Theory of the Thermal Breakaway of a Pinned Dislocation Line with Application to Damping Phenomena

Although the mechanical theory of Granato and Lücke for the strain-amplitude-dependent internal friction and modulus changes of solids containing dislocations gives a fair account of many of the observed effects, simple theoretical considerations show that the effect of thermal fluctuations should be very important. To extend the theory to finite temperatures, a detailed study of the possible static equilibrium configurations of a pinned dislocation line as a function of external stress is required. This is done here for the two specific examples of a dislocation with a single pinning point and a dislocation with a continuous pinning agent. It is shown in a general way how the damping and modulus change can be computed from these results, and a qualitative discussion of expected behavior is given. For high concentrations of pinning points, the theory is also applicable in the field of yield point phenomena, and the results found here are compared with previous calculations.