Texture evolution and inhomogeneous deformation of polycrystalline Cu based on crystal plasticity finite element method and particle swarm optimization algorithm

Texture evolution and inhomogeneous deformation of polycrystalline Cu during uniaxial compression are investigated at the grain scale by combining crystal plasticity finite element method(CPFEM) with particle swarm optimization(PSO) algorithm. The texture-based representative volume element(TBRVE) is used in the crystal plasticity finite element model, where a given number of crystallographic orientations are obtained by means of discretizing the orientation distribution function(ODF) based on electron backscattered diffraction(EBSD) experiment data. Three-dimensional grains with different morphologies are generated on the basis of Voronoi tessellation. The PSO algorithm plays a significant role in identifying the material parameters and saving computational time. The macroscopic stress–strain curve is predicted based on CPFEM, where the simulation results are in good agreement with the experimental ones. Therefore, CPFEM is a powerful candidate for capturing the texture evolution and clarifying the inhomogeneous plastic deformation of polycrystalline Cu. The simulation results indicate that the <110> fiber texture is generated finally with the progression of plastic deformation. The inhomogeneous distribution of rotation angles lays the foundation for the inhomogeneous deformation of polycrystalline Cu in terms of grain scale.

Modeling texture development during cold rolling of IF steel by crystal plasticity finite element method

With the consideration of slip deformation mechanism and various slip systems of body centered cubic （BCC） metals, Taylor-type and finite element polycrystal models were embedded into the commercial finite element code ABAQUS to realize crystal plasticity finite element modeling, based on the rate dependent crystal constitutive equations. Initial orientations measured by electron backscatter diffraction （EBSD） were directly input into the crystal plasticity finite element model to simulate the develop- ment of rolling texture of interstitial-free steel （IF steel） at various reductions. The modeled results show a good agreement with the experimental results. With increasing reduction, the predicted and experimental rolling textures tend to sharper, and the results simulated by the Taylor-type model are stronger than those simulated by finite element model.＇Conclusions are obtained that rolling textures calculated with 48 { 110} 〈 111 〉＋ { 112 } 〈 111〉＋ { 123 } 〈 111 〉 slip systems are more approximate to EBSD results.

Deformation mechanism of cold ring rolling in view of texture evolution predicted by a newly proposed polycrystal plasticity model

An explicit polycrystal plasticity model was proposed to investigate the deformation mechanism of cold ring rolling in view of texture evolution. The model was created by deducing a set of linear incremental controlling equations within the framework of crystal plasticity theory. It was directly solved by a linear algorithm within a two-level procedure so that its efficiency and stability were guaranteed. A subroutine VUMAT for ABAQUS/Explicit was developed to combine this model with the 3D FE model of cold ring rolling. Results indicate that the model is reliable in predictions of stress-strain response and texture evolution in the dynamic complicated forming process; the shear strain in RD of the ring is the critical deformation mode according to the sharp Goss component （{110}？100？） of deformed ring; texture and crystallographic structure of the ring blank do not affect texture type of the deformed ring;texture evolves rapidly at the later stage of rolling, which results in a dramatically increasing deformation of the ring.

A combined experimental and crystal plasticity study of grain size effects in magnesium alloys

This work presents a method to incorporate the micro Hall-Petch equation into the crystal plasticity finite element(CPFE) framework accounting for the microstructural features to understand the coupling between grain size, texture, and loading direction in magnesium alloys.The effect of grain size and texture is accounted for by modifying the slip resistances of individual basal and prismatic systems based on the micro Hall-Petch equation. The modification based on the micro Hall-Petch equation endows every slip system at each microstructural point with a slip system-level grain size and maximum compatibility factor, which are in turn used to modify the slip resistance. While the slip-system level grain size is a measure of the grain size, the maximum compatibility factor encodes the effect of the grain boundary on the slip system resistance modification and is computed based on the Luster-Morris factor. The model is calibrated using experimental stress-strain curves of Mg-4Al samples with three different grain sizes from which the Hall-Petch coefficients are extracted and compared with Hall-Petch coefficients predicted using original parameters from previous work. The predictability of the model is then evaluated for a Mg-4Al sample with different texture and three grain sizes subjected to loading in different directions. The calibrated parameters are then used for some parametric studies to investigate the variation of Hall-Petch slope for different degrees of simulated spread in basal texture,variation of Hall-Petch slope with loading direction relative to basal poles for a microstructure with strong basal texture, and variation of yield strength with change in grain morphology. The proposed approach to incorporate the micro Hall-Petch equation into the CPFE framework provides a foundation to quantitatively model more complicated scenarios of coupling between grain size, texture and loading direction in the plasticity of Mg alloys.

