General solutions of a penny-shaped crack in a piezoelectric material under opening mode loading

The effect of a penny-shaped crack on the deformation of an infinite piezoelectric material of the hexagonal crystal class 6 mm subjected to mode I electrical and mechanical loading has been studied using the theory of linear piezoelectricity and applying appropriate boundary conditions. Depending on material properties of piezoelectric materials, four different closed-form solutions to the fields of displacement, stresses, electric field and electric displacement are obtained, from which the dependence of stress intensity factor and electrical displacement intensity factor on the external loading is calculated. By including the contribution of electrostatic energy to the calculation of energy release rate, it is found that the energy release rate is a nonlinear function of the external loading if the electric field inside the crack is not zero at the crack tip. For piezoelectric materials subjected to tensile stress and electric field parallel to the poled direction, the stress intensity factor and electrical displacement intensity factor are independent of the applied electric field, while the electric field intensity inside the crack is a function of the applied stress and electric field. Depending on the direction of the applied electric field related to the poled direction, the electric field can display the shielding effect on the propagation of the crack. Such a result may be used to explain some nonlinear phenomena observed in the fracture mechanics of piezoelectric materials.