Multi-Axial Behavior of Ferroelectrics with Two Types of Micro–Macro Mechanical Models

Abstract

Ferroelectric ceramics exhibit a significantly different nonlinear behavior with external electric and mechanical fields applied at angles to the initial poled direction. This angle dependent response of the ferroelectric polycrystals are predicted by two types of models based on irreversible thermodynamics and physics of domain switching. The first type is a uniaxial model dealing with simultaneous evolution of three variants at a given instant. The back stress and electric fields, assumed as linear functions of remnant strain and polarization developed by the domain switching process, are introduced in the model to assist or resist further switching process. The second type is a three dimensional model that considers all six variants of a tetragonal crystal in each grain and the dissipation associated with grain boundary constraints are brought into the model through switching criterion. The pressure dependent constraints imposed by the surrounding grains on the grain of interest at its boundary during domain switching process is correlated with the resistance experienced by a ferroelectric single crystal on its boundary during domain switching. Taking all the domain switching possibilities, the volume fractions of each of the variants are tracked and homogenized for macroscopic behavior. Numerical simulations were carried out for the behavior of ferroelectrics using both the models and the outcome was found to be qualitatively comparable with experimental observations given in literature.