Exact Solution for an Anti-Plane Interface Crack between Two Dissimilar Magneto-Electro-Elastic Half-Spaces

This paper investigated the fracture behaviour of a piezo-electro-magneto-elastic medium subjected to electro-magneto-mechanical loads. The bimaterial medium contains a crack which lies at interface and is parallel to their poling direction. Fourier transform technique is used to reduce the problem to three pairs of dual integral equations. These equations are solved exactly. The semipermeable crack-face magneto-electric boundary conditions are utilized. Field intensity factors of stress, electric displacement, magnetic induction, cracks displacement, electric and magnetic potentials, and the energy release rate are determined. The electric displacement and magnetic induction of crack interior are discussed. Obtained results indicate that the stress field and electric and magnetic fields near the crack tips exhibit square-root singularity. 1. Introduction Mechanics of magneto-electro-elastic solid has gained considerable interest in the recent decades with increasable wide application of piezoelectric/piezomagnetic composite materials in engineering, particularly in aerospace and automotive industries. Recently, much attention has been paid to dislocation crack and inclusion problems in magneto-electro-elastic solids, which simultaneously possess piezoelectric, piezomagnetic, and magnetoelectric effects. Therefore, it is of vital importance to investigate the magneto-electro-elastic fields as a result of existence of defects, such as cracks, in these solids. The mode III interface crack solution for two dissimilar half-planes has been analyzed by Li and Kardomateas [1] while for two dissimilar layers by Wang and Mai [2] and by Li and Wang [3]. Li and Kardomateas [1] solved corresponding plane problem by means of Stroh’s formalism and complex variable methods. Li and Wang [3] investigated the problems involving an antiplane shear crack perpendicular to and terminating at the interface of a bimaterial piezo-electro-elastic ceramics. Wang and Mai [2] investigated the mode III-crack problem for a crack at the interface between two dissimilar magneto-electro-elastic layers. Extension of those investigation problems interested in fracture theory, on dielectric and magnetostrictive crack behaviour, is very important, and results and conclusions could have applications in the failure of PEMO-elastic devices and in smart intelligent structures [4]. However, to the authors’ best knowledge, no researches dealing with the interface-dielectric crack in PEMO-elastic two-phase composite have been reported in literature. When subjected to mechanical, electrical, and