Fracture analysis of piezoelectric materials with flat ellipsoidal cracks

The objective of this study is to investigate a three-dimensional, infinitely extended, anisotropic piezoelectric solid containing a flat ellipsoidal crack with emphasis laced on when one of the principal axes of the crack becomes zero. Utilizing the equivalent inclusion method, the electroelastic fields around the crack are obtained explicitly by treating the elastic moduli and piezoelectric coefficients of the flat ellipsoidal inclusion as zero, and neglecting the permittivity. With resulting strain, stress, electric field, and electric displacement, the interaction energy between the crack and electromechanical loads is calculated. Based on the Griffith fracture criterion, the fracture stresses and critical electric displacement of the crack respectively subjected to a simple tension, an in-plane shear, an out-of-plane shear, and an electric displacement are obtained in closed forms by utilizing the obtained interaction energy. It is shown that the resulting fracture stresses can be reduced to those for uncoupled linear elastic fracture mechanics when piezoelectric coupling is absent and the material is isotropic. Numerical results for a three-dimensional PIC-151 piezoelectric solid with a flat ellipsoidal crack are given to demonstrate the application of the proposed formulation. Analysis results also indicate that the electroelastic coupling nature reduces the fracture loads and consequently impedes crack growth. (C) 2002 Elsevier Science B.V. All rights reserved.