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

An electrically limited permeable crack with a frictionless contact zone at the right crack tip between two semi-infinite piezoelectric spaces under the action of a remote electromechanical loading is considered. Attention is focused on the influence induced from the permittivity of the medium inside the crack gap on the contact zone length and the fracture mechanical parameters. Assuming the electric displacement constant inside the open region of the crack, the problem is reduced to a combined Dirichlet-Riemann and Hilbert boundary value problems which have been solved exactly. Stress and electric displacement intensity factors as well as the crack tip energy release rate are found in a clear analytical form. Furthermore, transcendental equations for the determination of the real contact zone length have been obtained for a general case and for a small contact zone length in an especially simple form. The dependencies of the mentioned values on the intensities of the electromechanical loading are presented in tables and associated diagrams.