The in-plane and anti-plane problems of interfacial circular-arc cracks in transversely isotropic piezoelectric medium are separately considered.
The in-plane problem is solved by superposing two fields; one is perfectly bonded piezoelectric circular inclusion under uniform electric fields normal to the plane of isotropy, and the other is under a constant crack-face loading. The stress fields and stress intensity factors are easily obtained with the complex potentials, since the in-plane problem in the piezoelectric materials is identical to the one in elasticity.
A general solution is provided for the anti-plane problem of interfacial circular-arc cracks in transversely isotropic piezoelectric media. For example, a single circular-arc crack under anti-plane mechanical and in-plane electrical loadings at infinity is considered, and the exact solutions for stress intensity factor, electric displacement intensity factor, and energy release rate are obtained in an explicit form. The present result is identical to the existing solution of the perfectly bonded circular inclusion when the crack angle is zero, and the result is the same with the previous one in elasticity when the piezoelectic properties disappear.
