Simplified theory of dislocation damping including point-defect drag. I. Theory of drag by equidistant point defects

The theory of dislocation damping for movable pinning points is developed by using results found earlier by the authors for the relaxation strength and relaxation time for the damped vibrating-string model. In this way new formulas are not needed but only a reinterpretation of the constants of the old theory. This is justified by exact calculations for the case of n equidistant movable pinners. It is shown that the results can be represented in good approximation in the form of Debye relaxations. Four different such approximations are considered and compared. It is found that the main dependence of the effects on the parameters for any number of movable pinning points is the same as that for a continuously dragged string with only small changes of the order of 30% or less in numerical factors for the relaxation time and strength. These changes are of the same order as those introduced by a Debye approximation. The relation of the results to earlier work is discussed. In addition, the theory is placed within the framework of an even more general theory formulated in terms of a rigid-rod approximation.