Elliptical inclusion problem in antiplane piezoelectricity: Implications for fracture mechanics

An elliptical piezoelectric inclusion embedded in an infinite piezoelectric matrix is analyzed in the framework of linear piezoelectricity. Using the conformal mapping technique, a closed-form solution is obtained for the case of a far-field antiplane mechanical load and an inplane electrical load. The solution to a permeable elliptical hole problem is obtained as a limiting case of vanishing elastic modulus of the inclusion. This enables the study of the nature of crack tip electric field singularity which is shown to depend on the electrical boundary condition imposed on the crack faces. The energy release rate of a self-similarly expanding slender crack in the presence of electric fields is obtained by using the generalized M-integral. The energy release rate expression indicates that the electric field has a crack-arresting influence. This effect is inferred to have a more fundamental physical origin in the interaction between the applied electric field and the induced surface charges on the crack faces. An experimental result contradicting the theoretical prediction on the crack-arresting effect is also discussed.