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

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.

42 pages, 19 figures, 3 tables

References in corpus (4)

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• Stress-free states of continuum dislocation fields: Rotations, grain boundaries, and the Nye dislocation density tensor
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• Landau theory of crystal plasticity
• Normal form for renormalization groups
• The Emergence and Role of Dipolar Dislocation Patterns in Discrete and Continuum Formulations of Plasticity
• Homogeneous nucleation of dislocations as a pattern formation phenomenon
• Impact of lattice rotation on dislocation motion
• Cell structure formation in a two-dimensional density-based dislocation dynamics model
• Plastic deformation as a phase transition: a combinatorial model of plastic flow in copper single crystals
• Pattern formation in a minimal model of continuum dislocation plasticity