Theory of Mechanical Damping Due to Dislocations

A quantitative theory of damping and modulus changes due to dislocations is developed. It is found that the model used by Koehler of a pinned dislocation loop oscillating under the influence of an applied stress leads to two kinds of loss, one frequency dependent and the other not. The frequency dependent loss is found to have a maximum in the high megacycle range. The second type of loss is a hysteresis loss which proves to be independent of frequency over a wide frequency range which includes the kilocycle range. This loss has a strain-amplitude dependence of the type observed in the kilocycle range. The theory provides a quantitative interpretation of this loss.