self-consistent polycrystal constitutive modeling were performed to investigate the deformation mechanisms in the tensile test. The results show that the average grain size of Mg−Mn alloys decreases from 28.30 to 5.10 μm with Mn addition. Furthermore, with the increment of Mn content, the ductility of the as-extruded samples improves from 14.33% to 20.33%, and the yield strength increases from 84 to 180 MPa. The reason for this simultaneous improvement is that the critical resolved shear stress gap between basal slip and non-basal slip decreases from 173 to 115 MPa, which leads to the increase of non-basal slip activity. The adjustment of slip system difference by microalloying elements provides a way to develop Mg alloys with high strength and ductility.

Deformation mechanism of high ductility Mg-Gd-Mn alloy during tensile process

In this research, a high ductility Mg-Gd-Mn magnesium alloy was designed and developed, with an elongation capability surpassing 50%. To gain insights into the underlying mechanism behind the high ductility of the Mg-2Gd-0.5Mn alloy, quasi-in-situ electron backscattered diffraction and two-beam diffraction were conducted. The results reveal that the Mg-Gd-Mn alloy exhibits a distinct rare-earth texture, and the activation of non-basal slip systems is evident from the clear observation of non-basal slip traces during the later stages of deformation. However, the primary deformation mechanisms in Mg-Gd-Mn alloy remain basal <a> slip and {10–12} tensile twinning, and the remarkable ductility observed in Mg-Gd-Mn alloys can be attributed to the softening of non-basal slip modes, which leads to a coordinated deformation between various modes of deformation. To further validate this conclusion, an analysis was conducted using a visco-plastic self-consistent (VPSC) model to investigate the relative activity of basal and non-basal slip in Mg-Gd-Mn alloys. The obtained results align well with experimental observations, providing additional support for the hypothesis.

A Theoretical and Experimental Study of Predicting Forming-Limit Diagrams for Face-Centered Cubic, Body-Centered Cubic and Hexagonal Close-Packed Metals Using the Marciniak–Kuczynski Visco-Plastic Self-consistent Model

A Theoretical and Experimental Study of Predicting Forming-Limit Diagrams for Face-Centered Cubic, Body-Centered Cubic and Hexagonal Close-Packed Metals Using the Marciniak–Kuczynski Visco-Plastic Self-consistent Model

Texture adjustment approach of magnesium alloys via variable strain path calculated by an integrated finite element-viscoplastic self-consistent model

An integrated calculated approach based on weakly coupled finite element (FEM)-viscoplastic self-consistent (VPSC) model was established to simulate the texture evolution during the variable strain path extrusion process of magnesium alloys. The spiral die extrusion (SDE) process with additional circumferential shear deformation was applied to investigate the effect of path control on texture adjustment and verify the accuracy of the model. The results indicated that the additional spiral shear resulting from the overall inclined flow path effectively reduced the intensity of the {0002}//ED fiber texture by suppressing basal slip activation in the core area, while the local shear deformation along the spiral equal channel strain path led to the formation of an inclined {0002}//ND plane texture on the side. Using the modified Hall–Petch relationship, the correlation between texture and yield strength was quantified. Specifically, the weakening of the texture effectively suppressed {10–12} tensile twinning, which compensated for the deficiency of compressive yield strength without significantly sacrificing tensile yield strength, and thus improved the tension-compression asymmetry. Furthermore, the strongly inclined {0002}//ND plane texture inhibited the widespread activation of basal slip during tensile yielding, thereby enhancing the yield strength.

Compression Behavior and Textures of Ti57-Nb43 Alloy at High Temperatures.

