The piezoelectric (PE)-piezomagnetic (PM) bi-layered structures possess superior magnetoelectric coupling effect and broad application prospects in the design of smart devices. However, due to the mismatch of material properties between two layers, the PE-PM layered composites are more sensitive to defects on the interfaces. Therefore, it is significative to investigate the interfacial crack properties of PE-PM bi-layered structures.

Considering the complexities of interfacial fracture studies under electro-magneto-mechanical coupling environment, the extended finite element method (X-FEM) will be introduced by virtue of its inherent superiorities in solving the discontinuous problems. Moreover, in order to further enhance the calculated performance of X-FEM, the crack-tip fields of an interfacial crack in PE-PM bimaterials and a crack terminating at the interface between PE-PM bimaterials are derived by analytical methods. Based on above crack-tip fields, the 24-fold and 32-fold crack-tip enrichment functions of X-FEM are presented, which are respectively suitable for the interfacial cracks and cracks terminating at interfaces. And then, the X-FEM with modified crack-tip enrichment functions will be utilized to study the static/dynamic fracture problems of interfacial cracks in PE-PM bi-layered structures, systematacially and deeply.

By the numerical examples, this paper discusses the positive influences of appropriate computational parameters, such as crack-tip enrichment functions, size of enrichment domain and mesh density, on the calculating accuracy, efficiency and stability. Besides, it also analyses the effects of geometry, applied coupling loadings, material polarization, fracture toughness and the angles between crack and interface on the fracture properties of interfacial cracks in PE-PM bi-layered structures. The related investigations can not only reveal the fracture mechanism of PE-PM layered composite structures, but also improve and extend the X-FEM successfully.