On the velocity dependence of the dislocation drag coefficient from phonon wind

Abstract

At extreme strain rates, where fast moving dislocations govern plastic deformation, anharmonic phonon scattering imparts a drag force on the dislocations. In this paper, we present calculations of the dislocation drag coefficients of aluminum and copper as functions of temperature and density. We discuss the sensitivity of the drag coefficients to changes in the third-order elastic constants with temperature and density.

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].…”

“…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.…”

“…Temperature dependence: The drag coefficient depends on temperature via the phonon spectrum and the second (SOEC) and third-order (TOEC) elastic constants; the SOECs also affect the sound speeds. At temperatures (on the order of or) higher than the Debye temperature, the isotropic phonon spectrum can be Taylor expanded, exhibiting a linear temperature dependence to leading order [44,45]. In fact, at constant density this is the dominating effect since the elastic constants are more sensitive to density and pressure than to temperature [57,59].…”

“…Whenever temperature dependence is considered, it is assumed to be linear, sometimes including a small quadratic correction [34]. The latter assumption has its roots in the linear temperature dependence of the Debye phonon spectrum in its high temperature expansion [44,45]. However, none of the velocity dependencies mentioned above are well motivated from first principles, but are rather assumptions proposed ad hoc.…”

“…[40] the inverse kinetic equation is also presented (and reviewed in Section 2). 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].…”