Phase field simulations of a permeable crack parallel to the original polarization direction in a ferroelectric mono-domain

Two-dimensional phase field simulations of polarization switching-induced toughening of an electrically permeable crack parallel to the original polarization direction in a ferroelectric mono-domain were conducted based on the time-dependent Ginzburg–Landau equation. The mono-domain represented a small vicinity region of the crick tip and the crack was loaded by nominal applied mechanical and/or electrical tip fields. The simulation results show that a wing-shaped switched zone is formed forwards from the crack tip under applied loading, which is different from the backward wing-shaped switched zone for a permeable crack perpendicular to the original polarization direction. The mechanical load to induce a same size of switched zone for a crack parallel to the original polarization is much lower than that for a crack perpendicular to the original polarization direction. Consequently, the polarization switching-induced toughening for a crack parallel to the original polarization, which was characterized by the local J-integral, behaves differently from that of a permeable crack perpendicular to the original polarization direction.