Scaling theory of continuum dislocation dynamics in two and three dimensions

When crystalline materials deform plastically, complex dislocation structures have been observed experimentally.\footnote{P. Hahner et al., Phys. Rev. Lett. 81, 2470, 1998.} We provide a continuum plasticity theory to study the emergent self-similar morphologies.\footnote{Y.S.Chen et al., Phys. Rev. Lett. 105, 105501, 2010.} We analyze the self-similarity in terms of critical exponents for correlation functions of dislocation density, crystalline orientation and plastic distortion, and explore the connection to the power spectrum of the total free energy. In two and three dimensions, we apply anisotropic loadings, and observe little anisotropy in the critical properties. We explore the addition of quenched disorders to our continuum theory, to investigate the relation between dynamics (plasticity avalanches) and static dislocation morphologies.