Velocity dependent dislocation drag from phonon wind and crystal geometry

Abstract

The mobility of dislocations is an important factor in understanding material strength. Dislocations experience a drag due to their interaction with the crystal structure, the dominating contribution at high stress and temperature being the scattering off phonons due to phonon wind. Yet, the velocity dependence of this effect has eluded a good theoretical understanding. In a previous paper, dislocation drag from phonon wind as a function of velocity was computed from first principles in the isotropic limit, in part for simplicity, but also arguing that macroscopically, a polycrystalline metal looks isotropic. However, since the single crystal grains are typically a few microns up to a millimeter in size, dislocations travel in single crystals and cross boundaries, but never actually see an isotropic material. In this work we therefore highlight the effect of crystal anisotropy on dislocation drag by accounting for the crystal and slip plane geometries. In particular, we keep the phonon spectrum isotropic for simplicity, but dislocations are modeled according to the crystal symmetry (bcc, fcc, hcp, etc.). We then compare to the earlier purely isotropic results, as well as to experimental data and MD simulations where they are available.

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

“…In comparing the high velocity behavior with MD simulations we note that the limiting velocity changes from c T to a slip system and dislocation character dependent shear wave speed when anisotropic effects are taken into account [18,20]. Furthermore, the degree of divergence is enhanced for steady state dislocations in this case [19,20]. On the other hand, the inclusion of a constant acceleration term into the isotropic dislocation field has been shown to reduce the degree of divergence [62][63][64].…”

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].…”

“…In the first principles calculations of Refs. [44,45,47,51,52], the dissipation D was computed from the probability of scattering a phonon from state q to state q per unit time and unit dislocation length. The interaction Hamiltonian for this process was determined from a thirdorder expansion of the crystal potential in the continuum limit with respect to finite strain η ij .…”

“…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. Since the Hunter-Preston model evolves total dislocation densities, the dislocation character itself is not resolved.…”

“…For example, B ∼ √ v is based on Eshelby's arguments [46] for screw dislocations in an isotropic continuum supplemented by an anisotropic dispersion relation and cannot be used for any other dislocation character. This may have been the best estimate when it was put forward in the 1950s, but today we know it gives incorrect high velocity behavior even for screw dislocations [47]. A relativistic factor with power m = 1 was introduced in Refs.…”