Deterministic and Stochastic Continuum Models of Dislocation Patterning (FOR 1650)

FOR 1650: Dislocation based Plasticity

The main goal of this project is to understand how spontaneously emerging spatio-temporal fluctuations of dislocation fluxes give rise to inhomogeneous dislocation arrangements such as cell structures (dislocation patterning), and how in turn the presence of these dislocation patterns alters the dislocation fluxes and introduces new emergent length scales into the dislocation dynamics. To analyze the inter-related dynamics of dislocation patterns and dislocation fluxes/plastic flow, we use the CDD framework developed in DFG-FOR1650 over the past three years. We investigate the following specific questions: (i) can the CDD evolution equations explain the spontaneous formation of heterogeneous dislocation patterns in bulk samples (no boundary constraints) from small initial fluctuations, assuming that the dislocation fluxes to depend on dislocation microstructure in a deterministic manner? (ii) how can large fluctuations of the dislocation fluxes, which are an intrinsic feature of plastic flow, be incorporated into the CDD framework? Do these fluctuations assist the emergence of dislocation patterns, or do they rather create a "noise" which impedes pattern formation? (iii) Which factors control the presence or absence of dislocation patterns in small samples and confined geometries, i.e., how does the emergent length scale of dislocation patterns interact with external scales related to phase microstructure, grain and sample size?