基于位错密度的晶体塑性有限元方法的数值模拟及参数标定

运用ABAQUS有限元分析软件对基于位错密度的晶体塑性有限元方法(CPFEM)及其晶体塑性参数进行了深入的研究。结果表明,CPFEM晶体塑性本构可以准确地体现材料的力学性能。通过讨论不同晶体塑性参数,得到各个参数可以分别控制材料的屈服强度、硬化过程、剪切应变速率、极限强度等性能。此外,为了标定材料的晶体塑性参数引入多晶的代表体积单元(RVE)模型,并讨论了晶粒数以及晶粒规整度对于RVE模型的影响。结果表明,RVE模型的晶粒数达到临界值750个时能够体现等轴晶的宏观各向同性。结合晶体塑性RVE模拟和拉伸试验结果,对Inconel 718合金的晶体塑性参数进行标定,晶体塑性有限元的模拟结果和实验结果的误差小于5%。证明经过标定的晶体塑性参数可以准确反映Inconel 718的力学性能,也使得进一步研究该合金介观晶粒尺度的力学性能成为可能。     

THE PARTITION OF UNITY METHOD

A new finite element method is presented that features the ability to include in the finite element space knowledge about the partial differential equation being solved. This new method can therefore be more efficient than the usual finite element methods. An additional feature of the partition-of-unity method is that finite element spaces of any desired regularity can be constructed very easily. This paper includes a convergence proof of this method and illustrates its efficiency by an application to the Helmholtz equation for high wave numbers. The basic estimates for a posteriori error estimation for this new method are also proved. © 1997 by John Wiley & Sons, Ltd.     

Determination of lattice level energy efficiency for fatigue crack initiation

Fatigue crack initiation life prediction is a fundamentally challenging problem that is of prime importance as a significant portion of the fatigue life is spent in the initiation phase. In spite of the extensive efforts of research over the past two decades, the concept of crack initiation still remains as an enigma in science. The major challenges in predicting crack initiation life in industry are the evaluation of the crack initiation parameters such as the maximum resolved shear stress range, maximum slip band width and the energy efficiency coefficient. In this paper, we show that the energy efficiency can be successfully estimated with good accuracy by performing lattice level crystal plasticity‐based computational simulations on representative models. The lattice level plasticity‐based finite element computations are reported for the case of single crystal copper in this work, and the results show that this strategy leads to higher accuracy than the existing idea of approximating the efficiency factor. The results show that this strategy could be of great use in improving the reliability in prediction of crack initiation life. The effectiveness of this computational procedure would greatly reduce the financial investments necessary to perform experimental analysis of all structures to determine the crack initiation parameters, as it would require just a single measurement to quantify the measurement of efficiency.     

极薄带异步轧制滑移带演化的晶体塑性有限元分析

以单层晶极薄带轧制为研究对象,采用多尺度晶体塑性有限元方法模拟其在拉-压-剪复合应力状态下的宏观剪切带和微观滑移带演化,优化极薄带材轧制工艺。在微观层次上,每个晶粒被离散成若干个有限元单元,且每个积分点采用单晶体本构模型。宏-微观层次模拟的共同特征是滑移带演化高度的各向异性和局部化,微观层次的模拟更加明显。结果表明:新剪切带随轧制区施加额外剪切变形而形成,在拉-压-剪复合应力下,强剪切造成已缩窄的主次剪切带随轧制压下的增大而又扩展。单系滑移带在各变形晶粒内的演化差异很大,存在主次滑移,随压-剪复合应力状态的增强而形成亚滑移带。在拉-压-剪复合应力下,单滑移扩展和叠加形成贯穿晶界的累积滑移带,晶界起到很好的滑移承载和传递作用。     

Strain rate and orientation-dependent strain hardening of Mg–9Li–Al using crystal plasticity

A crystal plasticity finite element model was proposed considering slip and twinning interactions. The grain morphology and crystallographic orientations were introduced into the model to describe the microstructure of duplex polycrystalline Mg–9Li–Al. The activation of the slip systems and the strain localisation with respect to initial grain orientations were investigated. In addition, the effects of phase distributions and volume fractions on the macroscopic responses and on strain hardening rates were analysed. The results show that the strain hardening is rate-dependent but the texture is less sensitive to strain rate. The distribution of a phase and its volume fraction play primary roles in governing the mechanical response.     

