考虑细观变形特征的镁合金宏观本构模型及数值模拟

为了能有效描述镁合金宏观各向异性塑性行为,考虑了滑移、孪生、去孪生三种细观变形模式的特点,给出了相应的硬化函数;根据VonMises屈服准则,发展了一种镁合金宏观本构模型及其迭代算法。模型将变形模式的开启与晶粒取向相关联,同时针对镁合金孪生变形时引起的晶粒重新定向问题,描述了一种晶向偏转的方法。在此基础上编写了ABAQUS/UMAT材料用户子程序;利用开发的本构模型,开展了单轴拉伸、单轴压缩、单轴循环拉压加载条件下镁合金塑性行为的数值模拟,并对随机织构下的镁合金板材轧制过程进行了有限元仿真实验。模拟结果表明:单轴拉伸、单轴压缩和循环加载情形下的镁合金宏观硬化行为与实验结果基本吻合;轧制后镁合金板材表现出了应力-应变不均匀特性,多晶织构演化结果与实验结果基本一致。说明文中所提出的宏观本构模型、晶向偏转模型能够有效描述镁合金的宏观塑性行为和织构演化。     

单轴循环载荷下镁合金宏观塑性本构关系研究

基于微观织构演化,本文对镁合金的宏观塑性本构模型进行了改进,得到了室温下镁合金AZ31B和AZ61A单轴循环拉压载荷作用下的应力应变曲线。模型中区分了滑移、孪晶与去孪三种不同微观塑性变形机制,并且研究了它们对材料宏观循环塑性行为的影响。通过引入初始非零背应力来模拟循环应力应变曲线中拉压不对称性,给出了材料在单轴循环拉压载荷下背应力及屈服面的演化规律,并运用线性预测塑性回拉技术与隐式积分法求解相应的非线性方程组,编写了与.ABAQUS接口的UMAT用户子程序。预测与实验结果的比较显示该模型能较好地模拟镁合金材料在单轴循环拉压载荷作用下的力学行为,具有较高的准确性与良好的实用性。     

考虑微结构特征的陶瓷材料含损伤本构模型

为了研究不同微结构陶瓷材料的冲击破坏特征,以从微结构角度出发、描述陶瓷材料非弹性变形和断裂行为的Deshpande-Evan模型为基础构建本构模型,计算了无约束条件下材料的应力状态。为了验证改进模型的有效性,将VUMAT子程序编程方法将与ABAQUS有限元软件相结合,并将其应用于典型陶瓷材料（YAG透明陶瓷）冲击破坏过程的分析模拟。采用改进模型分析应变率、应力三轴度、晶粒尺寸及初始缺陷分布密度对YAG透明陶瓷动态力学行为和损伤演化机制的影响规律。结果表明：随着晶粒尺寸和裂纹分布密度的增加,YAG透明陶瓷破坏程度随之加剧,完全损伤区域面积也随之增加,晶粒尺寸对YAG透明陶瓷宏观破坏特征的影响程度要大于裂纹分布密度;YAG透明陶瓷失效强度以及断裂应变随着晶粒尺寸以及初始缺陷分布密度的增大而减小;随着应变率不断增加,YAG透明陶瓷在不同晶粒尺寸以及初始缺陷分布密度下的峰值应力和断裂应变均随之增加;裂纹扩展速度会随着晶粒尺寸的增加呈现出先增加而后平缓的趋势,裂纹扩展速度与初始缺陷分布密度系数成线性关系。改进模型可以描述YAG透明陶瓷微结构对其宏观破坏特征的影响,为进一步分析微结构对陶瓷材料宏观...     

基于微结构动态演化机制的单晶镍基高温合金晶体塑性本构及其有限元模拟

因其优异的高温力学性能,镍基单晶高温合金在航空航天和能源等领域得到了广泛的应用.镍基单晶高温合金优异的高温性能来源于其特有的两相微结构.基于代表体胞模型及分块均匀化方法,以位错密度为主要内变量,发展了一个包含两相微结构和位错演化信息的单晶镍基高温合金塑性行为的本构模型.该本构模型充分考虑了镍基单晶合金中位错在基体相和沉淀增强相中的多种演化机制,例如,基体位错八面体滑移、立方滑移、位错攀移、交滑移、位错弓出、位错切过沉淀增强相以及位错Kear-Wilsdolf(K-W)锁形成与解锁等.在商用有限元软件ABAQUS的框架下,编制了UMAT用户材料子程序.利用该用户子程序,对单晶和多晶镍基高温合金在不同温度、不同加载方向下的单调塑性、循环塑性、蠕变等典型行为进行了计算模拟.结果表明:该晶体塑性本构模型能"统一地"刻画镍基高温合金在不同温度、不同方向下的多种变形行为,并与实验结果具有良好的一致性.     

