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

Y. S. Chen, W. Choi, S. Papanikolaou, M. Bierbaum, J. P. Sethna

 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

Article in Intl. Journal of Plasticity

Article at arxiv.org