Investigation of the behavior of a crack in a piezoelectric material subjected to a uniform tension loading by use of the non-local theory

In this paper, the behavior of a crack in a piezoelectric material subjected to a uniform tension loading is investigated by means of the non-local theory. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the displacement jumps are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the crack length, the materials constants and the lattice parameter on the stress field and the electric displacement field near the crack tips. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present near crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to using the maximum stress as a fracture criterion.