The pioneering efforts of Koehler and of Granato and Lücke established, theoretically, the role of dislocations with respect to damping in metals and, in the latter case, provided a mechanism for amplitude-dependent damping. The original Granato and Lücke model, based on the bowing of dislocation segments and their eventual unpinning from solvent atoms situated along their lengths, was assumed to result solely from the applied stress. This approach has subsequently been extended to include thermal contributions to unpinning.
This study is concerned with refinements to the original treatment. Although dislocation bowing, etc., on slip planes was assumed to occur under the action of the resolved shear stress, no attempt was made to calculate that stress as a function of differing grain orientations in polycrystalline materials or of crystal structure. In the present case, the maximum shear stress cumulative probability, that is, the fraction of all possible slip plane orientations on which the shear stress exceeds some arbitrary value, is first determined from a 3-D Mohr's circle analysis. It is valid for all crystal structures and for all states of stress in randomly oriented polycrystalline materials. The resolved shear stress distribution function, which depends specifically on crystal structure, is next derived from the above cumulative probability. These functions are then introduced into the original Granato and Lücke treatment for the cases of simple tension and shear. The procedure outlined above may readily be generalized to include the effect of preferred orientation.