考虑位错密度和损伤的NiCoCrFe高熵合金晶体塑性有限元分析EI北大核心CSCD

结合实验和晶体塑性有限元方法研究准静态加载NiCoCrFe高熵合金有限变形过程中的宏观和微观力学响应、损伤行为以及微观结构演化。使用电子背散射衍射技术(EBSD)对拉伸实验变形前后NiCoCrFe的微观结构进行表征。通过修改强化模型和流动准则分别在CPFEM模型中引入位错密度内部状态变量和连续介质损伤因子,并结合拉伸实验应力-应变曲线确定NiCoCrFe相关的模型参数。结果表明:考虑位错密度和损伤的CPFEM模型可以有效地描述NiCoCrFe宏观和微观力学响应。CPFEM模型合理预测NiCoCrFe颈缩区域的变形形状和尺寸,其中实验获得的颈缩区域长度比预测结果小7%,CPFEM预测的颈缩区域宽度比实验结果大23%。CPFEM模型预测NiCoCrFe拉伸变形后的织构演化同EBSD表征结果大致相同,均表现为弱的(100)∥RD以及强的(111)∥RD纤维织构。在三维微观结构损伤分析中,CPFEM模型预测的损伤在应力集中以及位错密度集中的晶界处萌生,表现为晶间损伤机制,并且随着变形的增加损伤逐渐向晶粒内部扩展。     

孔洞在晶界上长大行为的模拟

通过编制率相关有限元用户子程序,运用晶体有限元,通过建立一个包含球形孔洞的双晶粒模型,对FCC晶体中孔洞在晶界的长大行为进行了分析。计算中,晶粒1的取向固定为(0°,45°,90°),晶粒2的取向分别为(35°,45°,90°),(60°,45°,90°),(0°,0°,0°),分别对应于单胞A,单胞B,单胞C,晶界与X轴方向的夹角θ分别取0°,45°,60°。计算结果表明:单胞的断裂模式与两晶粒的取向因子的差异有关,对于两晶粒的取向因子差异最大的单胞B,单胞沿晶界处的等效塑性应变比单胞其它地方的应变大,且最大等效塑性应变在三个单胞中为最大,单胞易于发生沿晶断裂。而对于两晶粒的取向因子差异最小的单胞C,沿晶界的等效应变较小,单胞易于发生穿晶断裂。晶界与X轴方向的夹角θ为45°时,单胞沿晶界处的等效应变较大,单胞易发生沿晶断裂。     

The concept of control points in hybrid discontinuous Galerkin methods—Application to geometrically nonlinear crystal plasticity

A new concept for hybrid discontinuous Galerkin (DG) methods is presented: control points. These are defined on the interelement boundaries. The concept makes it possible to formulate element shape functions without nodes. Moreover, the theory is not restricted to certain element shapes. Furthermore, one can formulate the discrete model such that the displacement is either continuous or discontinuous at the control points. Classical continuous isoparametric elements are included as special case. As an additional new feature, a regularization technique for very high strain rate sensitivity exponents up to 1000 in finite single crystal viscoplasticity is presented and implemented into the new hybrid DG framework. In addition, the numerical linearization used in an earlier work is carried out analytically in this work. To the knowledge of the authors, this work presents the first hybrid DG implementation of geometrically nonlinear plasticity, here in the context of single crystal plasticity. The regularization method in combination with the DG formulations facilitates a very simple implementation leading to a numerically efficient, robust, and locking‐free model. Two examples are investigated: the deformation of a planar double slip single crystal exhibiting localization in the form of shear bands and an oligocrystal under uniaxial load.     

A numerical study of fatigue crack closure induced by plasticity

Crack closure delays the intrinsic mechanisms responsible for crack growth, therefore, it must be considered in fatigue crack growth modelling. The objective of this work is to develop a numerical procedure to predict crack closure induced by plasticity. First the crack closure was experimentally measured on M(T) 6082‐T6 aluminium alloy specimens of 3 mm thickness. A pin microgauge was used with the compliance technique. Then different parameters of the numerical procedure were analysed, namely the finite element mesh and the crack propagation scheme. The size of crack‐tip elements has an important influence and it is recommended to be of the same order of cyclic plastic zone. Crack‐opening levels only 10% lower than experimental results were obtained considering kinematic hardening and two load cycles in each increment.