Phase field modeling of coupling evolution of fracture and dielectric breakdown in ferroelectric materials

Ferroelectric materials have attracted increasing attention due to their distinguished electromechanical coupling properties. Fracture and dielectric breakdown are two main failure behaviours of ferroelectric materials, which may occur simultaneously under large mechanical and electrical loads. Understanding the coupling evolution of fracture and dielectric breakdown is crucial for the application of ferroelectric materials under complex electromechanical environments. In the present study, a phase field model with multiple order parameters is developed to investigate the coupling evolution behaviours of fracture and dielectric breakdown of ferroelectric materials subjected to the mechanical and electrical loadings. In the phase field model, coupled electromechanical degradation functions are proposed to model the interface boundary conditions of fracture and dielectric breakdown. Generalized configurational forces of fracture and dielectric breakdown are obtained from the phase field model to analyse the driving forces for the evolution of fracture and dielectric breakdown. The interaction between fracture and dielectric breakdown is predicted by using the phase field model with a set of interface boundary conditions. The simulation results show that dielectric breakdown occurs at impermeable crack tips due to the concentrated electric field, while the stress distribution around the crack tip and the driving force of crack propagation are influenced by dielectric breakdown. The attraction of crack to electrical treeing path and the deflection of electrical treeing to crack path are predicted during the coupling evolution of fracture and dielectric breakdown. The results of this work provide an in-depth insight into the electromechanical coupling failure of fracture and breakdown of ferroelectric materials. The developed model framework can be employed to investigate more complex electromechanical coupling failures of dielectric, piezoelectric and ferroelectric materials and structures.