A nonlinear model of piezoelectric polycrystalline ceramics under quasi-static electromechanical loading

Abstract

Nonlinear characteristics of tetragonal perovskite type polycrystalline piezoelectric ceramics under electromechanical loading are theoretically simulated using a threedimensional micromechanical model. The model consists of many differently oriented grains which form the bulk material. Uni-axial, quasi-static loading is applied in the simulations. The calculations which are based on a linear constitutive and nonlinear domain switching model are performed at each grain. All grains are assumed to be statistically random oriented at the virgin state.The behavior of piezoelectric ceramics under constant compressive stress which is applied in the same direction of the cyclic electric field is investigated. The macroscopic response of the bulk ceramics to the applied loading is predicted by averaging the response of individual grains. It is assumed that a domain or a microstructure switches if the reduction in potential energy of the polycrystal exceeds a threshold of critical energy per unit volume of the material. Due to intergranular effects domain switching may occur in reality even for those grains, for which the critical energy level is not reached. This effect is modeled by introducing a probability for domain switching as a function of the actual energy level related to the critical energy level. By use of the probability functions, it is possible to model the nonlinearity even in a small electromechanical loading range. The effect of different probability functions, and material parameters are also analysed. The results of simulations have been compared with experimental data from literature.