The effect of dislocation inertia on the thermally activated low-temperature plasticity of materials. I. Theory

Abstract

A method is suggested for taking into account the effect of inertial properties of dislocations on the velocity of their thermally activated motion. The method is based on the results of a statistical analysis of the dislocation motion through a random array of point obstacles. Because of the scatter in geometrical parameters, the dislocations interact with different obstacles at different angles α, even when all the obstacles in the crystal are identical. A fraction of the angles, g, can be higher than the critical value αc. The corresponding obstacles are surmounted by the dislocation in an unactivated way. The dislocation inertia manifests itself as an increase in the value of g, hence in the mean path length λ−; covered by the dislocation after each thermal activation event. Ultimately this results in an increase of velocity of the thermally activated motion. The equations suggested permit a numerical solution and comparison of the theoretical results with the experiment. A numerical example is given.

A predictive analytical friction model from basic theories of interfaces, contacts and dislocations

“…Competition exists at finite temperatures between increased viscous drag contributions that increase the required stress and an activation rate increase that lowers it. Landau derived the effective velocity of dislocations as a function of statistical thermal surmounting of randomly spaced Peierls barriers [56]. The inclusion of this velocity correction term v eff $ ve ÀDH kT ð Þ , where DH is the activation enthalpy estimated to be 0.01 eV and k is the Boltzmann constant, has a minimal effect on the radiation force term, where force is nearly constant with velocity.…”

The Effect of the Superconducting Transition on Plastic Deformation of Ultrafine‐Grained Aluminum

“…[9] It was shown that, as distinct from the results of reference, [8] for large concentration of pinning points (L < 10 À7 m) the magnitude of Ds NS is to decrease with increasing concentration of the pinning points. A statistical analysis of the role of the inertia effects in thermally activated dislocation motion [10] led to similar conclusions regarding the dependence of Ds NS on the non-dimensional concentration of the pinning points, C ¼ aS À1/2 , where a is the lattice parameter and S is the average area per pinning point. With growing C, the flow stress increases in both N and S states, leading to a concomitant increase in Ds NS .…”

Modeling of Thermal-Assisted Dislocation Friction

“…For completeness, we note that an effective barrier is not quite the same as a temperature-dependent velocity as originally suggested by Landau [40] (see also [24] and references therein). Note that we are concerned here with the retarding force, rather than the velocity, hence the different form (Fig.…”