Extensive analyses were made of the fractal geometry of cellular dislocation structures that were observed in samples which had been deformed in a multiple-slip orientation. Several proposed methods for the determination of fractal dimensions were shown to give consistent results. Criteria were formulated which permitted fractal patterns to be distinguished from non-fractal patterns. In order to interpret the results, a theoretical model was suggested according to which dislocation-cell formation was associated with a noise-induced structural transition far from equilibrium. This permitted the observed fractal dimensions to be related to the stochastic properties of deformation via collective dislocation glide.

Fractal Analysis of Deformation-Induced Dislocation Patterns. M.Zaiser, K.Bay, P.Hähner: Acta Materialia, 1999, 47[8], 2463-76