Material properties of a polycrystal piezoelectric ceramic, a barium titanate
BaTiO3, were analyzed by the two-scale crystallographic homogenization method. Threedimensional
(3-D) micro-finite element (FE) model was constructed based on the electron
backscatter diffraction (EBSD) measured crystal orientation distribution images. The images
are piled up to a 3-D voxel data of crystal orientation distribution by repeating mechanically
and chemically polishing, and EBSD measurement of the ceramic. We obtained 13 EBSD
images of 128×100 pixels, which measurement interval was 0.635μm in-plane and the
average amount of polishing was 1.66μm in thickness (normal) direction of specimen. Each
voxel of EBSD was assigned into 8-node solid FE in-plane with maintaining resolution of
EBSD measurement, and was divided into three FEs along thickness direction with same
crystal orientation, because of improvement of aspect ratio of FE. The total number of FEs
was 499,200 (=128×100×13×3) which corresponded to over two millions degrees of freedom.
In order to realize a large-scale micro-analysis using EBSD-measured voxel FE model, the
coupled problem of the piezoelectric material was solved by parallel conjugate gradient (CG)
method combined with the block Gauss-Seidel (BGS) method. The coupled micro-FE
equation to obtain characteristic function vectors was separated into two linear equations,
such as the elastic deformation and electrostatic analyses, by employing the BGS method, and
then the equations were solved by the parallel CG solver while substituting coupling terms
each other. Therefore, nested iterative scheme was constructed on a PC cluster. In addition,
the representative volume element (RVE) size was determined based on the orientation distribution function analyses of EBSD voxel data. The least RVE size was 25,000μm3, which
corresponded to include 150 crystal grains