Prediction of crack paths in ferroelectrics with anisotropic fracture toughness

Abstract

Crack paths in ferroelectrics under combined electromechanical loading have been investigated both experimentally and numerically in the past. The influence of electric fields on the deflection behavior being of particular interest, specimens exhibiting a pronounced curvature of crack growth have been predominantly considered. In this regard, a series of three-point bending tests with eccentric notch has recently provided valuable experimental results under various electric loading conditions below the coercivity. Numerical simulations, however, nowadays do not match these crack paths satisfactorily. One important aspect is the distinctive and well-known anisotropy of fracture toughness in ferroelectrics. While isotropic simulations in anisotropic structural materials are demonstrably not suitable for predicting crack paths, different modeling approaches accounting for anisotropic crack resistance associated with global and local directions of polarization are investigated in this paper. Numerical simulations of crack paths are based on a new J-integral related criterion, incorporating the anisotropic elastic, piezoelectric and dielectric properties just as the fracture toughness and are compared to recent experimental findings.