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。     

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.      

晶体取向对单晶体断裂特征影响的模拟分析

结合Ni基单晶合金制三种不同晶体取向的紧凑拉伸试样试验,本文利用考虑有限变形和品格转动效应的晶体滑移有限元程序对单晶体三维断裂特征进行了模拟计算分析,详细考察了裂纹尖端三维应力场特征和断裂特征,结果表明:晶体取向对裂纹尖端应力场有较大影响,但应力沿试样厚度方向明显分成两个部分,在试样心部,应力沿厚度方向变化不大,在试样外表面则明显变化。裂纹尖端张开位移(CTDD)沿厚度方向类似分成两个部分。垂直于滑移面的应力分量致单晶体的准解理断裂,即裂纹的起裂和扩展途径均与该应力分量有关。     

晶体取向对单晶体断裂特征影响的模拟分析

结合Ｎｉ基单晶合金制三种不同晶体取各的紧凑拉伸试样试验，本文利用考虑有限变形和晶格转动效应的晶体滑移有限元程序对单晶体三维裂特征进行了模拟计算分析，详细考察了裂纹尖端三维应力场特征和断裂特征，结果表明：晶体取向对裂纹尖端应力场有较大影响，但应力沿试样厚度方向明显分成两个部分，在试样心部，应力沿厚度方向变化不大，在试样外表面则明显变化，裂纹尖端张开位移（ＣＴＯＤ）沿厚度方向类似分成两个部分，垂直于滑     

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.      

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。     

分子动力学模拟纳米镍单晶的表面效应

对单晶镍纳米丝、纳米薄膜零温准静态拉伸破坏过程进行了分子动力学模拟．模拟表明表面效应对单晶纳米材料的原子运动及整体力学行为有显著影响．自由表面增加纳米材料的塑性、降低其强度,影响纳米材料的变形机制．受表面效应的作用,纳米镍丝强度与弹性模量均低于纳米镍薄膜．纳米薄膜的断裂接近脆性断裂,断裂强度符合Griffith理想晶体脆断理论;纳米镍丝在断裂过程中表现出微弱塑性．     

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.      

高应变率拉伸加载下无氧铜的本构模型

为了研究材料在高应变率拉伸加载下的动态响应,利用新型爆炸膨胀环实验技术开展了无氧铜试 样环的拉伸加载实验,采用激光干涉测试技术获得了试样环拉伸变形过程的径向速度历史。数值计算发现经 典JC模型不能较好地描述无氧铜试样环的膨胀过程,于是对JC模型进行了修改:增加了应变的指数硬化项 来描述拉伸变形的累积效应;增加了应变率的线性项描述拉伸加载时的应变率效应;利用实验数据拟合了修 改后的RJC模型参数,最终较好描述了无氧铜试样环的膨胀变形过程。     

单晶Ⅰ型弹塑性开裂取向效应的离散位错动力学-近场动力学研究

本文采用基于近场动力学框架的位错动力学叠加模型对FCC单晶在四种不同取向下的I型弹塑性开裂行为进行模拟研究.在模型中，无需预设裂纹扩展路径和内聚力区域，裂纹扩展路径由位错与裂纹的相互作用自动确定.数值计算了FCC单晶体在不同取向时的位错分布演化和裂纹扩展路径.分析表明取向会影响韧性和断裂行为，并证实了单晶体的单轴拉伸开裂行为遵循施密特因子关系，即位错更倾向于在施密特因子大的滑移面上形核并滑移.计算得到位错裂纹演化结果显示，不同取向时位错在滑移系上的分布和演化行为会导致不同晶体断裂模式.     

纯铜后继屈服面的测试与晶体塑性模型模拟

通过纯铜薄壁圆管试样的实测和晶体塑性模拟,用单试样法和多试样法对分别经历拉伸、扭转和组合拉扭变形的试样后继屈服面进行研究.考虑预变形方式、测点数目、测试顺序和指定平移应变等不同条件,对后继屈服面测定结果差异及屈服面内凹现象进行探讨.在此基础上,比较了单试样和多试样两种方法的合理性与有效性.数值模拟采用能反映Bauschinger效应的晶体塑性模型,试样有限元模型每个单元的晶体取向均随机生成,能反映多晶材料变形特征.模拟试验加载过程与真实试验一致.研究表明:(1)采用本文方法可再现真实试验过程,模拟后继屈服面测试展示的现象与实测相近,证实了方法的有效性和合理性;(2)模拟测试与实测均发现,薄壁圆管组合拉扭加载测得的后继屈服面可能出现内凹,单试样法测得屈服面的内凹现象尤为显著;(3)若试验材料的材质比较一致,用多试样法测试后继屈服比用单试样法更合理.     

