Asymmetric fracture behavior in ferroelectric materials induced by flexoelectric effect

Ferroelectric materials are widely used in actuators, exciters, and memory devices due to their excellent electromechanical properties. However, the instinctive brittleness of ferroelectric materials makes them easy to fracture under external load. Since giant strain gradient can be easily generated near the crack tip, the flexoelectric effect is indispensable in the research of fracture properties of ferroelectric materials. With the combination of time-dependent Ginzburg-Landau theory and phase-field model, the electromechanical behavior of PbTiO3 in the vicinity of the crack tip is determined in this work. The simulation results demonstrate that the domain structure near the crack tip becomes asymmetric with the flexoelectric effect. The polarization switching-induced toughening, which is characterized by the J-integral, depends on the direction of the crack relative to the original polarization orientation. Furthermore, the longitude flexoelectric coefficient f(11) has more significant impact on the fracture toughness than that of the transverse flexoelectric coefficient f(12) and the shear flexoelectric coefficient f(44). The results of the present work suggest that the flexoelectric effect must be considered in the reliable design of ferroelectric devices.