Simplified theory of dislocation damping including point-defect drag. II. Superposition of continuous and pinning-point-drag effects

The combined effects which occur when two kinds of drag, one acting continuously along the dislocations and other at discrete points (point-defect drag), are derived. It is found that the damping and modulus change can always be expressed in good approximation as the sum of two Debye relaxations. For widely separated relaxation times, one corresponds to the point-defect drag and the other to continuous drag acting on the in-between loops. Expressions are given for the relaxation times and strengths for each of the two components for any number of movable pinning points. It is shown that the characteristic pinning-point-drag effects have nothing to do with whether the drag acts continuously or at discrete points, but depend on the fact that the movable pinners exert restoring and viscous forces which act only on a part of the dislocation displacement.