This work aims to develop an effective method for evaluating the stress concentration at the tip of permeable interfacial cracks near a circular hole in functionally graded piezoelectric bi-materials. The structure is loaded by anti-plane incident SH-wave and all material parameters are assumed to obey exponential variations. Fracture analysis is performed by the Green function method, which is used to solve the boundary conditions problem. The mechanical model of the cracks is constructed by crack-conjunction and crack-deviation techniques so that the crack problem is simplified as solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factors (DSIFs) at the inner and the outer crack tips can be derived. The validity of the present method is verified by comparison with references. Numerical cases reveal parametric dependence of DSIFs on the geometry of circular holes and cracks, the characteristics of the incident waves and the inhomogeneity of materials. The method proposed in this paper can circumvent the limitations of using dual integral equations to deal with asymmetric defects and opens up a new way for the research on fracture problems in functionally graded piezoelectric materials with more complex defects.

这项工作旨在开发一种有效的方法来评估功能梯度压电双材料中圆孔附近可渗透界面裂纹尖端的应力集中。该结构由反平面入射 SH 波加载，假设所有材料参数服从指数变化。断裂分析采用格林函数法，用于求解边界条件问题。裂纹的力学模型是通过裂纹连接和裂纹偏离技术构建的，从而将裂纹问题简化为求解一系列第一类 Fredholm 积分方程，从中得到内部动态应力强度因子（DSIF）。并且可以导出外部裂纹尖端。通过与参考文献的对比验证了本方法的有效性。数值案例揭示了 DSIF 对圆孔和裂纹的几何形状、入射波的特性和材料的不均匀性的参数依赖性。本文提出的方法可以规避使用对偶积分方程处理不对称缺陷的局限性，为研究具有更复杂缺陷的功能梯度压电材料的断裂问题开辟了新途径。