Dynamic fracture behavior for functionally graded piezoelectric bi-materials with interfacial cracks near a circular hole

Abstract

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.