The Axisymmetric Distribution of Stresses in an Infinite Elastic Solid Containing a Flat Annular Crack under Internal Pressure

Abstract

AbstractThe authors analyze the axisymmetric distribution of stress in an infinite elastic solid containing a flat annular crack under internal pressure which is one of three‐part mixed boundary value problems. Assuming that the deformation on the crack surface is continuous, we may represent it by Fourier series, and reduce the problem to the solution of an infinite system of algebraic equations. The displacement and stress components obtained are given by series involving infinite integrals. In particular, the integrals on the crack plane are expressed in terms of Gaußian hypergeometric functions. The radial distributions of the displacement and the stress components and the variations of the stress intensity factors at the crack tips with the ratio of the inner to the outer radius of the crack are shown graphically.