镁合金塑性机制研究综述

纯镁具有丰富的微观塑性机制，尤其是孪晶，导致其塑性变形错综复杂，力学性能也与常见的面心及体心立方金属有显著差异。由于现今学界对位错滑移与孪晶变形等塑性机制缺乏充分认识，镁合金性能调控效果尚不理想，与铝合金相比，镁合金的力学性能还有很大的提升空间。基于此背景，本文首先回顾了镁合金的发展历史与应用现状。然后介绍了镁中位错滑移与孪晶变形等塑性机制的研究进展，重点阐述位错、孪晶、晶界、析出相、溶质原子等重要的微结构，并简要介绍了计算机模拟方法。最后展望了强韧性能方面值得重视的若干研究方向。     

室温下镁合金板循环塑性随动强化本构模型研究

本文在具有各向异性屈服强度和拉压不对称的CPB06屈服准则的基础上,建立了基于随动强化的循环塑性本构模型．通过引入滑移、孪晶以及去孪等不同变形模式下的背应力演化方程,对室温下镁合金板材异常循环硬化行为进行了模拟．选取了AZ31B-O和AZ31B两种镁合金板材,通过拉伸-压缩-拉伸(T-C-T)和压缩-拉伸(C-T)等不同加载路径下的部分实验曲线确定模型的参数,采用三次插值多项式建立了背应力参数与上一变形模式中累积的等效塑性应变（即预应变）之间的函数关系．使用本模型对剩下的实验曲线进行了预测,发现预测结果与实验结果有良好的一致性,说明了当前模型的正确性．     

延性单晶非均匀变形的三维有限元模拟

对延性单晶在拉伸载荷作用下的应变局域化和颈缩等非均匀变形过程进行了三维有限元数值模拟。将相关晶体塑性本构模型及一种新的数值积分方法补充到ABAQUS6.1商用有限元软件中。该方法的特点是，利用晶体塑性的动力学方程，获得一个关于晶体弹性变形梯度的演化方程，采用半隐式积分方案进行求解。本文推导出一种新的应力变本构矩阵。按此方式更新本构矩阵，计算速度和计算稳定性大大提高。加载方式，边界条件和变形程度等因素影响着滑移系的启动状况，这是平面模型所不能预测的。本文利用三维有限元方法模拟了不同取向下滑移系的启动状况，全面地考虑了FCC单晶材料12个可能滑移系在变形过程中的启动状况，合理地模拟了FCC面心立方单晶沿不同取向加载时晶轴旋转导致的应变局域化和颈缩等非均匀变形过程。     

晶体塑性变形离散滑移模型及有限元分析

基于韧性单晶体实验现象，建立了描述晶体塑性变形的离散滑移模型．该模型的主要特点是：晶体滑移变形在宏观上是不均匀的，滑移带的分布是离散的．利用晶体塑性理论对模型进行了有限变形有限元分析，计算结果揭示了晶体滑移的离散行为，模拟的应力 应变曲线与实验曲线相吻合     

多晶体变形、应力的不均匀性及宏观响应

从单晶滑移变形分析的角度探讨多晶体塑性变形和应力的不均匀性及宏观力学响应：建议了 一种当前构形下以应力为基本变量的单晶黏塑性增量迭代计算方法；用Voronoi晶粒集合体 模型研究多晶体由于晶粒几何及取向的随机性造成的变形和应力的不均匀性, 进行了多晶集 合体的宏观响应和晶粒位向演化数值分析. 结果表明：(1)多晶体内等效塑性应变和应力分量在统计上呈现高斯分布，在应变硬化过程中, 随着塑性变形增加多晶体微观应力的统计变异系数会越来越大；(2)用Voronoi模型计算可得到沿最大剪应力方向的滑移变形带；(3)多晶体内最高三轴拉应力一般出现在晶界特别是三晶交界处；(4)Voronoi模型能用于织构分析.     

