A multiscale modelling analysis of the contribution of crystalline elastic anisotropy to intergranular stresses in ferroelectric materials

Abstract

Internal stresses (residual stresses) and their evolution under electromechanical loading play a significant role in the performance and lifetime of ferroelectric materials. Internal stresses can be induced by the manufacturing process or the packaging conditions. At a finer scale, due to the heterogeneity of ferroelectric materials (polycrystalline structure), part of the ferroelectric strain must normally be accommodated locally, resulting in internal stresses when an electromechanical load is applied. In most modelling approaches the contribution of crystalline elastic anisotropy to internal stresses is neglected compared to the domain switching contribution. Using a micromechanical modelling approach, we examine the contribution of crystalline elastic anisotropy to the macroscopic behaviour and to the internal stress distribution in ferroelectric polycrystals under electromechanical loading. It is shown that the predicted macroscopic ferroelectric strain and the level of intergranular stress can be underestimated by up to 50% if crystalline elastic anisotropy is neglected. Consequently it is recommended that, contrary to current practice, crystalline anisotropy be included in the micromechanical modelling of ferroelectric ceramics.