The influence of Maxwell stress on the fracture mechanics of 2D piezoelectric materials based on the PS model

The present work studies the influence of Maxwell stress on a straight but non-linear polarization saturation (PS) crack in a 2D piezoelectric material under combined mechanical and electric loadings at infinity. The non-linear piezoelectric fracture mechanics model, which is the PS model, is adopted in this paper. It is assumed that the crack is electrically semi-permeable. Based on the Stroh's formalism and the dislocation modelling of a crack, we derive the relationships of the field intensity factors and the local J-integral to the strip zone, the applied mechanical and electric loadings. Numerical results are also presented to discuss the effects of Maxwell stress on the intensity factors of stresses, the electric displacement and the size of the electrically yielded zone. It is found that the Maxwell stress can relieve the crack growth under a given mechanical and electric loading, especially for the case of low mechanical loading and high electric loading applied at infinity. It is also shown that the normalized stress intensity factor increases with both the mechanical and electric loading.