材料三维微结构表征及其晶体塑性有限元模拟

材料的力学性能，尤其是在有限变形下所呈现的宏观各向异性，是材料结构设计和服役寿命考虑的关键因素。由于宏观模型不能较好地反映材料微观结构（晶粒的形貌和取向等）对宏观塑性各向异性的影响，因此，本文建立了能实际反映晶粒形貌的三维Voronoi模型，并基于晶体塑性理论对铝合金在有限变形下的响应进行计算。首先，建立反映材料微结构的代表性体积单元RVE模型进行计算，并与实验结果进行对比验证。然后，以单向拉伸为例，分析了有限变形过程中试件的晶粒形貌和取向分布等微观因素对宏观各向异性演化的影响，并从材料和结构两个层面讨论了微观结构对宏观力学性能的影响。结果表明，本文模型能够反映微观结构对宏观力学性能的影响，为实际生产制造领域构件的力学性能提供可靠的预测。     

On the strain hardening and texture evolution in high manganese steels: Experiments and numerical investigation

We present a systematic investigation on the strain hardening and texture evolution in high manganese steels where twinning induced plasticity (TWIP) plays a significant role for the materials' plastic deformation. Motivated by the stress–strain behavior of typical TWIP steels with compositions of Fe, Mn, and C, we develop a mechanistic model to explain the strain-hardening in crystals where deformation twinning dominates the plastic deformation. The classical single crystal plasticity model accounting for both dislocation slip and deformation twinning are then employed to simulate the plastic deformation in polycrystalline TWIP steels. While only deformation twinning is activated for plasticity, the simulations with samples composed of voronoi grains cannot fully capture the texture evolution of the TWIP steel. By including both twinning deformation and dislocation slip, the model is able to capture both the stress–strain behaviors and the texture evolution in Fe–Mn–C TWIP steel in different boundary-value problems. Further analysis on the strain contributions by both mechanisms suggests that deformation twinning plays the dominant role at the initial stage of plasticity in TWIP steels, and dislocation slip becomes increasingly important at large strains.     

Continuum modeling of the response of a Mg alloy AZ31 rolled sheet during uniaxial deformation

Lightweight magnesium alloys, such as AZ31, constitute alternative materials of interest for many industrial sectors such as the transport industry. For instance, reducing vehicle weight and thus fuel consumption can actively benefit the global efforts of the current environmental industry policies. To this end, several research groups are focusing their experimental efforts on the development of advanced Mg alloys. However, comparatively little computational work has been oriented towards the simulation of the micromechanisms underlying the deformation of these metals. Among them, the model developed by Staroselsky and Anand [Staroselsky, A., Anand, L., 2003. A constitutive model for HCP materials deforming by slip and twinning: application to magnesium alloy AZ31B. International Journal of Plasticity 19 (10), 1843–1864] successfully captured some of the intrinsic features of deformation in Magnesium alloys. Nevertheless, some deformation micromechanisms, such as cross-hardening between slip and twin systems, have been either simplified or disregarded. In this work, we propose the development of a crystal plasticity continuum model aimed at fully describing the intrinsic deformation mechanisms between slip and twin systems. In order to calibrate and validate the proposed model, an experimental campaign consisting of a set of quasi-static compression tests at room temperature along the rolling and normal directions of a polycrystalline AZ31 rolled sheet, as well as an analysis of the crystallographic texture at different stages of deformation, has been carried out. The model is then exploited by investigating stress and strain fields, texture evolution, and slip and twin activities during deformation. The flexibility of the overall model is ultimately demonstrated by casting light on an experimental controversy on the role of the pyramidal slip 〈c + a〉 versus compression twinning in the late stage of polycrystalline deformation, and a failure criterion related to basal slip activity is proposed.     

NUMERICAL SIMULATION OF NON-PLANAR PLASTIC ANISOTROPY OF COLD ROLLING POLYCRYSTALLINE MATERIALS

The plastic anisotropy of sheet metal is usually caused by preferred orientation of grains, developed by mechanical deformation and thermal treatment. In the present study, a Taylor-like polycrystal model suggested by Asaro and Needleman is applied to investigate the evolution of the anisotropic behavior of a face centered cubic (FCC) polycrystalline metal, which is considered having {111} (110) slip systems, by stretching it along an arbitrary direction after it has undergonea plane-strata compression that rationally simulates the cold rolling process of FCC polycrystalline pure aluminium. By using the Taylor-like polycrystal model, pole figures are obtained to describe the texture development of polycrystalline aggregate after plane-strain compression, and then the plastic anisotropy of polycrystalline aggregate is evaluated by stretching the polycrystalline aggregate in different direction in term of yield stress. According to the results, the contours of longitudinal flow stress in three-dimensional orientation space are given and analyzed. Experiment results similar to the prediction of planar anisotropy can be found inthe literature written by Takahashi et al. that in directly show the correctness of the prediction of non-planar plastic anisotropy by this analysis.     

