用晶体弹塑性有限单元法研究双晶金属拉伸变形

本文从单晶体应力-应变关系的精确实验结果和多晶体滑移特性出发,建立相应的计算模型,并采用微观力学和晶体弹塑性有限单元法,研究双晶金属试样的拉伸变形,得到其应力-应变曲线,晶体内滑移变形和应力分布规律,以及晶界影响区对它们的影响。     

考虑晶体滑移面分解正应力的细观损伤模型

材料内部的解理、滑移面剥离等细观损伤是引起宏观失效的根源, 从细观尺度研究损伤的发生和发展有助于深入认识材料的变形和失效过程. 本文基于晶体塑性理论, 从滑移系的受力和变形出发研究材料的细观损伤, 建立了考虑滑移面分解正应力的细观损伤模型, 为晶体材料解理断裂的分析提供了新方法. 首先, 在晶体弹塑性变形构型的基础上引入损伤变形梯度张量的概念, 从变形运动学着手建立了考虑损伤能量耗散的本构方程, 并推导了塑性流动方程与损伤演化方程; 然后, 建立了相应的数值计算方法, 给出了应力与状态变量的更新算法, 推导了Jacobian矩阵的表达式; 接着, 以$[100]$取向的单晶铜材料为例, 通过有限元计算与试验结果的对比, 并采用粒子群优化算法标定了11个材料细观参数; 最后, 将所提细观损伤模型应用于RVE单轴拉伸过程的模拟, 得到了考虑损伤影响的应力应变曲线, 并分析了材料的塑性流动与损伤演化过程. 结果表明, 本文所提模型能够计算材料在受载过程中的损伤累积效应, 合理反映晶体材料的细观损伤机理.      

一种基于物理机制的后继屈服面演化模型

考虑滑移为晶体塑性的主要变形机制,推广单晶滑移理论至多晶体,建立滑移构元模型,研究了后继屈服面的移动、变形等演化规律。基于滑移构元的包氏效应和潜在硬化的影响,后继屈服面的尾部缩进,变得较“平坦”,而前端突出,形成“高曲率区域”。为了验证模型的有效性,本文分别预测了单轴拉伸、纯扭转和拉—扭组合比例/非比例加载下的后继屈服面演化过程,与已有实验结果符合一致。关键词:滑移构元模型,后继屈服面,包氏效应,潜在硬化,非比例加载      

铜单晶拉伸试样表面滑移带痕迹的晶体塑性分析

采用建立在晶体塑性理论基础上的晶体塑性有限变形计算方法,针对铜单晶试样单轴拉伸过程中晶体滑移在试样表面留下的滑移带痕迹进行了数值研究.作者利用三维有限元模拟不同取向铜单晶试样的拉伸变形,通过晶体塑性滑移面与试样表面交线的几何分析,得到了试样在不同晶向拉伸下不同滑移系启动造成的试样表面滑移痕迹,并对数值计算的试样表面滑移...     

考虑运动硬化的DD3镍基合金力学行为研究

详细介绍了镍基合金的晶体塑性本构模型,在Asaro大变形晶体塑性框架下,详细介绍了镍基合金的晶体塑性本构模型,在Asaro大变形晶体塑性框架下,引入了运动硬化规律,考虑了温度和应变率对晶体塑性变形的影响,通过针对每个滑移系考虑屈服准则和流动规律建立了晶体塑性模型. 对积分过程进行了推导,通过编写ABAQUS材料用户子程序(UMAT), 实现本构模型的有限元积分算法. 在此基础上模拟了DD3镍基单晶合金在单轴拉伸和循环载荷下的响应,并与实验数据进行了对比. 利用该模型可以很好地模拟镍基单晶所具有的各向异性特性,体现了镍基单晶在循环载荷作用下的拉-压不对称性.      

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。     

金属基复合材料单向和循环变形行为的数值模拟研究

利用晶体细观力学模型，依据组元材料的单晶体变形性质，以Ａｌ－Ａｌ２Ｃｕ自生复合材料为模型材料，用数值法模拟其拉伸和循环拉伸变形过程，得到了与有关实验结果相符的应力－应变曲线，研究了增强相间距和循环加载过程对复合材料变形行为的影响，通过考虑变形过程中组元相及其界面的应力分布规律，分析研究了循环变形过程中基体Ｂａｕｓｃｈｉｎｇｅｒ效应对于复合材料微观变形与损伤机制的作用，结果表明，晶体细观力学模拟计算     

全长锚固锚杆锚固单元力学性能实验研究

锚固单元的传力特性是影响全长锚固锚杆支护能力的重要因素。由于锚固单元界面构成复杂，本文主要考虑锚杆与粘结材料及其界面的力学特性，开展锚固单元界面剪切力学实验研究。实验结果表明，砂浆强度直接影响界面的峰值强度和剪切刚度；采用相同强度砂浆，界面的峰值强度、剪切刚度和残余剪切强度都与法向应力成正比；在相同法向应力作用下，剪切速率增加引起峰值剪切强度增大，但对残余剪切强度影响较小。依据实验剪切应力–位移曲线将锚固单元与岩石间界面的解耦过程分为“峰前–软化–滑移”三阶段，非连续变形分析方法数值模拟结果表明，加载初期的损伤主要受粘结材料抗拉强度的影响，临近峰值阶段与粘结材料张剪混合破裂相关；软化阶段和滑移阶段主要受粘结材料剪切特性和颗粒形状的影响；引入实验所获得的三线滑移模型曲线到全长锚固锚杆模型，模拟拔出数值实验结果表明较快拔出速率将影响锚杆变形能力。     

