Phase field analysis of crack tip parameters in ferroelectric polycrystals under large-scale switching

The determination of fracture parameters at cracks in ferroelectrics under large-scale domain switching is still a great challenge. In order to evaluate the crack-tip mechanical and electrical field intensity factors, the interaction integral (I-integral) technique is further developed to cope with the heterogeneous microstructures based on the polarization distribution and crack tip fields from phase field simulations. The enhanced I-integral exhibits several merits over previous techniques for determining the crack-tip intensity factors. First, small-scale switching assumption is unnecessary. Second, the intensity factors of different modes are decoupled. Third, it is independent of integration area size, regardless of the presence of grain boundaries and domain walls. These advantages ensure the successful application of the enhanced I-integral to study toughening effects in ferroelectric polycrystals due to large-scale domain switching. Using this approach, a tensile test of PbTiO₃ ferroelectric polycrystals with an impermeable crack is simulated. Simulations show that domain switching initiates not only from the crack tip but also from the grain boundaries due to high polarization gradient and stress concentration. Large-scale switching triggered by a critical load reduces the crack-tip stress intensity factors anomalously. In comparison to single crystals, the critical load for polycrystals is lower and even vanishes due to grain orientations. The results also demonstrate that the I-integral method possesses satisfactory accuracy and good area-independence for grain boundaries and domain walls.