3次元EBSD計測モデルに基づく結晶均質化有限要素解析による圧電セラミックス材料の特性評価

抄録

Material properties of a polycrystal piezoelectric ceramic, barium titanate BaTiO₃, were analyzed by the two-scale crystallographic homogenization method. Three-dimensional (3-D) micro-finite element (FE) model was constructed based on the electron backscatter diffraction (EBSD) measured crystal orientation distribution images. We obtained 13 EBSD images of 128 × 100pixels, which the measurement interval was 0.634μm in-plane and the average amount of polishing was 1.66μm in thickness (normal) direction of the specimen. Each voxel of EBSD was assigned into a solid FE in-plane with maintaining resolution of EBSD measurement. Since coefficient matrix of finite element equation for the electromechanical coupling problem is not positive definite and ill-condition, an iterative partitioned coupling procedure based on the block Gauss-Seidel (BGS) method with parallel conjugate gradient (CG) solver was applied to the multi-scale analysis. We investigated on micro finite element modeling with crystal orientation distribution and convergences of both the BGS method and the CG solver. The number of BGS iterations was about 15 in this analysis and it was independent on degrees of freedom of the micro-FE model based on the EBSD-measured images. The combined-method of the BGS and the CG solver was suitable for the large-scale analysis using experimental EBSD measurement-based realistic voxel FE model. The representative volume element (RVE) size was also determined based on the orientation distribution function analyses of EBSD voxel data. The least RVE size was 25000μm³, which corresponds to include 150 crystal grains.