Thermally activated motion of a dislocation through a random array of point obstacles

Abstract

The “rolling disk” method is used for obtaining the distribution functions of the bow‐out angles and segment lengths for a dislocation pressed by an external stress to an array of point obstacles randomly distributed in the glide plane. Based on these distribution functions, the thermally activated motion of infinite as well as finite‐length dislocation lines through the random array of obstacles is considered. Formulas are obtained for evaluating the mean rates of glide as functions of stress and temperature. A rather good agreemeut of the results with those obtained with computer‐simulation technique substantiates the validity of the theory suggested.

Distribution of point-obstacle distance during the motion of screw dislocations in MgO single crystals

“…The distribution of distances between short-range obstacles to dislocation motion can be gained from electron micrographs of crystals deformed inside the high voltage electron microscope. For impure MgO single crystals, the distribution obtained roughly agrees with statistical models by Kocks [3] and Landau [5] and is sensitive to a thermal treatment.…”

Simulation of single slip in FCC metals

“…This model is a synthesis of the barrier model of constant linear tension [17][18][19][20][21] and models of a dislocation source operating in a superbarrier mode [22]. The most considerable advance in the first model is that it is free of the assumptions of rectilinearity and infinity of dislocations.…”

Analytical calculation of parameters of thermally activated dislocation motion through a random array of point obstacles

“…The dislocation segment length means the segment chord length. The dislocation envelops each obstacle under the bending angle rp; the angle a = n -9 which is supplementary to rp is called the attack angle [9]. The height of the force barrier produced by the stopper in the glide plane is characterized by the critical attack angle a,.…”

“…This was based mostly on computer simulation, because this model involves exceedingly complex probability problems for which analytical solutions are difficult to find. In [l, 9,11,14,15] only analytical solutions could be found for some problems associated with the present theoretical model. However, their solutions were not sufficient to calculate the velocity of thermally activated dislocation motion through a random array of point obstacles without computer simulation.…”