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.

过去已经通过实验和数值研究了在组合机电载荷下铁电体中的裂纹路径。电场对偏转行为的影响是特别令人感兴趣的，主要考虑表现出明显的裂纹扩展曲率的试样。在这方面，一系列偏心缺口三点弯曲试验最近在矫顽力以下的各种电负载条件下提供了有价值的实验结果。然而，现在的数值模拟不能令人满意地匹配这些裂纹路径。一个重要的方面是铁电体中断裂韧性的独特且众所周知的各向异性。虽然各向异性结构材料中的各向同性模拟显然不适合预测裂纹路径，本文研究了考虑与全局和局部极化方向相关的各向异性抗裂性的不同建模方法。裂纹路径的数值模拟基于一个新的J -积分相关标准，将各向异性弹性、压电和介电特性与断裂韧性结合起来，并与最近的实验结果进行比较。