The state of stress induced by ring dislocations in a semi-infinite stepped shaft

The state of stress induced in an axi-symmetric solid formed from a half-space and a bonded semi-infinite rod, by a family of ring dislocations of arbitrary Burgers vector is found. Particular care is given to the interaction between the Cauchy singularity near the dislocation core and the geometric singularity at the rod/half-space junction.