Method of translations for elliptic mode I cracks in infinite bodies. Part 1. Polynomial loads

Abstract

We propose a method for evaluation of the displacement of the lips of an elliptic crack in an infinite body and, hence, for the determination of the stress intensity factors under the action of a polynomial load. The method is based on the Rice integral formula for the fields of stresses and displacements in two different states of the body, the Dyson theorem for the form of the field of displacements for a given polynomial load, the author's theory of translations of an elliptic crack in a nonuniform stress field, and the use of the existing solution for the case of uniform loading. The structure and complexity of the proposed method are similar to those of the well-known methods of weight functions based on the application of known particular solutions of the problem for a given body in constructing new more general solutions. For the special case of elliptic cracks in infinite bodies, the proposed method realizes the prediction of Fett concerning integration of the method of weight functions with general approaches of the theory of elasticity.