Three-dimensional finite element modeling of polarization switching in a ferroelectric single domain with an impermeable notch

Ferroelectric materials often possess defects, such as notches and voids. They are also brittle and susceptible to cracking at all scales ranging from electric domains to devices. Under mechanical and electrical loadings, the intensified stresses and electric fields in the vicinity of notches or voids may cause polarization switching in ferroelectric materials. Due to the polarization switching, the linear piezoelectric fracture mechanics cannot predict the nonlinear fracture behavior of ferroelectrics under mechanical and electrical loadings. To investigate the polarization switching and the nonlinear behavior of ferroelectrics, a three-dimensional nonlinear finite element model for ferroelectric materials is developed based on a principle of virtual work. The finite element model includes three physical fields, namely the polarization field, electric field and strain field, and the coupling between them. The developed finite element model is employed to investigate the polarization distribution near an impermeable notch in a ferroelectric single domain subjected to mechanical and electrical loadings. It is found that the polarization switching takes place near the notch tip if the mechanical loadings exceed a critical value. Furthermore, the simulation results show that an electric field parallel to the initial polarization increases the critical value while an electric field antiparallel to the initial polarization decreases it. In the simulation, we do not make any prior assumptions, i.e. without any switching criterion, on the polarization switching. The polarization switching is a result of the minimization of the total energy in the simulated ferroelectrics.