Multi-scale finite element analyses of sheet metals by using SEM-EBSD measured crystallographic RVE models

In this study, two multi-scale analyses codes are newly developed by combining a homogenization algorithm and an elastic/crystalline viscoplastic finite element (FE) method (Nakamachi, E., 1988. A finite element simulation of the sheet metal forming process. Int. J. Numer. Meth. Eng. 25, 283–292; Nakamachi, E., Dong, X., 1996. Elastic/crystalline viscoplastic finite element analysis of dynamic deformation of sheet metal. Int. J. Computer-Aided Eng. Software 13, 308–326; Nakamachi, E., Dong, X., 1997. Study of texture effect on sheet failure in a limit dome height test by using elastic/crystalline viscoplastic finite element analysis. J. Appl. Mech. Trans. ASME(E) 64, 519–524; Nakamachi, E., 1998. Elastic/crystalline viscoplastic finite element modeling based on hardening–softening evaluation equation. In: Proc. of the 6th NUMIFORM, pp. 315–321; Nakamachi, E., Hiraiwa, K., Morimoto, H., Harimoto, M., 2000a. Elastic/crystalline viscoplastic finite element analyses of single- and poly-crystal sheet deformations and their experimental verification. Int. J. Plasticity 16, 1419–1441; Nakamachi, E., Xie, C.L., Harimoto, M., 2000b. Drawability assessment of BCC steel sheet by using elastic/crystalline viscoplastic finite element analyses. Int. J. Mech. Sci. 43, 631–652); (1) a “semi-implicit” finite element (FE) code and (2) a “dynamic explicit” FE code. These were applied to predict the plastic strain induced yield loci and the formability of sheet metal in the macro scale, and simultaneously the crystal texture and hardening evolutions in the micro scale. The isotropic and kinematical hardening laws are employed in the crystalline plasticity constitutive equation. For the multi-scale structure, two-scales are considered. One is a microscopic polycrystal structure and the other a macroscopic elastic plastic continuum. We measure crystal morphologies by using the SEM-EBSD apparatus with a unit of about 3.8 μm voxel, and define a three dimensional (3D) representative volume element (RVE) for the micro polycrystal structure, which satisfy the periodicity condition of crystal orientation distribution. A “micro” finite element modeling technique is newly established to minimize the total number of finite elements in the micro scale. Next, the “semi-implicit” crystallographic homogenization FE code, which employs the SEM-EBSD measured RVE, is applied to the 99.9% pure-iron uni-axial tensile problem to predict the texture evolution and the subsequent yield loci in the various strain paths. These “semi implicit” results reveal that the plastic strain induced anisotropy in the micro and macro levels can be predicted by our FE analyses. The kinematical hardening law leads a distinct plastic strain induced anisotropy. Our “dynamic-explicit” FE code is applied to simulate the limit dome height (LDH) test problem of the mild steel DQSK, the high strength steel HSLA and the aluminum alloy AL6022 sheet metals, which were adopted as the NUMISHEET2005 Benchmark sheet metals (Smith, L.M., Pourboghrat, F., Yoon, J.-W., Stoughton, T.B., 2005. NUMISHEET2005. In: Proc. of 6th Int. Conf. Numerical Simulation of 3D Sheet Metal Forming Processes, PART A and B(Benchmark), pp. 409–451) to estimate formability. The “dynamic explicit” results reveal that the initial crystal orientation distribution has a large affects to a plastic strain induced texture and anisotropic hardening evolutions and sheet formability.     

Virtual improvement of ice cream properties by computational homogenization of microstructures

Optimal shape design of microstructured materials has recently attracted a great deal of attention in materials science. The shape and the topology of the microstructure have a significant impact on the macroscopic properties. This paper presents different computational models of random microstructures, to virtually improve the physical properties of ice cream. Several sensory properties of this heterogeneous material issued from food industry are directly controlled by the elastic and thermal conducting ones. The material effective elastic and thermal conducting properties are obtained through direct large scale numerical simulations. The different formulations address the problem of finding the shape of the representative microstructural element for random heterogeneous media that increase the elastic moduli and thermal conductivity compared to existing products. The computational models are established using finite element method and images of virtual microstructures. In this paper we propose a new model of microstructures. This model is constructed with hexagonal prismatic rods and plates with volume fractions around 0.7 for the hard phase represented by hexagons of ice. A comparison between three two-phase elastic heterogeneous microstructures models is drawn. This illustrates the concept of design of microstructures using computational homogenization tools.     