磁电弹复合材料和刚性导电导磁圆柱压头的二维微动接触分析

本文求解平面应变状态下磁电弹复合材料半平面和刚性导电导磁圆柱压头的二维微动接触问题。假设压头具有良好的导电导磁性,且表面电势和磁势是常数。微动接触依赖载荷的加载历史,所以首先求解单独的法向加载问题,然后在法向加载问题的基础上求解循环变化的切向加载问题。整个接触区可以分为内部的中心粘着区和两个外部的滑移区,其中滑移区满足Coulomb摩擦法则。利用Fourier积分变换,磁电弹半平面的微动接触问题将简化为耦合的Cauchy奇异积分方程组,然后数值离散为线性代数方程组,利用迭代法求解未知的粘着/滑移区尺寸、电荷分布、磁感应强度、法向接触压力和切向接触力。数值算例给出了摩擦系数、总电荷和总磁感应强度对各加载阶段的表面接触应力、电位移和磁感应强度的影响。     

The “Inverse Hall-Petch” effect on the impact response of single crystal copper

Based on the available experimental and computational capabilities, a phenomenological approach has been proposed to formulate a hypersurface in both spatial and temporal domains to predict combined specimen size and loading rate effects on the material properties [1-2]. A systematic investigation is being performed to understand the combined size, rate and thermal effects on the properties and deformation patterns of representative materials with different nanostructures and under various types of loading conditions [3- 16]. The recent study on the single crystal copper response to impact loading has revealed the size-dependence of the Hugoniot curve. In this paper, the "inverse Hall-Petch" behavior as observed in the impact response of single crystal copper, which has not been reported in the open literature, is investigated by performing molecular dynamics simulations of the response of copper nanobeam targets subjected to impacts by copper nanobeam flyers with different impact velocities. It appears from the preliminary results that the "inverse Hall-Petch" behavior in single crystal copper is mainly due to the formation and evolution of disordered atoms and the interaction between ordered and disordered atoms, as compared with the physics behind the "inverse Hall-Petch"behavior as observed in nanocrystalline materials.     

FCC晶体中不均匀变形对空洞长大的影响

通过编制率相关有限元用户子程序,采用一个单胞模型研究了FCC晶体中孔洞在单晶及晶界的长大行为,分析了由于晶体取向及变形失配对孔洞长大和聚合的影响。研究结果表明：孔洞的形状和长大方向与晶体取向密切相关;晶界上孔洞的长大速度大于单晶中孔洞的长大速度;晶粒间的变形失配加速了晶界上孔洞的长大趋势,因而使材料易发生沿晶断裂,随着晶粒间取向因子差异的增加,孔洞越易沿着晶界长大。     

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.     

Void growth and coalescence in single crystals

Void growth and coalescence in single crystals are investigated using crystal plasticity based 3D finite element calculations. A unit cell involving a single spherical void and fully periodic boundary conditions is deformed under constant macroscopic stress triaxiality. Simulations are performed for different values of the stress triaxiality, for different crystal orientations, and for low and high work-hardening capacity. Under low stress triaxiality, the void shape evolution, void growth, and strain at the onset of coalescence are strongly dependent on the crystal orientation, while under high stress triaxiality, only the void growth rate is affected by the crystal orientation. These effects lead to significant variations in the ductility defined as the strain at the onset of coalescence. An attempt is made to predict the onset of coalescence using two different versions of the Thomason void coalescence criterion, initially developed in the framework of isotropic perfect plasticity. The first version is based on a mean effective yield stress of the matrix and involves a fitting parameter to properly take into account material strain hardening. The second version of the Thomason criterion is based on a local value of the effective yield stress in the ligament between the voids, with no fitting parameter. The first version is accurate to within 20% relative error for most cases, and often more accurate. The second version provides the same level of accuracy except for one crystal orientation. Such a predictive coalescence criterion constitutes an important ingredient towards the development of a full constitutive model for porous single crystals.     