Three-dimensional crystal plasticity and HR-EBSD analysis of the local stress-strain fields induced during twin propagation and thickening in magnesium alloys

Present work focuses on analysis of the stress and strain fields inside and around the individual {10–12} twin in magnesium alloy. The 3D crystal plasticity model represents twin as an ellipsoidal inclusion surrounded by the matrix. Five different twin thicknesses and three different lateral twin lengths are used for stress/strain analysis. The simulations are complemented with experimental observations using high-resolution electron backscattered diffraction. The simulations and experiments show a similar distribution of the shear stress and the spatial activity of individual slip systems(basal, prismatic, pyramidal). Plasticity induced inside the twin is dominantly caused by the prismatic dislocations slip and does not influence twin back stress which is identical to pure elastic twin. The twin with larger lateral dimension requires lower equilibrium stress which suggests anisotropic twin propagation and increased thickness of such twins. The lateral twin propagation is mostly influenced by prismatic and pyramidal slip in the twin vicinity. The twin thickness can reach a maximal level that is driven by the critical resolved shear stress values for dislocation slip with the significant influence of basal slip.

Application of crystal plasticity modeling in equal channel angular extrusion

Some applications of crystal plasticity modeling in equal channel angular extrusion（ECAE） of face-centered cubic metals were highlighted.The results show that such simulations can elucidate the dependency of grain refinement efficiency on processing route and the directionality of substructure development,which cannot be explained by theories that consider only the macroscopic deformation behavior.They can also capture satisfactorily the orientation stability and texture evolution under various processing conditions.It is demonstrated that crystal plasticity models are useful tools in exploring the crystallographic nature of grain deformation and associated behavior that are overlooked or sometimes erroneously interpreted by existing phenomenological theories.

Texture evolution and slip mode of a Ti-5.5Mo-7.2Al-4.5Zr-2.6Sn-2.1Cr dual-phase alloy during cold rolling based on multiscale crystal plasticity finite element model

The complex micromechanical response among grains remains a persistent challenge to understand the deformation mechanism of titanium alloys during cold rolling.Therefore,in this work,a multiscale crystal plasticity finite element method of dual-phase alloy was proposed and secondarily developed based on LS-DYNA software.Afterward,the texture evolution and slip mode of a Ti-5.5Mo-7.2Al-4.5Zr-2.6Sn-2.1Cr alloy,based on the realistic 3D microstructure,during cold rolling(20%thickness reduction)were systematically investigated.The relative activity of the■slip system in theαphase gradually increased,and then served as the main slip mode at lower Schmid factor(<0.2).In contrast,the contribution of the■slip system to the overall plastic deformation was relatively limited.For theβphase,the relative activity of the<111>{110}slip system showed an upward tendency,indicating the important role of the critical resolved shear stress relationship in the relative activity evolutions.Furthermore,the abnormally high strain of very fewβgrains was found,which was attributed to their severe rotations compelled by the neighboring pre-deformedαgrains.The calculated pole figures,rotation axes,and compelled rotation behavior exhibited good agreement to the experimental results.

CRYSTALLOGRAPHIC HOMOGENIZATION FINITE ELEMENT METHOD AND ITS APPLICATION ON SIMULATION OF EVOLUTION OF PLASTIC DEFORMATION INDUCED TEXTURE

A crystallographic homogenization method is proposed and implemented to predict the evolution of plastic deformation induced texture and plastic anisotropy （earring） in the stamping of polycrystalline sheet metals. The microscopic inhomogeneity of crystal aggregate has been taken into account with the microstructure made up of a representative aggregate of single crystal grains. Multi-scale analysis is performed by coupling the microscopic crystal plasticity with the macroscopic continuum response through the present homogenization procedure. The macroscopic stress is defined as the volume average of the corresponding microscopic crystal aggregations, which simultaneously satisfies the equation of motion in both micro- and macro-states. The proposed numerical implementation is based on a finite element discretization of the macrocontinuum, which is locally coupled at each Gaussian point with a finite element discretization of the attached micro-structure. The solution strategy for the macro-continuum and the pointwiseattached micro-structure is implemented by the simultaneous employment of dynamic explicit FE formulation. The rate-dependent crystal plasticity model is used for the constitutive description of the constituent single crystal grains. It has been confirmed that Taylor＇s constant strain homogenization assumption yields an undue concentration of the preferred crystal orientation compared with the present homogenization in the prediction of texture evolution, with the latter having relaxed the constraints on the crystal grains. Two kinds of numerical examples are presented to demonstrate the capability of the developed code： 1） The texture evolution of three representative deformation modes, and 2） Plastic anisotropy （earring） prediction in the hemispherical cup deep drawing process of aluminum alloy A5052 with initial texture. By comparison of simulation results with those obtained employing direct crystal plasticity calculation adopting Taylor assumption, conclusions are drawn that the proposed dynamic explicit crystallographic homogenization FEM is able to more accurately predict the plastic deformation induced texture evolution and plastic anisotropy in the deep drawing process.

