Collinear permeable cracks between dissimilar piezoelectric materials

Abstract

In this paper, the generalized two-dimensional problem of collinear interfacial cracks, between two dissimilar piezoelectric media subjected to piecewise uniform loads at infinity, is studied by means of the Stroh formalism. It is different from the relevant analysis done by other authors that in the present work, cracks are considered to be traction-free, but permeable slits across which both the normal component of the electric displacement and the tangential component of the electric field are continuous, and thus avoiding the common assumption of electric impermeability. According to the above continuous conditions combined with the principle of analytical continuation, the considered problem is reduced to a Hilbert problem. Explicit, closed-form expressions for the electric field inside cracks, complex potentials in piezoelectric media and field intensity factors near the crack tips are obtained. These results show that the electric field inside cracks is dependent on the material constants and the applied loads. It is also shown that all the field singularities are dependent only on the applied mechanical loads, not on the applied electric loads, which is different from those results based on impermeable crack model.