Phase field simulation of domain structures in cracked ferroelectrics

The fracture of ferroelectrics is a complex process which is influenced by various factors, among which are the domain switching near the crack tip, the crack face boundary conditions and the applied electric field. Domain switching near crack tips induces major local nonlinearity, while the crack face boundary conditions vary considerably due to different working conditions. In this work, a phase field model and a generalization of the configurational force theory into this model are used to investigate the microstructure around the crack tip and to quantitatively study the influence of the applied electric field and the crack face boundary conditions (permeable, impermeable, semi-permeable and energetically consistent). Evaluation of the fracture properties is done by the nodal configurational force at the crack tip based on the generalized configurational force theory. Results show that the induced domain structure relies significantly on the loading and on the surface boundary conditions. Among the four different conditions considered, the energetically consistent conditions lead to the smallest crack driving force, and the permeable conditions lead to the largest crack driving force. Calculations also show that positive electric fields tend to inhibit fracture, whereas negative electric fields tend to promote fracture.