Effect of large-scale domain switching on intensity factors for a crack in 3D ferroelectric single crystals using the I-integral method

Due to their intrinsic brittleness, ferroelectric materials are prone to fracture under extreme electromechanical operational loads. The fracture of ferroelectric materials is usually accompanied by large-scale domain switching. This paper develops the interaction integral (I-integral) method for a crack in three-dimensional ferroelectrics through applying a virtual load increment to the current state. Unlike the widely-used switching-toughening model, the I-integral is not restricted to small scale switching. Due to designable choice of the virtual load increment, the I-integral allows to decouple the intensity factors of different fracture modes. The local intensity factors along the curved crack front can be directly extracted, since the I-integral is independent of integration volume. With these merits, the I-integral method is a very promising technique in fracture analysis of ferroelectrics under large-scale domain switching. Moreover, the I-integral method is used in combination with the phase field model to simulate a tensile test of nanoscale PbTiO₃ ferroelectric single crystal with a semi-circular surface crack. Results show that various patterns of polarization pairs appear as soon as the applied load is increased beyond a critical value. The stable domain structures are divided into two layers by the plane where the crack is located and in each layers several polarization vortices formed eventually. Apart from the geometry and loading conditions, the position where the crack front is located with respect to the polarization vortex is a key factor affecting the switching-induced change of the stress intensity factor.