On contact zone models for an electrically impermeable interface crack in a piezoelectric bimaterial

An electrically impermeable interface crack between two semi-infinite piezo electric planes under remote mechanical tension-shear and electrical loadin g is studied. Assuming the stresses, strains and displacements are independ ent on the coordinate x(2) the expressions for the elastic displacement and potential jumps as well as for the stresses and electrical displacement al ong the interface via a sectionally holomorphic vector function are found. Introducing an artificial contact zone at the right crack tip and assuming the materials possess the symmetry class 6 mm the problem is reduced for a wide range of bimaterial compounds to a combination of combined Dirichlet-R iemann and Hilbert boundary value problems which are solved analytically. F rom these solutions clear analytical expressions for characteristic mechani cal and electrical parameters are derived. As particular cases of the above mentioned solution the classical (oscillating) and contact zone solutions are obtained. Further, a comparison with an associated solution for an elec trically permeable crack has been performed, The fracture mechanical parame ters for all models via the remote loads are found analytically and importa nt relationships between these parameters are obtained, Due to these relati onships an important algorithm of a numerical method applicable for the inv estigation of an inter-face crack in a finite sized piezoelectric bimateria l is suggested.