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

TL;DR

This paper develops a continuum dislocation dynamics theory in three dimensions, revealing that dislocation patterning naturally forms fractal, self-similar structures with universal critical exponents across different physically motivated dynamics.

Contribution

It demonstrates that fractal pattern formation is a universal feature of 3D dislocation dynamics, supported by correlation function analysis showing power-law behaviors.

Findings

Dislocation patterns exhibit fractal, self-similar structures.

Correlation functions follow power-law distributions.

Universal critical exponents characterize different dynamics.

Abstract

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.