Dislocation drag from phonon wind in an isotropic crystal at large velocities

Abstract

The anharmonic interaction and scattering of phonons by a moving dislocation, the photon wind, imparts a drag force v B (v, T, ρ) on the dislocation. In early studies the drag coefficient B was computed and experimentally determined only for dislocation velocities v much less than transverse sound speed, c T . In this paper we derive analytic expressions for the velocity dependence of B up to c T in terms of the third-order continuum elastic constants of an isotropic crystal, in the continuum Debye approximation, valid for dislocation velocities approaching the sound speed. In so doing we point out that the most general form of the third order elastic potential for such a crystal and the dislocation-phonon interaction requires two additional elastic constants involving asymmetric local rotational strains, which have been neglected previously. We compute the velocity dependence of the transverse phonon wind contribution to B in the range 1%-90% c T for Al, Cu, Fe, and Nb in the isotropic Debye approximation. The drag coefficient for transverse phonons scattering from screw dislocations is finite as v → c T , whereas B is divergent for transverse phonons scattering from edge dislocations in the same limit. This divergence indicates the breakdown of the Debye approximation and sensitivity of the drag coefficient at very high velocities to the microscopic crystalline lattice cutoff. We compare our results to experimental results wherever possible and identify ways to validate and further improve the theory of dislocation drag at high velocities with realistic phonon dispersion relations, inclusion of lattice cutoff effects, MD simulation data, and more accurate experimental measurements. arXiv:1907.00101v2 [cond-mat.mtrl-sci] 1 Oct 2019

Температурная Зависимость Автоволновых Характеристик Локализованной Пластичности

“…Будем считать, что в основе автоволновых механизмов пластического течения, как и в основе механизмов пластичности вообще [12], лежит движение дислокаций. Проблема их подвижности детально разработана в [13,14], где показано, что скорость движения дефектов в поле напряжений контролируется вязкостью фононного газа (в металлах также и электронного [15]…”

Analytic model of the remobilization of pinned glide dislocations: Including dislocation drag from phonon wind

“…With increasing velocity the drag becomes highly nonlinear, ultimately diverging as v → c t . The velocity dependence of the dislocation drag coefficient from phonon wind, the dominating contribution to drag at high stress and moderate to high temperatures, was discussed in a series of previous papers [45,47,51,52] which generalized earlier work of Alshits and collaborators reviewed in [44]. For a review of experimental work done on dislocation drag, see [1].…”

“…The energy dissipated per unit length of a moving dislocation is D = F v = Bv 2 [44,52]. In the first principles calculations of Refs.…”

“…Here we restrict our discussion to the purely isotropic limit, consistent with the previous section, but do include longitudinal phonons (in contrast to Refs. [45,52]). In order to numerically evaluate B for aluminum and copper at ambient pressure and room temperature along the lines of those references, we employ the numerical implementation of the theory described in the previous paragraph, PyDislocDyn [65], which is written in Python and Fortran, is open source, and developed by one of the authors.…”

“…In order to include the drag coefficient of Blaschke et al [45,47,51,52], an analytical approximation for dislocation drag as a function of local stress, material density, and temperature, B(σ, ρ, T ), valid in the isotropic limit for ambient and high temperatures must be developed. This is presented in Section 3, and is based on previous work [45,52]. We also note that a generalization of the original model developed by Blaschke et al [9,47,51] included a dependence on the dislocation line character (edge vs. screw), which has been shown to have interesting effects on dislocation drag -and hence the stress versus strain rate relations.…”