Bending crystals: emergence of fractal dislocation structures

Area of Science:

• Materials Science
• Condensed Matter Physics
• Computational Modeling

Background:

• Understanding the formation of mesoscale dislocation structures in deformed crystals is crucial for predicting material behavior.
• Existing models often face computational challenges in bridging the gap between microscale and macroscale phenomena.

Purpose of the Study:

• To develop a minimal continuum model for mesoscale plasticity.
• To explain the formation of cellular dislocation structures observed in deformed crystals.
• To reproduce experimentally observed fractal morphologies and scaling features.

Main Methods:

• A minimal continuum model based on dislocation density tensor evolution.
• Simulation starting from random, smooth initial conditions.
• Analysis of emergent self-similar structures, fractal morphologies, and scaling of cell sizes and misorientations.

Main Results:

• The model successfully generates self-similar dislocation structures resembling experimental observations.
• Fractal morphologies and key scaling features of cell sizes and misorientations are reproduced.
• The model bridges the computational gap in mesoscale multiscale modeling.

Conclusions:

• The developed model provides a framework for understanding emergent dislocation structures on the mesoscale.
• This work offers a new perspective on self-similar structure formation in nonequilibrium systems.
• The model contributes to multiscale modeling by addressing mesoscale complexities.