Effective properties of polycrystalline piezoelectric ceramics

Abstract
The paper focuses on the overall linear elastic, piezoelectric and dielectric response of polycrystalline piezoelectric ceramics. The effective material constants are calculated using the effective medium approximation and single-crystal data for the individual grains. This self-consistent approach takes into account the full electromechanical interaction coupling of the grains with their surroundings in a statistical way and makes use of the rigorous treatment of the piezoelectric inclusion problem and explicit representations of the electroelastic Eshelby tensor recently published in the literature. Numerical results for the effective properties of BaTiO₃ ceramics for different microstructural arrangements of crystal orientations are presented. Although we restricted ourselves to the linear material behaviour neglecting all nonlinear effects, the calculated results show remarkable agreement with experimental data and give an interesting insight into the effect of elastic, piezoelectric and dielectric interactions on the macroscopic material behaviour.