The effect of path cut on Somigliana ring dislocations in a half-space

This paper provides solutions for the stress and displacement fields induced in a half-space by an edge dislocation of constant magnitude, where the dislocation line is a circular ring lying in a plane parallel with the free surface. Two types of edge dislocations are considered; the prismatic form with a displacement discontinuity vector normal to the surface and cases with radial dislocation vectors. The latter are not true Volterra dislocations and produce different results for different path cuts these effects are investigated in some detail. The primary application of these results is for analysis of axisymmetric problems – the radial dislocations would be impossible in finite material.