Quasi-Stationary Propagation of Dislocation Kink

Motion of kinks on a dislocation is analysed on the basis of the string model for the dislocation. The equation of the motion is expressed in terms of the mass M per unit length of the dislocation, the line tension T , the Peierls force and an external stress, where viscous resistances are neglected. The equation is solved numerically under the initial condition that the dislocation can cross over the Peierls barrier in the direction of the force due to the external stress with the minimum energy. The solution shows, 1) the kinks propagate quasi-stationarily, 2) the propagation velocity approaches \(√T/M\) nearly independently of the Peierls force and of the applied stress, 3) after long time the velocity component of dislocation segments in the direction normal to the dislocation line approaches the sound velocity, showing that the velocity-dependent mass should be taken into the string model.