Fractal analysis of deformation-induced dislocation patterns

The paper reports extensive analyses of the fractal geometry of cellular dislocation structures observed in Cu deformed in multiple-slip orientation. Several methods presented for the determination of fractal dimensions are shown to give consistent results. Criteria are formulated which allow the distinguishing of fractal from non-fractal patterns, and implications of fractal dislocation patterning for quantitative metallography are discussed in detail. For an interpretation of the findings a theoretical model is outlined according to which dislocation cell formation is associated to a noise-induced structural transition far from equilibrium. This allows relating the observed fractal dimensions to the stochastic properties of deformation by collective dislocation glide. (C) 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved.