Junction reaction hardening by dislocation loops

Abstract

The movement of a flexible dislocation line through a random array of circular dislocation loops has been studied, using a digital computer, on the basis of the line tension approximation. The dislocation moves on a {111} plane of a face-centred cubic crystal and interacts with {110} prismatic loops by the formation of short junction reactions at the points of intersection. The critical stress required to propagate the dislocation through the loops is μb/1·75L, where L is the average spacing of the reactive loops cutting the glide plane (one-third of all the loops are reactive). This result is independent of the radius and sense of the loops and the edge-screw character of the glide dislocation. It is slightly increased when the loops are distributed more uniformly, in disagreement with the factor two reduction predicted by Westmacott et al: (1966). The present estimate of loop hardening is comparable with the tetragonal distortion model of Fleischer (1962), and is in agreement with the measured hardening of quenched aluminium. It is almost identical with the value for a random array of simple obstacles with a flat spectrum of strengths. The present result is an order of magnitude larger than the previous estimate by Friedel (1963), which was based on the zig-zag model. This model is applicable only at zero stress, since it neglects the additional pinning points that are encountered by a dislocation when it bows under stress. The critical stress may be increased if the mobility of the loops allows the formation of longer junctions.