Fields near elliptical crack tip in piezoelectric ceramics

Abstract

The field equations of three-dimensional problems in a transversely isotropic piezoelectric medium become four simultaneous partial differential equations of second order, in which the displacement components and electric potential are taken as the essential unknowns. In this paper the general solutions of the above mentioned equations, expressed by the newly introduced potential functions, are deduced. Therefore, the obtained general solutions are applied to solve a problem in an infinite piezoelectric medium with an elliptical crack on whose surfaces uniformly distributed mechanical and electric loads are exerted, and the crack surfaces are assumed to be parallel to the material plane of isotropy. The analytical expressions of the stress and electric displacement fields near the crack tip show an extremely complicated coupling relationship between the mechanical and electric variables. To illustrate the results acquired in this paper an example for a kind of piezoelectric ceramics applied in engineering is computed finally.