Abstract

This paper gives a quantitative analysis of the effect of near-tip microcracks on electric-field-induced stress intensity factors in isotropic elastic dielectrics. Nucleation of the microcracks is assumed to be governed by the electric-field-induced mean stress or the maximum normal stress. Based on the solutions for the effect of a single microcrack on the local electric field at the main crack, simple formulae are derived for the electric-field-induced stress intensity factors in the presence of the microcracks. It is found that the relative change in the stress intensity factor due to the microcracks for a conducting crack is equal and opposite to that for an insulating crack provided that the distribution of microcrack orientations is random. In particular, the microcracking zone is found to amplify the electric-field-induced stress intensity factor in some cases, especially for stationary insulating cracks, while the microcracking zone wake has an antishielding effect for sufficiently grown conducting cracks. These results are in sharp contrast with the well-known toughening effects of microcracks in elastic media under pure mechanical loads. This is attributed to the fact that the interaction between the microcracks and the main crack in elastic dielectrics under electrical loading is governed essentially by electrostatics, while the shape of the microcracking zone is determined by the electric field induced elastic stress field