Coulomb traction on a penny-shaped crack in a three dimensional piezoelectric body

The axisymmetric problem of a penny-shaped crack embedded in an infinite three-dimensional (3D) piezoelectric body is considered. A general formulation of Coulomb traction on the crack surfaces can be obtained based on thermodynamical considerations of electromechanical systems. Three-dimensional electroelastic solutions are derived by the classical complex potential theory when Coulomb traction is taken into account and the poling direction of piezoelectric body is perpendicular to the crack surfaces. Numerical results show that the magnitude of Coulomb tractions can be large, especially when a large electric field in connection with a small mechanical load is applied. Unlike the traditional traction-free crack model, Coulomb tractions induced by an applied electric field influence the Mode I stress intensity factor for a penny-shaped crack in 3D piezoelectric body. Moreover, compared to the current model, the traditional traction-free crack model always overestimates the effect of the applied electric load on the field intensity factors and energy release rates, which has consequences for 3D piezoelectric fracture mechanics.