Abstract
In this paper we study the elasticity problems of a planar crack, lying in an infinite three-dimensional solid, the front of which differs only slightly from a circle. The crack system is subjected to loadings that induce shear mode stress intensity factors at the crack front. Quantities such as relative crack surface displacement, in-plane shear mode intensity factor K2 and anti-plane shear mode intensity factor K3 are derived in detail. The method used is based on a perturbation technique developed by Rice (J. Appl. Mech.52, 571–579 (1985)) of calculating the first-order variation of the elastic field of a crack when its front is perturbed from some regular reference geometry. The configurational stability problems of harmonic wave form perturbations of the front of a circular crack under axisymmetric shear loading are studied using the derived formulae. The shape that a planar crack under remote uniform shear loading would take so that the energy release rate distributes uniformly along the crack front is discussed by calculating proper perturbations on a circular crack that meets the above requirement.
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