Dislocation annihilation in plastic deformation: II. Kocks-Mecking Analysis

The Kocks-Mecking theory is reformulated by finding a new expression for the recovery rate term. A thermodynamic analysis on an annihilating dislocation segment is performed to determine this rate. By assuming that the velocity distribution of the segment is thermally activated, and that its maximum velocity is bounded by the speed of sound in the material, it is possible to obtain an expression for the energy barrier for annihilation. This is composed of a dislocation formation energy term, approximated by the strain energy around the segment; a migration energy term, taken to be equal to the stored mechanical energy that triggers cross-slip; and a statistical entropy contribution due to the degrees of freedom available to the dislocation for annihilation. It is demonstrated that the statistical entropy plays a crucial role in plasticity; it is determined by the possible dislocation paths and is bounded by both the speed of sound in the material and the proximity of neighbouring dislocations, S=kBlnε˙0ε˙N, where ε˙ is the strain rate, ε˙0 is a constant related to the speed of sound in the material, kB is the Boltzmann constant and N accounts for the interaction of neighbouring dislocations which increases the number of microstates. It is shown that the key material parameters describing plasticity in pure face-centred cubic metals are the stacking fault energy, the cross-slip activation volume and the distance from a dislocation core at which its strain field vanishes. The theory is applied to Cu, Al, Ni and Ag for a wide range of temperatures, showing good agreement with experimental results.