Modelling of Barium Titanate Microstructure Based on Both the Boundary Element Method and a Homogenization Technique

This paper presents the results of research undertaken to develop a grain boundary element (BE) formulation for the micromechanical analysis of multilayer barium titanate ceramics. The BE formulation of the elastic problem is generated for single grains and polycrystalline aggregate of barium titanate (BaTiO3) ceramics. In order to obtain BaTiO3 powder, the solid-state technique was applied. The microstructure of sintered BaTiO3 powder was examined in detail by scanning electron microscopy. Furthermore, image processing techniques and some numerical algorithms were employed to discretize the grain boundaries of ceramics. The single crystals of homogenous BaTiO3 are represented as anisotropic elastic regions. A comprehensive numerical code is generated and image processing techniques are applied in order to discretize the boundaries of grains and obtain the exact coordinates of elements on the boundaries. Average thorium is developed to obtain the macro-stress and macro-strain. The numerical results show that the developed method is valid for analysing polycrystalline materials. The numerical investigations also show that the developed algorithm is accurate enough to investigate the mechanical properties of a multilayer piezoelectric actuator. It is also found that the position of the interface as well as the type of material plays an important role in determining the effective properties of the multilayer actuator.