Solutions for a Mode III Growing Crack in a Piezoelectric Plane Under Two Kinds of Electric Boundary Conditions

The solutions for a mode III crack growing along an arbitrary propagation path in a piezoelectric plane are studied under the impermeable surface condition and the electrical contact surface condition respectively. According to the two kinds of electric boundary conditions, the Hilbert and Riemann boundary value problems in a half-plane including opening smooth arc are obtained from the theoretical analysis. Moreover, the equipollence of the solution forms under these two electric boundaries is proven, and unified solutions for the stress and electric displacement distribution in the crack-tipfield of the piezoelectric plane are achieved.