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Center for Nonlinear Studies |
I present a continuum dislocation dynamics model[1] to explain the emergent mesoscale self-similar cellular dislocation structures observed in plastically-deformed crystals. In three dimensions, we evolve the geometrically necessary dislocations (GNDs) to minimize the elastic free energy in a single crystal within an isotropic approximation, starting from a smooth initial deformation. Whether or not climb is forbidden, GNDs always evolve into self-similar structures. This striking self-similar morphology is measured in terms of correlation functions of physical observables, like the geometrically necessary dislocation density, the plastic distortion, and the crystalline orientation. We provide a generic scaling theory to show that all these correlation functions, exhibiting spatial power-law behaviors, share a single universal critical exponent[2]. Under uniaxial loading, we develop experimental observers (simulating X-ray diffraction experiments) to visualize the underlying dynamics of sub-grain cell structures in k-space[3]. We extend our theory to couple vacancy concentration density into dislocation dynamics, to study dislocation climb.
Host: Turab Lookman, T-4, txl@lanl.gov, 665-0419