On mechanical stresses at cracks in dielectrics with application to dielectric breakdown

Abstract

The problem of an electric field applied to an isotropic dielectric containing a crack is considered as far as induced distortions and mechanical stresses are concerned. Near-tip distortions occur when the crack contains a conducting fluid or the surfaces are lined by a conducting layer. Previous treatments of the problem failed to distinguish between material and Maxwell stresses and an unphysical singularity in stress, which was divergent in elastic strain energy, was permitted. In this work, the material stress is identified, and a model is developed in which only physically realistic stress singularities are present. These results are obtained by treating the crack as a narrow but open ellipse rather than a slit crack as in previous models. A conventional crack-tip stress intensity factor KI characterizes the near-tip mechanical fields in the results obtained in this paper. The magnitude of KI due to an electrostatic field is deduced for a conducting central through crack in plane strain. The results suggest a model for dielectric breakdown caused by mechanical propagation of flaws. Data for dielectric breakdown and fracture of MgO and Al2O3 correlate in a way that supports this concept.