ANALYTICAL SOLUTION OF T-STRESS FOR PENNY-SHAPED CRACK IN 3D TRANSVERSELY ISOTROPIC LINEAR ELASTIC MEDIUM

Abstract

This thesis presents an analytical solution of the T-stresses for a penny-shaped crack in a transversely isotropic, linearly elastic infinite medium under general mixed-mode loadings. A complete stress field for two fundamental loading conditions associated with a pair of self-equilibrated unit normal and tangential point forces acting on both crack surfaces is obtained first via a technique of potential theory. Such explicit solutions are then utilized along with the proper limiting process to derive closed-form Green’s functions for the T-stresses. By using a method of superposition, the T-stresses of a penny-shaped crack subjected to general self-equilibrated tractions on the crack surface can be obtained explicitly in terms of an integral formula. Numerical results for some special loading conditions are then compared with available benchmark solutions to verify the formulation and derived solutions. Finally, influence of loading conditions and material properties will be investigated and discussed.