Dislocation Velocities in a Linear Chain

Abstract

Dislocation velocities as a function of applied stress are computed for a modified Frenkel-Kontorova model. The analysis is approximate in that only localized normal modes of motion (local modes) are considered and it is found that steady-state velocities are attained because of imperfect transfer of energy between successive local modes. The significant stress parameter for this model is found to be the dynamic Peierls stress ${\sigma }_{\mathrm{PD}}$ with the property that dislocation motion will be maintained for any stress $\sigma >{\sigma }_{\mathrm{PD}}$, without the aid of thermal motion, upon condition that the dislocation has surmounted one potential barrier while the stress is applied. For the model parameters here considered, ${\sigma }_{\mathrm{PD}}\sim {10}^{-2\mathrm{}}{\sigma }_P$, where ${\sigma }_P$ is the static Peierls stress. The model calculations show the extreme stress sensitivity of dislocation velocity at low velocities which has been observed experimentally. Finite-difference calculations show that the local-mode approximation gives reasonably good accuracy up to dislocation velocities approximately 0.7 the speed of wave propagation for infinite wave length in the linear chain.