(A) study on a class of three dimensional crack problems

Abstract

The axisymmetric problem of an infinitely long fiber perfectly bonded to an elastic matrix with an annular crack under torsion and the mode decomposition scheme in axisymmetric crack and three dimensional crack via two-state conservation integrals are investigated. First, the axisymmetric problem of an infinitely long fiber perfectly bonded to an elastic matrix which contains an annular crack surrounding the fiber is investigated for the case of torsion field. The problem is formulated as a singular integral equation of the first kind with a Cauchy type kernel using the integral transform technique. The resulting equation is solved by using the numerical scheme to obtain the relevant physical quantities and the mode III stress intensity factors. The mode III stress intensity factors at the crack tips are presented when (a) the inner crack tip is away from the interface and (b) the inner crack tip is at the interface. Second, a numerical scheme is proposed to obtain the individual stress intensity factors in an axisymmetric crack and in a three dimensional mixed mode crack. The method is based on the path independence of J and M integral and mutual or two-state conservation integral, which involves two elastic fields. Some numerical example are presented to investigate the effectiveness and applicability of the method for an axisymmetric crack and a three dimensional penny shaped crack problem under mixed mode. Path-independence of the J and two-state integrals enables us to compute the individual stress intensity factors accurately and effectively from the domain integral expression. The solution procedure has been established and shown to be computationally efficient and operationally simple, involving only the choice of appropriate auxiliary solutions and the calculation of the J and two-state integrals with the aid of the domain integral expression.