Shielding effect of ring dislocation dipole on penny-shaped crack

Mechanical behavior of strongly crystalline materials can be significantly influenced by the internal dislocation structure and their iteration with micro crack-like defects. Thus, study on the crack-dislocation interaction problems can help to understand the failure mechanism of crystalline materials. Previous theoretical analysis have been mostly limited to plane problems, where the cracks are idealized as straight slit with infinite or zero out plane dimension and the dislocations slip along an inclined straight path starting from the crack tip. In this paper, we explore a new interaction mechanism under axisymmetric deformation state. An unconventional case of a penny-shaped crack interacts with a ring dislocation dipole is considered. Both the ring dislocation dipole and crack are modelled as axisymmetric edge dislocation loops. Solutions for the dislocation loops are obtained using the GKS based method. The mixed boundary value problem is converted into Abel integral equations, which can be solved analytically. Exact closed form solutions for the stress intensity factors (SIFs) in terms of elementary functions are obtained. Numerical studies are conducted to investigate the shielding effect of the ring dislocation dipole on the crack tip SIFs. Conditions for the dislocation to shield the crack are discussed. The present solutions can also be used as weight functions to study the axisymmetric interaction between penny shaped crack and other types of eigenstrain sources.