The nonlinear electromechanical behavior of a cracked ferroelectric single crystal subjected to pure electrical loading is investigated by a three-dimensional phase field model for different crack face electrical boundary conditions. Phase field simulations show that crack face electrical boundary conditions have significant influence on the electrical and mechanical responses of the ferroelectric single crystal to an external electric field. The coercive field for the polarization switching of a single crystal with an electrically permeable crack is about 50% larger than that for a single crystal with an electrically impermeable crack. The remanent strain and the strain variation induced by polarization switching in a single crystal with a permeable crack are larger than those with an impermeable crack. The different macroscopic nonlinear behaviors are attributed to different polarization switching processes. It is found that domain switching takes place from the surface of a single crystal with a permeable crack, while it begins from the vicinity of the crack tip when the crack is impermeable. A ferroelectric single crystal with an impermeable crack exhibits strip 90° domain switching under a negative electric field, which is consistent with experimental observation.
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