Effects of strain state and slip mode on the texture evolution of a near-α TA15 titanium alloy during hot deformation based on crystal plasticity method

A thorough understanding of the texture evolution of near-αtitanium alloys during the hot metal forming can help obtain an optimal crystallographic texture and material performance.The strain state has an obvious effect on the texture evolution of near-αtitanium alloys during the hot metal forming.In this paper,the texture evolution of a near-αTA15 titanium alloy during the hot metal forming under different strain states were discussed based on the crystal plasticity finite element method.It is found that the basal and prismatic slip systems are regarded as the dominant slip modes due to the similar low critical resolved shear stress during the hot metal forming of the TA15 sheet rotating the lattice around the[1010]and 0001 axis,respectively.Once both of them cannot be activated,the pyramidal-2 slipping occurs rotating the lattice around the[1010]axis.The relationship between the texture evolution and strain state is established.All the(0001)orientations form a band perpendicular to the direction of the first principal strain.The width of the band along the direction of the second principal strain depends on the ratio of the compressive effect to the tensile effect of the second principal strain.This relationship can help control the crystallographic texture and mechanical properties of the titanium alloys component during the hot metal forming.

Theoretical analysis of texture evolution in cold rolling process of single crystal aluminum

The crystal plasticity finite element method(CPFEM),which incorporates the crystal plasticity constitutive law into the finite element method,was developed to investigate the rolling processes of the cubic oriented and Goss oriented Al single crystal. The simulation results show that after rolling the crystal predominantly rotates around the transverse direction(TD) for both orientations. The rotations around the rolling direction(RD) and the normal direction(ND) are negligible. The reduction plays a significant role in the texture evolution. The TD rotation angle increases with increasing reduction. The deformation bands exist in the rolled specimens with the cubic initial orientation. Compared with the cubic oriented specimens,the TD rotation angles in the Goss oriented specimens are very small.

Simulation of polycrystalline aluminum tensile test with crystal plasticity finite element method

The crystal plasticity was implemented in the finite element method(FEM) software ABAQUS through the user subroutine UMAT. By means of discretizing the space at the grain level with the Voronoi diagram method, a polycrystal model was built and used in the FEM analysis. The initial orientation of each grain was generated based on the orientation distribution function(ODF). The developed model was successfully applied in simulation of polycrystalline aluminium samples deformed by the tensile tests. The theoretical strain—stress relation was in good agreement with the experimental result. The simulation results show that the grain size has significant effect on the deformation behavior. The initial plastic deformation usually occurs at grain boundaries, and multiple slip often results in an enhanced local hardening at grain boundaries.

Temperature-dependent constitutive modeling of a magnesium alloy ZEK100 sheet using crystal plasticity models combined with in situ high-energy X-ray diffraction experiment

A multiscale crystal plasticity model accounting for temperature-dependent mechanical behaviors without introducing a larger number of unknown parameters was developed.The model was implemented in elastic-plastic self-consistent(EPSC)and crystal plasticity finite element(CPFE)frameworks for grain-scale simulations.A computationally efficient EPSC model was first employed to estimate the critical resolved shear stress and hardening parameters of the slip and twin systems available in a hexagonal close-packed magnesium alloy,ZEK100.The constitutive parameters were thereafter refined using the CPFE.The crystal plasticity frameworks incorporated with the temperature-dependent constitutive model were used to predict stress–strain curves in macroscale and lattice strains in microscale at different testing temperatures up to 200℃.In particular,the predictions by the crystal plasticity models were compared with the measured lattice strain data at the elevated temperatures by in situ high-energy X-ray diffraction,for the first time.The comparison in the multiscale improved the fidelity of the developed temperature-dependent constitutive model and validated the assumption with regard to the temperature dependency of available slip and twin systems in the magnesium alloy.Finally,this work provides a time-efficient and precise modeling scheme for magnesium alloys at elevated temperatures.

