Elastic interaction of a dislocation loop with a traction-free surface

The elastic interaction of a dislocation loop with the traction-free surface S of an elastically isotropic half-space is calculated for arbitrary orientations of the Burgers vector of the loop, b, and the normal of the loop plane, n, with respect to S. Using the double force approximation (infinitesimal loop approximation) expressions are derived for the interaction energy and for the image force by which the loop is attracted to S.