A Microstructural Model for Micro-Cracking in Piezoceramics

Piezoelectric ceramics are employed in several applications for their capability to couple mechanical and electrical fields, which can be advantageously exploited for the implementation of smart functionalities. The electromechanical coupling, which can be employed for fast accurate micro-positioning devices, makes such materials suitable for application in micro electromechanical systems (MEMS). However, due to their brittleness, piezoceramics can develop damage leading to initiation of micro-cracks, affecting the performance of the material in general and the micro-devices in particular. For such reasons, the development of accurate and robust numerical tools is an important asset for the design of such systems. The most popular numerical method for the analysis of micro-mechanical multi-physics problems, still in a continuum mechanics setting, is the Finite Element Method (FEM). Here we propose an alternative integral formulation for the grain-scale analysis of degradation and failure in polycrystalline piezoceramics. The formulation is developed for 3D aggregates and inter-granular failure is modelled through generalised cohesive laws