Stationary Propagation of Kink in Dislocation

Abstract

Motion of a kink in a dislocation is analysed as a function of viscous resistance force and of an applied stress. On the basis of the string model for dislocation, the motion of kink is determined by a wave equation in terms of line energy, the Peierls force, a viscous resistance force and an applied stress. The numerical solution of the wave equation shows that the motion of kink under the viscous resistance force becomes soon stationary: The kink propagates in a difinite form and at a constant velocity nearly independent of an initial condition. The propagation velocity is proportional to the external stress when the viscous resistance is proportional to the real velocity of the lattice ions produced by the propagation of the kink, and is proportional to the square root of the external stress when the viscous resistance is proportional to the square of the real velocity.