A crack along a part of an interface electrode in a piezoelectric bimaterial under anti-plane mechanical and in-plane electric loadings

Abstract

An electrically conducting crack along a part of an electrode in the interface of a piezoelectric bimaterial under the action of anti-plane mechanical and in-plane electric loadings is analyzed. The electrode is assumed to be much thinner than the piezoelectric material, and therefore, its mechanical properties are neglected. Using special representations of field variables via sectionally analytic functions, a combined Dirichlet–Riemann boundary value problem is formulated and solved analytically. Explicit expressions for the shear stress, the electric field and the crack faces’ sliding displacement are derived. These quantities are also presented graphically along the corresponding parts of the material interface. The intensity factors for stress and electric field are determined as well. The dependencies of the mentioned values on the magnitude of the external electric loading and different ratios of the crack and electrode lengths are presented.