Non-singular term effect on the fracture quantities of a crack in a piezoelectric medium

The static problem of a crack in a piezoelectric plate subjected to biaxial loading at infinity is analyzed. The aim of this paper is to estimate the influence of non-singular terms originated by the load biaxiality on the stress fields and on the elastic and electric displacements in the vicinity of the crack tip. An analytical method for seeking the electro-elastic solution is proposed. The novel procedure involves a transformation of similarity induced by the fundamental matrix that enables to express the equations governing the problem in terms of complex potentials. The application of the boundary conditions leads then to the formulation of Hilbert problems whose solutions allow to obtain the generalized stress and displacement components. Numerical results and graphs are presented and discussed for various loading conditions. The non-singular solution is compared to the asymptotic one, generally considered in the literature when analyzing fracture problems. In particular, it is shown that the direction of incipient crack extension, sought through the maximum circumferential stress criterion, can be seen to deviate from the crack axis as the collinear load increases, although geometry and applied load are symmetric.