The singular nature of the self-stress field of a plane dislocation loop in an anisotropic elastic meidum

Using a line integral representation due to Brown, the in-plane self-stress field singularity near a point Q on a plane dislocation loop is extracted. The result obtained is valid for a medium of arbitrary elastic anisotropy. The singular nature of the dislocation self-stresses is of two types: (1) an inverse distance singularity characteristic of an infinite straight dislocation tangent to the loop at Q, and (2) a curvature-dependent logarithmic singularity which is proportional to a “line tension-like” quantity associated with this tangent dislocation.