General treatment of mode III interfacial crack problems in piezoelectric materials

Abstract

The anti-plane problem of N collinear interfacial cracks between dissimilar transversely isotropic piezoelectric media, which are subjected to piecewise uniform out-of-plane mechanical loading combined with in-plane electric loading at infinity, and also a line loading at an arbitrary point, is addressed by using the complex function method. In comparison with other relevant works, the present study has two features: one is that the analysis is based on the permeable crack model, i.e. the cracks are considered as permeable thin slits, and, thus, both the normal component of electric displacement and the tangential component of electric field are assumed to be continuous across these slits. The other feature is that explicit closed-form solutions are given not only in piezoelectric media, but also inside cracks when the media are subjected to the most general loading. It is shown that the singularities of electric displacement and electric field in the media are always dependent on that of stress for the general case of loading, and all the singularities of field variables are independent of the applied uniform electric loads at infinity. For the interfacial cracks the electric field is square-root singular at the crack tips and shows jumps across the interface, while the normal component of the electric field is linearly variable inside the crack, but the tangential component is square-root singular. However, for a homogeneous medium with collinear cracks, the electric field is always nonsingular in the medium while the electric displacement exhibits square-root singularity. Moreover, in this case, the electric field inside any crack is equal to a constant when uniform loads are applied at infinity.