Friday, February 22, 2013
Mean-field and Statistical Thermodynamic Formulation of Models for Dislocation Systems
Bob Svendsen, Chair Professor, Institute for Mechanics of Materials, RWTH Aachen University
Collective dislocation behavior in many material systems is highly dissipative in nature and results in the formation and evolution of a wide variety of microstructures such as tangles, networks, cell-wall systems, sub-grains, persistent slip bands in cyclic deformation, as well as static and propagating deformation bands under constant loading-rate conditions. Such processes take place in general over an extremely wide range of length- and timescales. Accounting for these in the modeling of such processes and systems has been and continues to be one of the main challenges in the modeling of collective dislocation behavior. The purpose of the current work is the general investigation and comparison of approaches to the formulation of non-equilibrium thermodynamic models for dislocation systems. In particular, both mean-field and statistical approaches are of interest. As an example of the former, an approach will be presented based on dislocation field theory and irreversible thermodynamics, resulting in a Cahn-Hilliard-like phase-field model formulation for dislocation transport and dynamics. On the statistical side, an approach will be developed based on application of the General Equation for Nonequilibrium Reversible-Irreversible Coupling (GENERIC). This results in a Fokker-Planck relation for dislocation transport and dynamics in phase space. Time permitting, a second statistical approach complementary to the BBGKY-based one of Groma will also be sketched and discussed.