FUNDAMENTAL EIGENSTRAIN SOLUTIONS FOR AXISYMMETRICAL CRACK PROBLEMS

In this paper the fundamental eigenstrain solutions are derived for ax isymmetric crack problems. The solutions are found in terms of Papkovi ch-Neuber potentials, which in turn are expressed using one function f rom the family of Lipschitz-Hankel integrals. In order to achieve the most concise form, two methods are used in the analysis: integration m ethod for the axial opening eigenstrain ring and direct solution metho d for the radial opening eigenstrain ring and the ring of shear. The b ehaviour 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 obser vation approaches the eigenstrain ring. It is also demonstrated that t he 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.