Hodes A. An arc crack in electrically passive and electrostrictive materials

A problem of determining of stress-strain state of an electrically passive and electrostrictive plane with a circular inclusion made of another material with an arc interface crack under the action of loadings applied at infinity is considered. The purpose of the work is to develop an effective algorithm to determine fracture parameters of the plane with partially debonded circular inclusion. The given problem is considered as an uncoupled problem of electroelasticity. It is resolved for non-contact and contact models of the crack. Within the framework of the non-contact model an exact solution of the considered problem is obtained from the problem of linear relationship for a piecewise-analytical function. Within the framework of the contact model the problem is reduced to the singular integral equation with Cauchy type kernel. New methods based on collocation method and expanding of unknown function in series in Jacobi polynomials is developed to resolve approximately this singular integral equation. This method allows to consider the possibility of existing of the contact zone as well as oscillating singularities of near "open" crack tips. Crack opening and stress intensity factors obtained within the framework of contact and non-contact crack models are compared, boundaries of applicability of these models are determined. The results of the dissertation work may be used in the calculation practice of research and design institutions.