Finite element simulation of influences of grain interaction on rolling textures of fcc metals

A rate dependent crystal plasticity constitutive model considering self and latent hardening in finite element analysis was developed to simulate rolling textures of pure aluminum. By changing the assignment of orientations to finite elements, i.e. assigning the same set of orientations to all elements or different orientations to different elements, the influences of grain interaction on the formation of rolling textures were numerically simulated with this kind of crystal plasticity finite element model. The simulation results reveal that the grains without considering grain interaction rotate faster than those considering grain interaction, and the rotation of grain boundary is slowed down due to the grain interaction. For a good simulation more elements should be assigned to one grain, in which the effects of both the boundary and interior parts of grain contribute to the formation of rolling textures.

Mechanical Anisotropy of Selective Laser Melted Ti-6Al-4V Using a Reduced-order Crystal Plasticity Finite Element Model

In this study,a reduced-order crystal plasticity finite element(CPFE)model was developed to study the effects of the microstructural morphology and crystallographic texture on the mechanical anisotropy of selective laser melted(SLMed)Ti-6Al-4V.First,both hierarchical and equiaxed microstructures in columnar prior grains were modeled to examine the influence of the microstructural morphology on mechanical anisotropy.Second,the effects of crystallographic anisotropy and textural variability on mechanical anisotropy were investigated at the granular and representative volume element(RVE)scales,respectively.The results show that hierarchical and equiaxed CPFE models with the same crystallographic texture exhibit the same mechanical anisotropy.At the granular scale,the significance of crystallographic anisotropy varies with different crystal orientations.This indicates that the present SLMed Ti-6Al-4V sample with weak mechanical anisotropy resulted from the synthetic effect of crystallographic anisotropies at the granular scale.Therefore,combinations of various crystallographic textures were applied to the reduced-order CPFE model to design SLMed Ti-6Al-4V with different mechanical anisotropies.Thus,the crystallographic texture is considered the main controlling variable for the mechanical anisotropy of SLMed Ti-6Al-4V in this study.

Texture evolution prediction of 2219 aluminum alloy sheet under hydro-bulging using cross-scale numerical modeling

A simultaneous prediction of macroscopic deformation and microstructure evolution is critical for un-derstanding the deformation mechanism of components.In this work,the hydro-bulging process of 2219 aluminum alloy sheet was investigated using cross-scale numerical modeling,in which the macroscopic finite element method(FEM)and crystal plasticity finite element method(CPFEM)were combined.The calculated texture evolution exhibits good agreement with the experimental results,and the stress er-ror between the two scales is generally small.The effects of different strain states on texture evolution and slip mode are further discussed.As the strain ratioηincreases,the volume fractions of the initial Rotated Copper texture component andγ-Fiber texture component decrease significantly,which tend to be stabilized at P texture component.The initial Rotated Cube texture component is inclined to rotate towards the Cube texture component,while the volume fraction of this orientation is relatively stable.The lower strain ratio can considerably enhance the activity of more equivalent slip systems,promoting a more uniform strain distribution over grains.The difficulty of grain deformation changes as the lat-tice rotates.The grain with easy-to-deform orientation can gradually rotate to a stable orientation during plastic deformation,which has a lower Schmid factor.

Role of slip and {10-12} twin on the crystal plasticity in Mg-RE alloy during deformation process at room temperature

The deformation mechanism of slips and twins has a considerable influence on the plasticity of magnesium alloys. However, the roles of slips and twins in the room-temperature deformation of Mg-rare earth(Mg-RE) alloys with high contents of rare earth elements is rarely investigated. Here, the microstructural evolution and deformation mechanism of an aged Mg-5 Y-2 Nd-3 Sm-0.5 Zr alloy during uniaxial compression at room temperature were systematically investigated using in-situ electron-backscattered diffraction and transmission electron microscopy. The results indicated that in the early stage of deformation, the Mg-RE alloy was mainly controlled by the slip of dislocations in the basal plane and the coordinated c-axis strain of the {10-12} twin. With an increase in the strain, the grain orientation became more suitable for the initiation of pyramidal Ⅱ dislocations in the later stage of deformation;these dominated the deformation mechanism. In the twin evolution of the Mg-RE alloy, there were three types of twin-twin interaction behaviors:(i) single twin variant 'parallel' structure,(ii) single twin variant 'cross' structure, and(iii) multi twin variant 'cross' structure. In addition, three types of twin-grain boundary interaction behaviors were summarized:(i) twin 'refracting through' grain boundary,(ii) twin'parallel through' grain boundary, and(iii) twin 'fusing through' grain boundary, which are expected to act as new means and solutions for the twin strengthening of magnesium alloys.

