A constitutive model for ferroelectric polycrystals

A constitutive model is developed for the non-linear switching of ferroelectric polycrystals under a combination of mechanical stress and electric field. It is envisaged that the polycrystal consists of a set of bonded crystals and that each crystal comprises a set of distinct crystal variants. Within each crystal the switching event, which converts one crystal variant into another, gives rise to a progressive change in remanent strain and polarisation and to a change in the average linear electromechanical properties. It is further assumed that switching is resisted by the dissipative motion of domain walls. The constitutive model for the progressive switching of each crystal draws upon elastic-plastic crystal plasticity theory, and a prescription is given for the tangent moduli of the crystal, for any assumed set of potentially active transformation systems. A self-consistent analysis is used to estimate the macroscopic response of tetragonal crystals (representative of lead titanate) under a variety of loading paths. Also, the evolution of the 'switching surface' in stress-electric field space is calculated. Many of the qualitative features of ferroelectric switching, such as butterfly hysteresis loops, are predicted by the analysis. (C) 1999 Elsevier Science Ltd. All rights reserved.