Sequences of dislocation patterns

Understanding the formation of sequences of dislocation patterns involves first understanding why certain patterns are in an appropriate sense stable, and then understanding why one stable pattern is favoured over another. Similitude implies that if pattern A is favoured over pattern B at one dislocation density, it will also be favoured at a higher dislocation density. A change of pattern must be induced either by a breakdown of similitude or by kinematic considerations. Kinematic considerations alone may cause one dislocation pattern to develop into another. The change occurs under a prescribed flow stress. Since the work done by the external stress in moving a dislocation across the pattern is proportional to the scale of the pattern, the scale of the pattern is inversely proportional to the applied stress. While the breakdown of similitude allows the energetic relations of different patterns to vary as the dislocation density increases, increase in dislocation density may also break down the similitude of kinematic behaviour by altering the likelihood of cross slip or of climb.