Dislocation stress-velocity dependence in alloys

The frictional stress $\sigma \mathrm{}\left(v\right)\mathrm{}$ is calculated for a dislocation gliding at an average velocity $v$ on a plane containing a fixed random distribution of weak obstacles of finite interaction range, in the presence of viscous forces. For very low-viscous forces the dislocation travels quasistraight, over-coming each obstacle independently of the relative positions of the other ones. Dislocation glide is possible only for $v\gtrsim \frac{1}{50}{v}_s$. where $v_s$ is the sound velocity in the solid. The frictional stress has the usual viscous drag component plus an extrinsic component proportional to the solute concentration, which vanishes asymptotically for $v>>\frac{1}{50}{v}_s$. For high-viscous forces, glide is possible at all velocities for stresses above a critical stress ${\sigma }_c$. For $\sigma \approx {\sigma }_c$ the motion is sensitive to the obstacle statistics. For $\sigma \gtrsim 2{\sigma }_c$ the motion is mostly drag controlled, with characteristics similar to those observed in the presence of low-viscous forces.