The effect of path cut on Somigliana ring dislocation elastic fields

In this paper we look at ring dislocations (circular loops) in an infinite isotropic full-space. The dislocation direction is either axial or radial. Unlike dislocations in plane analysis the path cut has a significant effect on the elastic fields. Solutions for the dislocations are given for a variety of path cuts with closed form expressions for the displacement and stress fields. When considered alone these dislocations do not obey Frank’s rule; these anomalies and other fundamental properties are discussed.