Fundamental eigenstrain solutions for axisymmetric crack problems

Abstract

In this paper the fundamental eigenstrain solutions are derived for axisymmetric crack problems. The solutions are found in terms of Papkovich-Neuber potentials, which in turn are expressed using one function from the family of Lipschitz-Hankel integrals. In order to achieve the most concise form, two methods are used in the analysis: integration method for the axial opening eigenstrain ring and direct solution method for the radial opening eigenstrain ring and the ring of shear. The behaviour of the elastic stress fields in the vicinity of each type of eigenstrain ring is analysed. It is shown that the relevant component of stress exhibits a second order of singularity as the point of observation approaches the eigenstrain ring. It is also demonstrated that the ring curvature a −1 serves as the measure of the deviation of the stress field from the appropriate plane strain solution. Implications of the results for the solution of crack problems are discussed.