The mechanical behavior, microstructures, as well as the crystallographic textures of the Ti57-Nb43 alloy were investigated on cylindrical specimens compressed at high temperatures, in the range of 700-1000 °C, and strain rates between 0.001 and 1.0 s-1. Hardening, followed by softening behaviors, were observed as a function of strain due to the occurrence of dynamic recrystallization/recovery in hot deformation. The modified five-parameter Voce-type equation described well the stress-strain curves, but, for the present alloy, it was also possible with only four parameters. A new two-variables polynomial function was employed on the four parameters that described well the flow curves as a direct function of temperature and strain rate. It permitted the reduction in the number of parameters and had the predictive capacity for the flow stress at any temperature, strain, and strain rate in the investigated range. The crystallographic textures were similar at all temperatures, with an increase in intensity from 900 °C. The textures could be characterized by a double <100> and <111> fiber and a unique component of (001) <110>, the latter inherited from the initial hot-rolling texture. Viscoplastic polycrystal self-consistent deformation modeling reproduced the measured textures showing that dynamic recrystallization did not alter the development of the deformation texture, only increased its intensity.

Study on the Internal Stress and Thermal Anisotropy in Magnesium Alloys Using a Thermal Elastic Viscoplastic Self-Consistent Model.

A thermal elastic viscoplastic self-consistent model is utilized to examine the thermal stress induced by the thermal anisotropy of single crystals during heat treatments. This model considers temperature-dependent elastic constants and critical resolved shear stress associated with thermal dilation. Simulation results demonstrate that under cooling, the elastic lattice strain increases significantly when constrained compared to unconstrained cooling. The deformation mechanism observed under cooling with constraint resembles tension along the constrained direction at room temperature. Polycrystals offer more deformation mechanisms to accommodate thermal anisotropy compared to single crystals, resulting in lower applied stress at the constrained boundary. Among the various observed textures, the maximum amplitude of residual lattice strain follows the following order: rolled > extruded > random. Lower thermal anisotropy in the entire polycrystal structure leads to reduced internal stress. For a single crystal within aggregates, the {00.2} plane experiences tensile lattice strain, while the {10.0} and {11.0} planes undergo compressive lattice strain due to the greater contraction of single crystals along the <c> direction compared to the <a> direction during cooling.

Study on the deformation behavior of AZ31B-O magnesium alloy with the VPSC model

The mechanical anisotropy of the magnesium alloy AZ31B-O was investigated using the Viscoplastic-Self-Consistent (VPSC)-Twinning and Detwinning (TDT) model. The anisotropic behavior of the material under uniaxial strain was studied using five distinct sheet orientations. In order to investigate the mechanical behavior under uniaxial compression, four alternative specimen orientations were employed. The VPSC model with the TDT mechanism was used to simulate the uniaxial tension and compression experiments. For tensile strain, the magnesium alloy samples were mainly regulated by base slip and prismatic slip. In compression of magnesium alloy samples, it was dominated by basal slip and {10–12} twinning. In all compression specimens, the grain c-axes are parallel to the compression axis regardless of the initial orientation. The r-values under different uniaxial strain paths have been also predicted by using the VPSC-TDT model. The negative r-values under uniaxial compression along RD to TD were further explained. The contribution of {10–12} twinning to plastic strain and the extra hardening induced by {10–12} extension twinning were discussed in depth. This study confirms that the extra hardening induced by {10–12} extension twinning will perform an important function when the twin volume fraction reaches a degree of about 50% with the active pyramidal slip at the same time.

Field fluctuations viscoplastic self-consistent crystal plasticity: Applications to predicting texture evolution during deformation and recrystallization of cubic polycrystalline metals

Recent advances pertaining to modeling of grain fragmentation during deformation and recrystallization of polycrystalline metals using viscoplastic self-consistent (VPSC) polycrystal plasticity are combined into a field fluctuations VPSC (FF-VPSC) model. The FF-VPSC model is a higher-order formulation calculating the second moments of lattice rotation rates based on the second moments of stress fields inside grains and resulting intragranular misorientation distributions. The misorientation distributions are used to define a grain fragmentation sub-model for improving predictions of deformation texture evolution and to formulate kinetics sub-models for nucleation as well as to influence the stored energy governing grain growth for the predictions of recrystallization texture evolution. Formation of a copper-like texture in moderately high stacking fault energy (SFE) Cu and a brass-like texture in low SFE brass during rolling to very large strains are successfully predicted using the model. Remarkably, the model also predicts recrystallization textures from the deformation textures of the two metals after adjusting tradeoffs between transition-bands and grain boundary nucleation mechanisms. Additionally, rolling and recrystallization of an interstitial-free steel, tension and recrystallization of AA5182-O, and recrystallization of an additively manufacturing cobalt-based alloy MarM-509 are simulated to predict texture evolution. Through these case studies involving multiple alloys and thermo-mechanical processes we show that, in addition to being predictive with good accuracy, the key advantage of the model lies in its versatility. The FF-VPSC model, simulation results, and insights from the results are presented and discussed in this paper.