Orientation effects in nanoindentation of single crystal copper

Numerical simulations and experimental results of nanoindentation on single crystal copper in three crystallographic orientations [(1 0 0), (0 1 1) and (1 1 1)] using a spherical indenter (3.4 μm radius) were reported. The simulations were conducted using a commercial finite element code (ABAQUS) with a user-defined subroutine (VUMAT) that incorporates large deformation crystal plasticity constitutive model. This model can take full account of the crystallographic slip as well as the orientation effects during nanoindentation. Distributions of the out-of-plane displacements and shear stresses as well as shear strains were obtained for indentation depths of up to 310 nm. The experimental studies were conducted using an MTS Nano Indenter (XP) system from which the load–displacement relationships were obtained while the surface topography as well as the surface profile along a line scan of indents were obtained using a Digital Instruments (Dimension 3100) atomic force microscope (AFM). The top views of the indent pile-up patterns under the spherical indenter show two-fold, three-fold, and four-fold symmetries for the (0 1 1), (1 1 1), and (1 0 0) orientations, respectively. Attempt was made to relate the anisotropic nature of the surface topographies around the indents in different crystallographic orientations of the single crystal copper specimens with the active slip systems and local texture variations. A reasonably good agreement had been obtained on several aspects of nanoindentation between the experimental and numerical results reported in this investigation as well as similar results reported in the literature. Thus, material properties of single crystal copper can be determined based on an appropriate numerical modeling of the nanoindentation on three crystallographic orientations.     

Effect of secondary orientation on notch-tip plasticity in superalloy single crystals

Numerical and experimental evolutions of slip fields in notched Ni-Base Single Crystal superalloy tensile specimens are presented as a function of secondary crystallographic orientation. The numerical predictions based on three-dimensional anisotropic elasticity and crystal plasticity are compared with experimental observations. The results illustrate the strong dependence of the slip patterns and the plastic zone size and shape on the secondary orientation of notches, which can have important consequences on crack initiation. Specific orientations or non-symmetric notch geometries lead to non-symmetric patterns on both sides of the sample. The computations show that strongly different plastic zones are expected in the core of the sample and at free surfaces. The ability of the anisotropic elastic model to anticipate the plastic domains, based on identifying dominant slip systems, is confirmed by the crystal plasticity computations, at low load levels. An important observation is that kink shear banding is a real deformation mode operating at crack tips and notches in high strength nickel-based single crystal superalloys for specific orientations.     

Strain hardening in bent copper foils

A series of systematic tensile and microbend tests were conducted on copper foil specimens with different thicknesses. The specimens were made of a copper foil having almost unidirectional crystal orientations that was considered to be nearly single-crystal. In order to investigate the effects of slip system interactions, two different crystal orientations relative to the tensile direction were considered in the tests: one is close to coplanar double-slip orientation, and the other is close to the ideal cube orientation (the tensile direction nearly coincides to [0 0 1]) that yields multi-planar multi-slip deformation. We extended the microbend test method to include the reversal of bending, and we attempted to divide the total amount of strain-hardening into isotropic and kinematic hardening components. In the tensile tests, no systematic tendency of size dependence was observed. In the microbend tests, size-dependent kinematic hardening behavior was observed for both the crystal orientations, while size dependence of isotropic hardening was observed only for the multi-planar multi-slip case. We introduce an extended crystal plasticity model that accounts for the effects of the geometrically necessary dislocations (GNDs), which correspond to the spatial gradients of crystallographic slips. Through numerical simulations performed using the model, the origin of the size-dependent behavior observed in the microbend tests is discussed.     

Computational nanoscale plasticity simulations using embedded atom potentials

In determining structure–property relations for plasticity at different size scales, it is desired to bridge concepts from the continuum to the atom. This raises many questions related to volume averaging, appropriate length scales of focus for an analysis, and postulates in continuum mechanics. In a preliminary effort to evaluate bridging size scales and continuum concepts with descritized phenomena, simple shear molecular dynamics simulations using the Embedded Atom Method (EAM) potentials were performed on single crystals. In order to help evaluate the continuum quantities related to the kinematic and thermodynamic force variables, finite element simulations (with different material models) and macroscale experiments were also performed. In this scoping study, various parametric effects on the stress state and kinematics have been quantified. The parameters included the following: crystal orientation (single slip, double slip, quadruple slip, octal slip), temperature (300 and 500 K), applied strain rate (10⁶–10¹² s⁻¹), specimen size (10 atoms to 2 μm), specimen aspect ratio size (1:8–8:1), deformation path (compression, tension, simple shear, and torsion), and material (nickel, aluminum, and copper). Although many conclusions can be drawn from this work, which has provided fodder for more studies, several major conclusions can be drawn.

• The yield stress is a function of a size scale parameter (volume-per-surface area) that was determined from atomistic simulations coupled with experiments. As the size decreases, the yield stress increases.

• Although the thermodynamic force (stress) varies at different size scales, the kinematics of deformation appears to be very similar based on atomistic simulations, finite element simulations, and physical experiments.

Atomistic simulations, that inherently include extreme strain rates and size scales, give results that agree with the phenomenological attributes of plasticity observed in macroscale experiments. These include strain rate dependence of the flow stress into a rate independent regime; approximate Schmid type behavior; size scale dependence on the flow stress, and kinematic behavior of large deformation plasticity.