Mode-III crack problems in a cubic piezoelectric medium

Mode-III crack problems in a cubic piezoelectric medium are investigated. Electromechanical fields near the crack tip are derived, and explicit expressions are obtained. It is shown that the asymptotic stress and electric fields are characterized by the inverse square root of the distance from the tip with at most two independent coefficients. The energy release rate associated with the crack is determined, and comparison is made with the counterpart in materials of hexagonal symmetry. The fundamental problem concerning a screw dislocation which is accompanied by other line singularities of different physical nature is addressed. A class of crack problems is solved by reducing it to the standard Riemann-Hilbert problem in complex function theory. It is concluded that under certain conditions, for the same crack configuration and loading, the stress intensity factors found for isotropic elastic materials are applicable to cubic piezoelectric media. Finally, three crack problems are explicitly solved.