An intermediate crack model for flaws in piezoelectric solids

The aim of this paper is to study a crack model for piezoelectric bodies. In recent years it became evident that the electrically impermeable or the perfect electric contact boundary conditions on the crack faces are inadequate for many physical situations, over- or underestimating the electric field influence on the propagation process. The crack model here investigated is intermediate between these two limit cases. The generalized plane problem for an infinite piezoelectric body with a central crack is converted into a system of integro-differential equations, then reduced to an integro-differential equation similar to Prandtl's equation of aerodynamics. For poled ceramics with transversely isotropic symmetry, the integral equation is numerically solved using quadrature formulae for both plane and antiplane states of deformation. The energy release rate calculated with the discrete solution is then compared with that given by the exact solution for an elliptic hole embedded in the infinite piezoelectric body. A range of values of the cavity thickness is found, for which the considered crack model is a good approximation of the exact two-body problem, while the impermeable and the perfect contact models are not appropriate.