Estimation of the number of pinning points per network length from an analysis of an amplitude dependent damping peak

Abstract

The Granato--Luecke model (J. Appl. Phys., 27, 789 (1956)) of dislocation unpinning at zero absolute temperature predicts a damping peak as a function of strain amplitude. Over the past twenty years, numerous experimental results have been interpreted by use of this model, regardless of the temperature of the observations. This procedure is often possible because, at elevated temperatures, the zero-temperature form of the equations can be retained by replacing the critical mechanical stress for dislocation unpinning by the thermal breakaway stress. In an extension of the theory to the high-strain side of the unpinning peak, Rogers (J. Appl. Phys., 33, 781 (1962)) developed expressions for low strain amplitudes and high strain amplitudes. At high enough strain amplitudes a damping proportional to 1/epsilon/sub 0//sup 2/ (where epsilon/sub 0/ is the strain amplitude) is expected on physical grounds, whereas the expression of Rogers predicts damping proportional to 1/epsilon/sub 0/. A corrected expression is derived in this paper. This allows relatively simple numerical calculations to be made, which indicate the range of epsilon/sub 0/ over which the assumption that the logarithmic decrement for the unpinning peak is proportional to 1/epsilon/sub 0//sup 2/ is applicable. Numerical calculations can also be used to determine themore » number of pins. 2 figures. (RWR)« less