Multi-scale parallel finite element analyses of LDH sheet formability tests based on crystallographic homogenization method

A multi-scale parallel finite element (FE) procedure based on the crystallographic homogenization method was applied to the LDH sheet formability test analysis. For the multi-scale structure, two scales are considered. One is a microscopic polycrystal structure and the other is a macroscopic elastic plastic continuum. The analysis code can predict the formability of sheet metal in macro-scale, simultaneously the crystal texture and hardening evolutions in the micro-scale (Nakamachi E et al. Int J Plasticity 2007;23:450–8). Since huge computation time is required for the nonlinear dynamic multi-scale FE analysis, parallel computing technique based on domain partitioning of FE model for macro-continuum is introduced into the multi-scale code using the message passing interface (MPI) library and PC cluster (Kuramae H et al. In: Proceedings of the eighth international conference on computational plasticity, Part 1, 2005. p. 622–5). The explicit time stepping solution scheme in the nonlinear multi-scale FE dynamic problem is well-suited for parallel computing on distributed memory environment such as PC cluster because solving simultaneous equation is not required. We measured crystal morphologies of four automotive sheet metals, aluminum alloy sheet metals A6022-T43 and A5182-O, an asymmetrically rolled aluminum alloy sheet metal A6022-ASR, and mild steel HC220YD, by using the scanning electron microscope (SEM) with electron back scattered diffraction (EBSD) analyses, and defined a three-dimensional representative volume element (RVE) of micro polycrystal structure, which satisfy the periodicity condition of crystal orientation distribution. We evaluate not only macroscopic formability of the automotive sheet metals by the multi-scale LDH test analysis, but also microcrystalline texture evolution during plastic deformation. Furthermore, a relationship between the macroscopic formability and the microcrystal texture evolution was discussed through looking at multi-scale FE results. It is concluded that the mild steel HC220YD was the highest formability than the aluminum alloy sheet metals because of remaining and generating the γ-fiber texture, such as {1 1 1}〈1 1 0〉–{1 1 1}〈1 1 2〉 orientations, during plastic deformation.