Comparing theoretical predictions of radiation-free velocities of edge dislocations to molecular dynamics simulations

Transonic defect motion is of interest for high strain-rate plastic deformation as well as for crack propagation. Ever since Eshelby's 1949 prediction [J. D. Eshelby, Proc. Phys. Soc. A 62, 307 (1949)] in the isotropic limit of a “radiation-free” transonic velocity $v_{\text{RF}}=\sqrt{2}{c}_{\text{T}}$, where shock waves are absent, there has been speculation about the significance of radiation-free velocities (if they truly exist) for defect mobility. Here, we argue that they do not play any significant role in dislocation dynamics in metals, based on comparing theoretical predictions of radiation-free velocities for transonic edge dislocations with molecular dynamics simulations for two face-centered cubic metals: Ag, where theory predicts radiation-free states, and Cu, where it does not.

Figure 1

Schematic of our atomistic models.

Figure 2

Instantaneous dislocation velocity and surface traction for an edge dislocation in Ag at $v_{\text{average}}=1.73$ km/s.

Figure 3

We show steady-state edge dislocations in Ag using the stress driven simulation method (a) as well as a hybrid method (b) where the dislocation is accelerated into the transonic regime using the strain rate driven method before switching to the stress-driven method to maintain a steady-state transonic edge dislocation.

Figure 4

The mobility relation of an edge dislocation in (a) Ag and (b) Cu [39].

Figure 5

Drag coefficient as a function of velocity in Ag.

Figure 6

Plots of ${\sigma }_{yy}$ allow us to identify shock waves generated by transonic dislocation in Ag. Red atoms represent the stacking fault between LP and TP. Dislocations move from left to right, so the LP is at the rightmost termination of the stacking fault. Mach cones are easily seen in the local stress distribution, as illustrated in (c).

Figure 7

Turning off the driving stress does not maintain any dislocation velocity, contrary to expectations at a radiation-free velocity. (Only one exemplary simulation is shown here).