It was noted that the understanding of sequences of dislocation patterns involved an appreciation of the reason for the stability of certain patterns. The principle of similitude implied that if pattern A, say, were preferred to pattern B at a given dislocation density, it would also be preferred at a higher dislocation density. A change in pattern could be induced by a breakdown of similitude, or by kinematic effects. The latter alone could cause one dislocation pattern to develop into another. Such a change occurred at a prescribed flow stress. As the work done by the external stress in moving a dislocation across the pattern was proportional to the scale of the pattern, the latter was inversely proportional to the applied stress. A breakdown of similitude permitted the energetic relationships of various patterns to vary as the dislocation density increased. However, an increase in dislocation density could also break down the similitude of kinematic behaviour by affecting the probability of cross-slip or climb.

Sequences of Dislocation Patterns. F.R.N.Nabarro: Materials Science and Engineering A, 2001, 317[1-2], 12-6