Fractal Dislocation Patterning During Plastic Deformation

During the later stages of plastic deformation, strain hardening of face-centered cubic metals goes along with the formation of cellular dislocation patterns appearing on various scales. The paper presents an analysis of the fractal geometry of these dislocation structures. A theoretical model is presented according to which dislocation cell formation is associated with a noise-induced structural transition far from equilibrium. The observed fractal dimensions are related to the stochastic process of dislocation glide, and implications for quantitative metallography are discussed.