Through-Thickness Texture Gradient in Hot-Rolled 25Mn-2.5Si-2Al TWIP Steel

Texture is one of the important factors affecting sheet metal forming performance.The through-thickness texture gradient during the hot-rolling process of twinning induced plasticity（TWIP）steel sheet was investigated using electron backscatter diffraction and X-ray diffraction.With increasing reduction of the TWIP steel,the fraction of∑1 decreased,whereas the fractions of∑3,∑9,and∑27increased.During 53%reduction,a similar trend could be found from its surface to the center.The gradients of intensities of the fibers decreased with increasing hot-rolling reduction.The intensities of face-centered cubic（fcc）shear textures E and Y were higher in the center than that at the surface for both reductions.During 20% reduction,the intensity of fcc plain strain texture S orientation increased from the center to the surface.

7075-T6铝合金在Taylor冲击实验中的宏观力学响应及细观结构演化

将实验和晶体塑性有限元(CPFEM)方法相结合,研究了7075-T6铝合金在Taylor冲击实验中的宏观力学响应以及其细观结构的演化。使用电子背散射衍射技术(EBSD)对实验前7075-T6铝合金的细观结构进行表征。通过修改强化模型和流动准则在CPFEM模型中引入位错密度作为内部状态变量,并结合动态压缩实验得到的应力-应变曲线确定7075-T6铝合金相关的模型参数。结果表明:考虑位错密度的CPFEM模型可有效地描述7075-T6铝合金在不同速度Taylor冲击实验中的宏观和微观力学响应。与实验结果对比,CPFEM模型合理地预测了冲击后子弹的外部轮廓变化,其预测的撞击面半径和子弹剩余长度与实验结果误差均在10%以内。此外,CPFEM模型预测7075-T6铝合金冲击后的织构演化同动态冲击后结果大致相同,均表现为生成了较多的R-Cube织构和Goss织构,而Cube织构和Cu织构大量减少。随着冲击速度的增加,R-Cube织构、S织构的体积分数逐渐增大,Cube织构、Cu织构和Brass的体积分数逐渐减少。同时,CPFEM模型预测到撞击后子弹颈缩段的产生。随着冲击速度的增加,子弹的对数应变和位错密度均有上升,最大值均出现在撞击面;在同一速度下,撞击面上外表面处平均位错密度的值小于轴心处的值。

自然时效态2198铝锂合金板材各向异性晶体塑性有限元模拟

基于电子背散射衍射(EBSD)数据建立了自然时效态2198铝锂合金板材的晶体塑性有限元模型,并利用控制变量法研究了5个塑性基本参数(初始硬化模量、应变率敏感系数、参考应变率、初始临界分剪切应力和饱和流动应力)对塑性变形行为的影响,通过引入代价函数,并对各个塑性参数进行优化,最终得到了能够描述自然时效态2198铝锂合金板材各向异性的塑性参数,所预测的沿RD和TD方向的应力-应变曲线与试验结果符合较好。通过晶体塑性有限元法,预测了自然时效态2198铝锂合金板材单向拉伸过程中晶体取向演变与12个滑移系对塑性变形的贡献。发现(111)[10-1]滑移系对自然时效态2198铝锂合金板材单向拉伸的塑性变形贡献最大。沿RD方向拉伸时,自然时效态2198铝锂合金板材出现强烈的[011]//TD织构。

On the role of the constitutive model and basal texture on the mechanical behaviour of magnesium alloy AZ31B sheet

The recently developed elastic-viscoplastic self-consistent model with various self-consistent schemes was applied to study the effect of basal texture on the mechanical behavior of magnesium alloy AZ31B sheet. The influence of the basal texture was investigated using various initial textures generated by artificially tilting the measured texture of the reference AZ31B sheet around in a transverse direction. The material parameters for the various models were fitted to experimental uniaxial tension and compression along the rolling direction and were then used to study the effects of the basal texture on the yield stress, R value, ultimate stress and uniform strain under uniaxial tension. The effect of the basal texture on sheet metal forming was further assessed by calculating the limit strain under in-plane plane strain tension. An assessment of the predictive capability of polycrystal plasticity models was made based on comparisons of predictions and experimental observations. Among the available self-consistent approaches, the Affine self-consistent scheme resulted in the best overall performance.