Anti-plane Yoffe-type crack in ferroelectric materials

Extending the polarization saturation (PS) model and Yoffe crack model for ferroelectric materials, a moving PS model is proposed to study the problems of crack propagation considering the electrical nonlinearity. The model is solved using continuous distribution dislocation method. And the explicit expressions of the size of the electric saturation zone, intensity factors and the local energy release rate for the moving PS model are derived. It can be deducted from this model that the intensity factors and the size of the electric saturation zone are independent of the velocity of the crack. The local energy release rate for the moving PS model has the form of that for a stationary crack multiplied by the local energy release rate universal function f(v). And it increases monotonically with increasing v. When the velocity of the crack v → 0, the moving PS model will reduce to the static PS model. When the size of the electric saturation zone r → 0, the moving PS model is in agreement with the moving linear piezoelectric model.