Micromechanical modelling of remanent properties of morphotropic PZT

The present paper investigates the capability of micromechanical material models to predict the ferroelectric behaviour of morphotropic PZT ceramics in a rate-independent approximation based on realistic microscopic material parameters. Starting point is a three-dimensional tetragonal model, which builds on the model of Pathak and McMeeking [2008. Three-dimensional finite element simulations of ferroelectric polycrystals under electrical and mechanical loading. Journal of the Mechanics and Physics of Solids 56, 663–683]. Volume fractions of the crystallographic variants represent the domain structure inside the grains. Interactions between the grains are taken into account by means of a representative volume element of the grain compound. A simplified set of realistic microscopic material parameters of the lattice in terms of Young's modulus, Poisson's ratio, dielectric constant, and spontaneous strain and polarisation is derived from experimental data and theoretical results given in the literature. The simulation of the macroscopic remanent polarisation and strain response due to two load cases shows explicitly that the tetragonal model is not capable to reproduce the behaviour of morphotropic PZT. Therefore, the model is extended by the rhombohedral phase, allowing a mixture of both phases with varying quantities inside the grains. A comparison of our results with experimental data shows a remarkably good agreement, revealing the capability of the extended model.