Multi Scale Finite Element Analyses By Using SEM-EBSD Crystallographic Modeling and Parallel Computing

A crystallographic homogenization procedure is introduced to the conventional static-explicit and dynamic-explicit finite element formulation to develop a multi scale – double scale – analysis code to predict the plastic strain induced texture evolution, yield loci and formability of sheet metal. The double-scale structure consists of a crystal aggregation – micro-structure and a macroscopic elastic plastic continuum. At first, we measure crystal morphologies by using SEM-EBSD apparatus, and define a unit cell of micro structure, which satisfy the periodicity condition in the real scale of polycrystal. Next, this crystallographic homogenization FE code is applied to 3N pureiron and “Benchmark” aluminum A6022 polycrystal sheets. It reveals that the initial crystal orientation distribution – the texture – affects very much to a plastic strain induced texture and anisotropic hardening evolutions and sheet deformation. Since, the multi-scale finite element analysis requires a large computation time, a parallel computing technique by using PC cluster is developed for a quick calculation. In this parallelization scheme, a dynamic workload balancing technique is introduced for quick and efficient calculations. INTRODUCTION Recently, the demands for a high formability and high strength automotive panels to reduce the weight, fuel consumption and the environmental pollution are rapidly increased. Therefore, a new computational design tool based on the crystallographic structure analysis and the finite element (FE) analysis is strongly required[1]-[3]. Here, a crystallographic homogenization procedure is newly introduced to the conventional static-explicit and dynamic-explicit finite element procedure for a multi scale – double scale – analysis[4]. It can predict the plastic strain induced texture evolution, hardening, yield loci and formability of sheet metal. This multi scale finite element code can be used for the high strength and high formability sheet material design. This double-scale structure consists of a micro-crystalstructure and a macro-continuum. At first, we model a 3D micro-crystalstructure, which satisfy the periodicity of orientation by using SEM-EBSD measurement results. Next, crystallographic homogenization FE analyses are executed to predict the texture evolution and yield loci, and Benchmark3 A6022 sheet deformation. In these multi scale analyses, a parallel computing scheme is employed to reduce the time consuming. MULTI SCALE ELASTIC PLASTIC FINITE ELEMENT FORMULATION Figure1 shows a double scale structures, such as a macro-continuum Ω and a micro-crystalstructure Y. In the micro-structure, a unit cell consists of an polycrystal aggregation and is very small compared with the macro region Ω by a scale factor 1 << λ [4]. FIGURE 1. Macro-continuum and micropolycrystal structure –Double scale –.