Dislocation Velocities in a Two-Dimensional Model

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Abstract
The dynamics of an edge dislocation in a two-dimensional crystal model are investigated using a localized unstable normal mode of vibration of the model. The model used is a simple-cubic lattice with linear central and noncentral nearest-neighbor interactions and a piecewise linear restoring force between atoms on the slip plane. The atoms below the slip plane are fixed. Lattice parameters are chosen to allow specific stable and unstable configurations of the lattice, and it is assumed that the dislocation progresses by passing alternately through stable and unstable states. It is found that there is one localized unstable mode of vibration whose components are very large in the neighborhood of the dislocation. This localized mode is used to approximate dislocation motion in the unstable state, and it is altered—by symmetrizing it with respect to the stable lattice configuration—to approximate motion in the stable state. Two coordinates, given by harmonic equations of motion, then characterize the dynamics of the dislocation. The relation between the two coordinates gives an energy-loss mechanism which leads to a steady-state dislocation velocity when a shear stress is applied to the lattice. Transient and steady-state velocities and the minimum stress necessary to maintain a steady-state velocity are calculated. The same quantities are found using computer simulation of a finite lattice, and a comparison is made. Reasonably good agreement is found for velocities up to about 0.7 times the velocity of sound in the continuum in the direction of slip. The analytic theory underestimates the minimum stress necessary to maintain a steady-state velocity.

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