A fracture criterion of a penny-shaped crack in transversely isotropic piezoelectric media

By utilizing the eigenstrain formulation and Cauchy's residue theorem, a unified explicit expression for the electroelastic fields inside a flat ellipsoidal crack embedded in an infinite piezoelectric solid subjected to electromechanical loads is presented. In particular, an explicit expression is obtained for a penny-shaped crack in a transversely isotropic piezoelectric medium. Three loading cases, a simple tension, a pure shear, and an electric displacement, have been considered to examine the behavior of penny-shaped cracking. The results show that the applied shear stress does not couple with the electric displacement, unlike the simple tension case. Furthermore, the change of potential energy due to the presence of the crack is evaluated. With this result and based on the Griffith theory, the fracture stresses and critical electric displacement are presented in closed forms. Explicit expressions for stress and electric displacement intensity factors are also given. It is verified that the resulting fracture stresses and stress intensity factors can be reduced to those for uncoupled linear elastic fracture mechanics when piezoelectric coupling is absent and the material is isotropic. (C) 1997 Elsevier Science Ltd.