Contribution of Defect Dragging to Dislocation Damping. I. Theory

Abstract

The contribution of dragging of point defects attached to dislocation lines, to dislocation damping, to elastic modulus, and to logarithmic decrement, is developed. It is shown that the dragging leads to an initial increase in decrement in a suitable frequency range, determined by other related parameters: dislocation loop length, line tension, and damping constants. The theory predicts a dependence on frequency of ${\omega }^{-1\mathrm{}}$, in contrast to the Koehler-Granato-Lücke (KGL) frequency dependence of $\omega$, explaining the failure of previous experiments to confirm the KGL theory. In a similar manner, the generally accepted dependences on point-defect density are shown to be incorrect at lower frequencies, below a few kHz in copper. For example, it is shown that the dislocation decrement should be proportional to the two-thirds power of the modulus defect, rather than proportional to the square of the modulus defect as previously expected, at large point-defect densities on dislocation lines.