An Embedded Elliptical Crack, in an Infinite Solid, Subject to Arbitrary Crack-Face Tractions

Abstract

In this paper, following a critical assessment of earlier work of Green and Sneddon, Segedin, Kassir, and Sih (who obtained solutions for specific cases of normal loading on the crack face and the cases of constant and linear shear distribution on the crack face), Shah and Kobayashi (whose work is limited to the case of third-order polynomial distribution of normal loading on the crack face), and Smith and Sorensen (whose work is limited to the case of a third-order polynomial variation of shear loading on the crack face), a general solution is presented for the case of arbitrary normal as well as shear loading on the faces of an embedded elliptical crack in an infinite solid. The present solution is based on a generalization of the potential function representation used by Shah and Kobayashi. Expressions for stress-intensity factors near the flaw border, as well as for stresses in the far-field, for the foregoing general loadings, are given.