Effect of deformation mode on double-peak texture evolution in pre-twinning Mg-3Al-1Zn alloy during high-speed impacting loading

An investigation of the quantitative effect of the deformation process on the deformation mode, texture evolution, and their internal relationship could help control the mechanical properties of targeted materials. In this study, the deformation mechanism and texture evolution of pre-twinning AZ31 magnesium alloy under medium temperature with high-speed impact loading are investigated through electron backscattered diffraction and the coupled simulation of the finite element method and viscoplastic self-consistent models. Basal and < c + a > pyramidal slips are the dominant accommodation modes. The activation of nonbasal slip is promoted, and the number of twins increase with an increase in the impact pressure, leading to a decrease in the relative activity of the basal slip. Based on typical grain rotation statistics, the effects of basal slip, pyramidal <c + a> slip, and extension twins on grain rotation are studied. With an increase in the pressure, the relative activity difference between the basal slip and pyramidal <c + a> glide decreases, which is beneficial for the formation of a double-peak basal texture and the enhancement of the intensity of the double-peak texture. The twin density affects the split angle between the double peaks.

Internal Elastic Strains of AZ31B Plate during Unloading at Twinning-Active Region

Magnesium alloys, being the lightest structural metals, have garnered significant attention in various fields. The characterization of inelastic behavior has been extensively investigated by researchers due to its impact on structural component performance. However, the occurrence of twinning in the absence of any applied driving force during unloading has lacked reasonable explanations. Moreover, the influence of deformation mechanisms other than twinning on inelastic behavior remains unclear. In this study, uniaxial tension and compression tests were conducted on hot-rolled magnesium alloy plates, and neutron diffraction experiments were employed to characterize the evolution of macroscopic mechanical response and microscopic mechanisms. Additionally, a twinning and detwinning (TDT) model based on the elastic visco-plastic self-consistent (EVPSC) model has been proposed, incorporating back stress to describe the deformation behavior during stress relaxation. This approach provides a comprehensive understanding of the inelastic behavior of magnesium alloys from multiple perspectives and captures the influence of microscale mechanisms. A thorough understanding of the inelastic behavior of magnesium alloys and a reasonable explanation for the occurrence of twinning under zero-stress conditions offer valuable insights for the precise design of magnesium alloy structures.

Simulation of Mechanical Response in Machining of Ti-6Al-4V Based on Finite Element Model and Visco-Plastic Self-Consistent Model

The predictions of mechanical responses (stress–strain variations) in the machining of Ti-6Al-4V alloy are important to analyze the deformation conditions of machining to optimize the machining parameters and investigate the generation of a machined surface. The selection of a constitutive model is an essential factor that determines the deformation behavior in the machining simulation model. In this paper, two constitutive models of a modified Johnson–Cook (JC) equation and visco-plastic self-consistent (VPSC) model were used to investigate the stress–strain evolutions in the machining process of Ti-6Al-4V. A finite element (FE) machining model was established, considering the influences of grain refinement and deformation twins, based on a modified JC equation. The VPSC model was fitted based on the macro-strain rate sensitivity of the JC equation. The prediction results of the stress–strain curves of two models were compared, and their validities were further proved. The results show that flow stress hardening and inhomogeneities are caused by multi-scale grain refinement during the machining process of Ti-6Al-4V. Five slip deformation modes and one compressive twinning mode were activated in the VPSC model to be consistent with the macro-deformation behavior predicted with the FE model. The validations show the effectiveness of the modified JC equation, considering microstructural changes and the fitted VPSC model, in predicting dynamic behavior in the machining process of Ti-6Al-4V. The results provide two aspects of macro-deformation and polycrystal plasticity to elucidate the stress variations that occur during the machining of Ti-6Al-4V.