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．     

位错热激活滑移的数值模拟

在三维离散位错动力学模型中,用Langevin力描述温度对位错的影响作用,模拟了位错克服晶格Peierls应力与阻尼应力的滑移过程．模拟结果表明,位错克服Peierls应力的热激活效应随温度的升高而增大,随应变率的增高而减小．利用热激活本构模型描述了位错热激活滑移过程,拟合了Peierls应力的激活能,结果表明含温度的离散位错动力学模型能较正确地模拟位错的热激活滑移过程．但Peierls阻碍的非离散化处理使激活能与指前因子均随温度升高而增大,这表明离散位错动力学模型模拟Peierls阻碍存在不足之处,其本质原因是介观级的位错动力学模型目前还无法正确模拟微观级的位错芯性质．     

A multi-scale computational model of crystal plasticity at submicron-to-nanometer scales

Plastic flow in crystal at submicron-to-nanometer scales involves many new interesting problems. In this paper, a unified computational model which directly combines 3D discrete dislocation dynamics (DDD) and continuum mechanics is developed to investigate the plastic behaviors at these scales. In this model, the discrete dislocation plasticity in a finite crystal is solved under a completed continuum mechanics framework: (1) an initial internal stress field is introduced to represent the preexisting stationary dislocations in the crystal; (2) the external boundary condition is handled by finite element method spontaneously; and (3) the constitutive relationship is based on the finite deformation theory of crystal plasticity, but the discrete plastic strains induced by the slip of the newly nucleated or propagating dislocations are calculated by dislocation dynamics methodology instead of phenomenological evolution equations used in conventional crystal plasticity. These discrete plastic strains are then localized to the continuum material points by a Burgers vector density function proposed by us. Various processes, such as loop dislocation evolution, dislocation junction formation etc., are simulated to verify the reliability of this computational model. Specifically, a uniaxial compression test for micro-pillars of Cu is simulated by this model to investigate the ‘dislocation starvation hardening’ observed in the recent experiment.     

Incorporation of twinning into a crystal plasticity finite element model: Evolution of lattice strains and texture in Zircaloy-2

A crystal plasticity finite element code is developed to model lattice strains and texture evolution of HCP crystals. The code is implemented to model elastic and plastic deformation considering slip and twinning based plastic deformation. The model accounts for twinning reorientation and growth. Twinning, as well as slip, is considered to follow a rate dependent formulation. The results of the simulations are compared to previously published in situ neutron diffraction data. Experimental results of the evolution of the texture and lattice strains under uniaxial tension/compression loading along the rolling, transverse, and normal direction of a piece of rolled Zircaloy-2 are compared with model predictions. The rate dependent formulation introduced is capable of correctly capturing the influence of slip and twinning deformation on lattice strains as well as texture evolution.     

An efficient constitutive model for room-temperature,low-rate plasticity of annealed Mg AZ31B sheet

Metals and alloys with hexagonal close packed (HCP) crystal structures can undergo twinning in addition to dislocation slip when loaded mechanically. The complexity of the plastic response and the limited extent of twinning are impediments to their room-temperature formability and thus their widespread adoption. In order to exploit the unusual deformation characteristics of twinning sheet materials in designing novel forming operations, a practical plane stress material model for finite element implementation was sought. Such a model, TWINLAW, has been constructed based on three phenomenological deformation modes for Mg AZ31B: S (slip), T (twinning), and U (untwinning). The modes correspond to three testing regimes: initial in-plane tension (from the annealed state), initial in-plane compression, and in-plane tension following compression, respectively. A von Mises yield surface with initial non-zero back stress was employed to account for plastic yielding asymmetry, with evolution according to a novel isotropic and nonlinear kinematic hardening model. Texture and its evolution were represented throughout deformation using a weighted discrete probability density function of c-axis orientations. The orientation of c-axes evolves with twinning or untwinning using explicit rules incorporated in the model.     

A novel yield function for single crystals based on combined constraints optimization

A novel yield function representing the overall plastic deformation in a single crystal is developed using the concept of optimization. Based on the principle of maximum dissipation during a plastic deformation, the problem of single crystal plasticity is first considered as a constrained optimization problem in which constraints are yield functions for slip systems. To overcome the singularity that usually arises in solving the above problem, a mathematical technique is used to replace the above constrained optimization problem with an equivalent problem which has only one constraint. This single constraint optimization problem, the so-called combined constraints crystal plasticity (CCCP) model, is implemented into a finite element code and the results of modeling the uniaxial tensions of the single crystal copper along different crystallographic directions and also hydroforming of aluminum tubes proved the capability of the proposed CCCP model in accurately predicting the deformation in polycrystalline materials.     

