A Micromechanics-Based Hysteresis Model for Ferroelectric Ceramics

Based on the mechanics of domain switch and irreversible thermodynamics, a micromechanics-based model that incorporates the effect of polarization strain and electric polarization in the switched domain is developed to predict the evolution of new domain and the associated hysteresis loops of a ferroelectric ceramic. The new domain concentration c r associated with the remanent polarization P r , and the new domain concentration c c at the coercive field E c , are also found in terms of the saturation polarization P s , the coercive field E c , and the dielectric permittivity of the parent domain. The theory is developed with a homogenization technique for a coupled, dual-phase electromechanical system with an evolving microstructure, whose driving force arises from the reduction of Gibbs’ free energy and whose resistance force comes from the energy dissipation due to domain wall movement. The developed theory is applied to a lanthanum doped lead zirconate titanate (PLZT), first for the calculation of its hysteresis electric displacement versus electric field ( D vs. E) relation and the butterfly-shaped longitudinal strain versus electric field (∊ vs. E) relation, and then for its nonlinear compressive stress-strain relation and nonlinear depolarization. The results are shown to provide the essential features of the hysteresis behavior and found to be in quantitative accord with the experimental data.