A dislocation density based crystal plasticity finite element model: Application to a two-phase polycrystalline HCP/BCC composites

We present a multiscale model for anisotropic, elasto-plastic, rate- and temperature-sensitive deformation of polycrystalline aggregates to large plastic strains. The model accounts for a dislocation-based hardening law for multiple slip modes and links a single-crystal to a polycrystalline response using a crystal plasticity finite element based homogenization. It is capable of predicting local stress and strain fields based on evolving microstructure including the explicit evolution of dislocation density and crystallographic grain reorientation. We apply the model to simulate monotonic mechanical response of a hexagonal close-packed metal, zirconium (Zr), and a body-centered cubic metal, niobium (Nb), and study the texture evolution and deformation mechanisms in a two-phase Zr/Nb layered composite under severe plastic deformation. The model predicts well the texture in both co-deforming phases to very large plastic strains. In addition, it offers insights into the active slip systems underlying texture evolution, indicating that the observed textures develop by a combination of prismatic, pyramidal, and anomalous basal slip in Zr and primarily {110}〈111〉 slip and secondly {112}〈111〉 slip in Nb.     

Micromechanical quantification of elastic,twinning, and slip strain partitioning exhibited by polycrystalline,monoclinic nickel–titanium during large uniaxial deformations measured via in-situ neutron diffraction

We draw upon existing knowledge of twinning and slip mechanics to develop a diffraction analysis model that allows for empirical quantification of individual deformation mechanisms to the macroscopic behaviors of low symmetry and phase transforming crystalline solids. These methods are applied in studying elasticity, accommodation twinning, deformation twinning, and slip through neutron diffraction data of tensile and compressive deformations of monoclinic NiTi to ~18% true strain. A deeper understanding of tension–compression asymmetry in NiTi is gained by connecting crystallographic calculations of polycrystalline twinning strains with in situ diffraction measurements. Our analyses culminate in empirical, micromechanical quantification of individual elastic, accommodation twinning, deformation twinning, and slip contributions to the total macroscopic stress–strain response of a monoclinic material subjected to large deformations. From these results, we find that 20–40% of the total plastic response at high strains is due to deformation twinning and 60–80% due to slip.     

3-D simulation of spatial stress distribution in an AZ31 Mg alloy sheet under in-plane compression

A complete 3-D crystal plasticity finite element method (CPFEM) that considered both crystallographic slip and deformation twinning was applied to simulate the spatial distribution of the relative amount of slip and twin activities in a polycrystalline AZ31 Mg alloy during in-plane compression. A microstructure mapping technique that considered the grain size distribution and microtexture measured by electron backscatter diffraction (EBSD) technique was used to create a statistically representative 3-D microstructure for the initial configuration. Using a 3-D Monte Carlo method, a 3-D digital microstructure that matched the experimentally measured grain size distribution was constructed. Crystallographic orientations obtained from the EBSD data were assigned on the 3-D digital microstructure to match the experimentally measured misorientation distribution. CPFEM captured the heterogeneity of the stress concentration as well as the slip and twin activities of a polycrystalline AZ31 Mg alloy during in-plane compression.     

Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets

Magnesium alloy sheets have been extending their field of applications to automotive and electronic industries taking advantage of their excellent light weight property. In addition to well-known lower formability, magnesium alloys have unique mechanical properties which have not been thoroughly studied: high in-plane anisotropy/asymmetry of yield stress and hardening response. The reason of the unusual mechanical behavior of magnesium alloys has been understood by the limited symmetry crystal structure of HCP metals and thus by deformation twinning. In this paper, the phenomenological continuum plasticity models considering the unusual plastic behavior of magnesium alloy sheet were developed for a finite element analysis. A hardening law based on two-surface model was further extended to consider the general stress–strain response of metal sheets including Bauschinger effect, transient behavior and the unusual asymmetry. Three deformation modes observed during the continuous in-plane tension/compression tests were mathematically formulated with simplified relations between the state of deformation and their histories. In terms of the anisotropy and asymmetry of the initial yield stress, the Drucker–Prager’s pressure dependent yield surface was modified to include the anisotropy of magnesium alloy. The numerical formulations and characterization procedures were also presented and finally the correlation of simulation with measurements was performed to validate the proposed theory.