A microstructural model for homogenisation and cracking of piezoelectric polycrystals

Abstract

An original three-dimensional generalised micro-electro-mechanical model for computational homogenisation and analysis of degradation and micro-cracking of piezoelectric polycrystalline materials is proposed in this study. The model is developed starting from a generalised electro-mechanical boundary integral representation of the micro-structural problem for the individual bulk grains and a generalised cohesive formulation is employed for studying intergranular micro-damage initiation and evolution into intergranular micro-cracks. To capture the electro-mechanical coupling at the evolving damaging intergranular interfaces, standard mechanical cohesive laws are enriched with suitable electro-mechanical terms. The boundary integral formulation allows the expression of the microstructural piezo-electric boundary value problem in terms of generalised grain boundary and intergranular displacements and tractions only, which implies some definite modelling advantages, namely: a) the natural inclusion of the intergranular cohesive laws in the formulation; b) a meaningful simplification of the analysis pre-processing stage, i.e. input data and mesh preparation; c) the reduction of the number of degrees of freedom of the overall analysis with respect to other popular numerical methods. The developed formulation has been applied to the computation of the effective properties, i.e. material homogenisation, of crystal aggregates and to the investigation of micro-cracking in PZT-4 ceramics, providing consistent results.