An Extension of a Theory of Mechanical Damping Due to Dislocations

The theory of damping due to dislocations developed by Granato and Lücke concerning a model of a dislocation line pinned by major (unbreakable) and minor (breakable) pins, the latter distributed at random along its length, is extended in two ways: the hysteretic breakaway loss is calculated for higher amplitudes; and the frequency dependent or dynamic loss is shown to be, also, amplitude dependent. The presence in a crystal of two dislocation systems of different average loop lengths is considered as an explanation of the discrepancy between some of the experimental results and the G and L theory. The configuration of the combined dynamic and breakaway loss for the long loop system for various LN/Lc ratios and LN values is described, where LN, Lc are the average loop lengths between major and minor pins, respectively. An interesting feature is the prediction of a low amplitude maximum in the decrement. The theory does not extend to the high frequency region and like the G and L theory is unreliable for LN/Lc less than 5.

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