非均质Cosserat连续体细-宏观均匀化条件

基于平均场理论的多尺度模拟关键问题之一是给定恰当的表征元(RVE)边界条件,以使均匀化过程满足Hill-Mandel细宏观能量等价条件,也即Hill宏观均匀化条件。对于非均质Cosserat连续体,已有的研究工作只能得到合理的混合平动位移-偶应力表征元边界条件,常用的一致平动位移-转角以及周期边界条件等均不能使用,给计算均匀化算法推导和实施带来了困难,也阻碍了多尺度分析方法的进一步发展与应用。为此,本文在推导和建立一个新的Hill定理版本基础上,不仅成功地给定了多种强形式表征元边界条件,而且构造出了合理的弱形式周期边界条件,这些条件既满足细宏观能量等价也符合一阶平均场理论基本假定,可在均匀化方法中推广与应用。     

A version of Hill＇s lemma for Cosserat continuum

On the basis of Hill＇s lemma for classical Cauchy continuum, a version of Hill＇s lemma for micro-macro homogenization modeling of heterogeneous Cosserat continuum is presented in the flame of average-field theory. The admissible boundary conditions required to prescribe on the representative volume element for the modeling are extracted and discussed to ensure the satisfaction of Hill-Mandel energy condition and the first-order average field theory.     

金属材料的强度与应力-应变关系的球压入测试方法

压入法获取材料单轴应力-应变关系和抗拉强度对服役结构完整性评价有重要的基础意义.假定材料均匀连续、各向同性、应力应变关系符合Hollomon律,基于能量等效假定,即代表性体积单元(representativevolume element, RVE)的vonMises等效和有效变形域内能量中值等效假定,本文提出了关联材料载荷、深度、球压头直径和Hollomon律的四参数半解析球压入(semi-analyticalspherical indentation,SSI)模型.通过球压入载荷-深度试验关系获得材料的应力-应变关系和抗拉强度.考虑压入过程中的损伤效应,针对金属材料提出了用于球压入测试的材料弹性模量修正模型.对11种延性金属材料完成了球压入试验,采用本文提出的球压入试验方法测到的弹性模量、应力-应变关系和抗拉强度与单轴拉伸试验结果吻合良好.      

3D multiscale modeling to predict the elastic modulus of polymer/nanoclay composites considering realistic interphase property

The elastic modulus of a nanocomposite reinforced with nanoclay was studied using the 3D finite-element method. It is widely accepted that interphase between nanoparticle and matrix plays an important role in the performance of the nanocomposite. Thus, a representative volume element (RVE) consisted of three phases (i.e. matrix, interphase and nanoclay) was simulated. In addition, to have a realistic estimation of elastic modulus of the interphase region, the modulus was computed using the available analytical formula. Since the nanoclays have been known as platelets and to investigate the effect of the third dimension, the nanoclay was simulated as a thin cuboid. The effect of various geometrical parameters, such as the change of the nanoclay contact area at a constant volume fraction of nanoclay, the variation of the nanoclay angle in the planes perpendicular and parallel to the loading direction, and the RVE dimensions, on the elastic modulus of a nanocomposite was considered. The results revealed that the increase in contact area of the nanoclay at a constant volume of nanoclay led to an increase in the elastic modulus of the nanocomposite. Furthermore, the change in the angle of nanoclay with respect to the plane parallel to loading direction has considerable effects on the elastic modulus of the nanocomposite, whereas this effect is negligible for the alignment angle perpendicular to the plane of the loading direction. Finally, unlike the previous studies, the results of the finite-element modeling were compared with three-phase theory of Mori–Tanaka.     

基于Gurson损伤力学模型的糜棱岩成因有限元分析

应用孔洞损伤的Gurson模型,建立糜棱岩原岩细观孔洞损伤体胞单元,提出糜棱岩成因的损伤力学观点,统一解释糜棱岩成因研究中一些独特的地质现象.对一种具体原岩———花岗岩的细观孔洞损伤体胞单元作了有限元计算分析,并根据计算结果讨论了各种应力对糜棱化过程的影响.     

梯度增强Cosserat连续体的广义Hill定理

基于经典Cauchy连续体的Hill定理,在平均场理论的框架下导出了梯度增强Cosserat连续体细、宏观均匀化方法的广义Hill定理。在梯度增强Cosserat连续体中,不仅宏观样条点上的应变和应力张量,而且它们的梯度均作用于与该样条点相关联的细观表征元（RVE）。依据此广义Hill定理,对梯度增强Cosserat连...     

Fourier-based incremental homogenisation of coupled unilateral damage–plasticity model for masonry structures

In structural analysis of large masonry structures, nondemanding computation effort, numerical stability and simplified model assembly and meshing often have a higher priority over precise details of local stress or strain responses. This paper presents the development of a Fourier-based incremental homogenisation technique, where the macro–micro transformations of mechanical variables are derived by incremental variational problems to minimise the potential energy in representative volume elements (RVEs) with respect to local fluctuating displacement fields expanded in Fourier series. In addition to the proposed homogenisation technique, a unilateral damage–plasticity constitutive model for mortar joints in the RVE is developed within the framework of thermomechanics, which accounts for the stiffness and strength degradation (or recovery) due to the transverse crack opening/closing in the mortar joints. The numerical solution for the homogenisation problem and the performances of the proposed coupled-damage plastic mode and Fourier-based homogenisation scheme verified by detailed case studies are presented. It has been shown that the computational effort of the analysis with the proposed modelling technique can be considerably reduced by more than 20% as compared with that of the discrete modelling technique.