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 nonequilibrium systems.
Highlights
We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals
An imposed distortion generates a complex morphology even for a single crystal of a pure material—polycrystalline grains form at high temperature where dislocation climb allows for polygonization, cell structures form at low temperatures when climb is forbidden
Experiments differ in characterizing the cell structures; some show convincing evidence of fractality [1,2,3] with structure on all length scales [Fig. 1(c)], while others show structures with a single characteristic scale setting their cell size and cell wall misorientation distributions [4,5,6] [Fig. 1(d)]
Summary
We provide a minimal continuum model for mesoscale plasticity, explaining the cellular dislocation structures observed in deformed crystals. When climb is forbidden, cell wall structures evolve with power-law correlations and self-similarity—providing a clear morpho- Notice that the glideonly simulations show CÃii ðRÞ $ R2À with % 0:5, indicating a fractal, self-similar cell structure, albeit cut off by lattice and system size effects.
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