The self-force on a planar dislocation loop in an anisotropic linear-elastic medium

Abstract A proper prescription for the in-plane self-force on each element of a plane dislocation loop is developed by computing the first variation of the loop self-energy during an arbitrary virtual planar change in the loop configuration. The appropriate self-energy is defined to be the strain energy exterior to a tube of radius e surrounding the loop. The expression derived for the self-force on a loop element ds depends on the local curvature at ds , on certain elastic data for an infinite straight dislocation tangent to the loop at ds , and only weakly on the ‘cut-off’ radius e. The theory of stress fields of dislocations in anisotropic media is sufficiently advanced to permit easy numerical evaluation of the self-force expression. The analysis further reveals that the singular behavior of the self-stresses in the plane of the loop near an element ds is that of an infinite straight dislocation tangent to ds plus a curvature-dependent logarithmic singularity which is proportional to the line-tension of this tangent dislocation.