General treatment of mode III interfacial crack problems in piezoelectric materials

The anti-plane problem of N collinear interfacial cracks between dissimilar transversely isotropic piezoelectric media, which are subjected to piecewi se uniform out-of-plane mechanical loading combined with in-plane electric loading at infinity, and also a line loading at an arbitrary point, is addr essed by using the complex function method. In comparison with other releva nt works, the present study has two features: one is that the analysis is b ased on the permeable crack model, i.e. the cracks are considered as permea ble thin slits, and, thus, both the normal component of electric displaceme nt and the tangential component of electric field are assumed to be continu ous across these slits. The other feature is that explicit closed-form solu tions are given not only in piezoelectric media, but also inside cracks whe n 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 al l the singularities of field variables are independent of the applied unifo rm electric loads at infinity. For the interfacial cracks the electric fiel d is square-root singular at the crack tips and shows jumps across the inte rface, while the normal component of the electric field is linearly variabl e inside the crack, but the tangential component is square-root singular. H owever, for a homogeneous medium with collinear cracks, the electric field is always nonsingular in the medium while the electric displacement exhibit s square-root singularity. Moreover, in this case, the electric field insid e any crack is equal to a constant when uniform loads are applied at infini ty.