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.     

Cylindrical void in a rigid-ideally plastic single crystal II: Experiments and simulations

Experimental results and finite element simulations of plastic deformation around a cylindrical void in single crystals are presented to compare with the analytical solutions in a companion paper: Cylindrical void in a rigid-ideally plastic single crystal I: Anisotropic slip line theory solution for face-centered cubic crystals [Kysar, J.W., Gan, Y.X., Mendez-Arzuza, G., 2005. Cylindrical void in a rigid-ideally plastic single crystal I: Anisotropic slip line theory solution for face-centered cubic crystals, International Journal of Plasticity, 21, 1481–1520]. In the first part of the present paper, the theoretical predictions of the stress and deformation field around a cylindrical void in face-centered cubic (FCC) single crystals are briefly reviewed. Secondly, electron backscatter diffraction results are presented to show the lattice rotation discontinuities at boundaries between regions of single slip around the void as predicted in the companion paper. In the third part of the paper, the finite element method has been employed to simulate the anisotropic plastic deformation behavior of FCC single crystals which contain cylindrical voids under plane strain condition. The results of the simulation are in good agreement with the prediction by the anisotropic slip line theory.     

An atomistically-informed dislocation dynamics model for the plastic anisotropy and tension-compression asymmetry of BCC metals

Atomistic simulations have shown that a screw dislocation in body-centered cubic (BCC) metals has a complex non-planar atomic core structure. The configuration of this core controls their motion and is affected not only by the usual resolved shear stress on the dislocation, but also by non-driving stress components. Consequences of the latter are referred to as non-Schmid effects. These atomic and micro-scale effects are the reason slip characteristics in deforming single and polycrystalline BCC metals are extremely sensitive to the direction and sense of the applied load. In this paper, we develop a three-dimensional discrete dislocation dynamics (DD) simulation model to understand the relationship between individual dislocation glide behavior and macro-scale plastic slip behavior in single crystal BCC Ta. For the first time, it is shown that non-Schmid effects on screw dislocations of both {110} and {112} slip systems must be implemented into the DD models in order to predict the strong plastic anisotropy and tension-compression asymmetry experimentally observed in the stress-strain curves of single crystal Ta. Incorporation of fundamental atomistic information is critical for developing a physics-based, predictive meso-scale DD simulation tool that can connect length/time scales and investigate the underlying mechanisms governing the deformation of BCC metals.     

含冷却孔镍基合金次级取向效应的应变梯度晶体塑性有限元研究

单晶镍基合金具有优异的耐高温、高强、高韧等性能, 这些力学性能受制造过程引入的次级取向和冷却孔的影响. 已有研究大多关注单孔薄板的变形机理和力学性能, 而工程中应用的往往是多孔薄板, 当前亟需阐明多孔的塑性滑移带变形机理、次级取向效应以及冷却孔引起的应变梯度效应. 文章采用基于位错机制的非局部晶体塑性本构模型对含冷却孔镍基单晶薄板的单拉变形进行了数值模拟. 此模型基于塑性滑移梯度与几何必需位错的关系引入了位错流动项, 因此可有效刻画非均匀变形过程中的应变梯度效应. 为了全面揭示含孔镍基薄板的次级取向效应, 系统研究了[100]和[110]取向(两种次级取向)下镍基薄板的单拉变形行为, 并重点探究了在两种次级取向下冷却孔数量对薄板塑性行为的影响. 此外, 还分析了镍基合金板变形过程中各个滑移系上分切应力变化、主导滑移系开动以及几何必需位错密度的演化过程, 并讨论了塑性滑移量及其分布特征对不同次级取向镍基合金板强度的影响. 研究表明, 单孔和多孔的[110]薄板抗拉强度均低于[100]薄板, 多孔薄板的塑性变形过程比单孔薄板更为复杂且受次级取向影响更大, 并且发生滑移梯度位置主要位于冷却孔附近以及塑性滑移带区域. 研究结果可为工程中镍基合金的设计和服役提供理论指导.      

Micromechanical modelling of the effect of plastic deformation on the mechanical behaviour in pseudoelastic shape memory alloys

Except for the recoverable strain induced by phase transformation, NiTi alloys are very ductile even in the martensite phase. The purpose of the present paper is to study the influence of permanent deformation, which results from plastic deformation of martensite, on the mechanical behaviour of pseudoelastic NiTi alloys. Based on phenomenological theory of martensitic transformation and crystal plasticity, a new three dimensional micromechanical model is proposed by coupling both the slip and twinning deformation mechanisms. The present model is implemented as User MATerial subroutine (UMAT) into ABAQUS/Standard to study the influences of plastic deformation on the stress and strain fields, and on the evolution of martensite transformation. Results show that with the increasing of plastic deformation the residual strain increases and the phase transformation stress–strain curves from the martensite to austenite become steeper and less obvious. Both characteristics, stabilisation of martensite and impedance of the reverse transformation, due to plastic deformation are captured.