Woosong Choi

Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator

When external stresses in a system—physical, social or virtual—are relieved through impulsive events, it is natural to focus on the attributes of these avalanches. However, during the quiescent periods between them, stresses may be relieved through competing processes, such as slowly flowing water between earthquakes or thermally activated dislocation flow between plastic bursts in crystals. Such smooth responses can in turn have marked effects on the avalanche properties. Here we report an experimental investigation of slowly compressed nickel microcrystals, covering three orders of magnitude in nominal strain rate, in which we observe unconventional quasi-periodic avalanche bursts and higher critical exponents as the strain rate is decreased. Our experiments are faithfully reproduced by analytic and computational dislocation avalanche modelling that we have extended to incorporate dislocation relaxation, revealing the emergence of the self-organized avalanche oscillator: a novel critical state exhibiting oscillatory approaches towards a depinning critical point. This theory suggests that whenever avalanches compete with slow relaxation—in settings ranging from crystal microplasticity to earthquakes—dynamical quasi-periodic scale invariance ought to emerge.

Bending crystals: emergence of fractal dislocation structures.

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.

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.

Is Dislocation Flow Turbulent in Deformed Crystals

Intriguing analogies were found between a model of plastic deformation in crystals and turbulence in fluids. A study of this model provides remarkable explanations of known experiments and predicts fractal dislocation pattern formation. Further, the challenges encountered resemble those in turbulence, which is exemplified in a comparison with the Rayleigh-Taylor instability.

“Irregularization” of systems of conservation laws

We explore new ways of regulating defect behavior in systems of conservation laws. Contrary to usual regularization schemes (such as a vanishing viscosity limit), which attempt to control defects by making them smoother, our schemes result in defects which are more singular, and we thus refer to such schemes as “irregularizations”. In particular, we seek to produce delta shock defects which satisfy a condition of stationarity. We are motivated to pursue such exotic defects by a physical example arising from dislocation dynamics in materials physics, which we describe.