Scaling theory of continuum dislocation dynamics in three dimensions: Self-organized fractal pattern formation

We focus on mesoscopic dislocation patterning via a continuum dislocation dynamics theory (CDD) in three dimensions (3D). We study three distinct physically motivated dynamics which consistently lead to fractal formation in 3D with rather similar morphologies, and therefore we suggest that this is a general feature of the 3D collective behavior of geometrically necessary dislocation (GND) ensembles. The striking self-similar features are measured in terms of correlation functions of physical observables, such as the GND density, the plastic distortion, and the crystalline orientation. Remarkably, all these correlation functions exhibit spatial power-law behaviors, sharing a single underlying universal critical exponent for each type of dynamics.

► We present an extensive derivation of a continuum law for dislocation dynamics.
► We show that the dynamics exhibits cell wall structures.
► Two variants of glide-only dynamics and one including climb are explored.
► We show that the correlation functions represent the structural properties.
► Analytical relations of correlation functions are derived with one critical exponent.