Elastic T-stress solutions for penny-shaped cracks under tension and bending

This paper presents the exact close form solutions for elastic T-stress of a penny-shaped crack in an infinite body under remote tension and bending. Penny-shaped crack problems have been analysed extensively in the literature, but all the focus has been on the determination of stress intensity factors. In the current work, using the potential method and Hankel transformation technique, the complete solutions of stress components parallel to and perpendicular to the cracked plane are derived first. Elastic T-stress is then obtained from the asymptotic stress field near the crack front. Further, three-dimensional finite element analysis is conducted to verify the derived exact solutions. It is found that under tension loading, the elastic T-stress is uniformly compressive along the crack front; while under bending, the elastic T-stress is varying from compressive to tensile along the crack front. In both tension and bending cases, T-stress strongly depends on the Poissonʹs ratio of the material.