Bending crystals: Emergence of fractal dislocation structures

TL;DR

This paper introduces a minimal continuum model that explains the formation of fractal dislocation structures in deformed crystals, capturing experimental morphologies and scaling behaviors.

Contribution

It presents a novel mesoscale continuum model that reproduces self-similar dislocation structures and bridges the mesoscale gap in multiscale modeling.

Findings

Reproduces fractal morphologies of dislocation structures

Matches experimental scaling of cell sizes and misorientations

Provides a framework for understanding mesoscale plasticity

Abstract

We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. Our dislocation density tensor evolves from random, smooth initial conditions to form self-similar structures strikingly similar to those seen experimentally - reproducing both the fractal morphologies and some features of the scaling of cell sizes and misorientations analyzed experimentally. Our model provides a framework for understanding emergent dislocation structures on the mesoscale, a bridge across a computationally demanding mesoscale gap in the multiscale modeling program, and a new example of self-similar structure formation in non-equilibrium systems.