Seminar by Prof. Klaus Hackl

Ruhr-Universität, Bochum (Germany)

A variational approach to the evolution of distribution functions with application to dynamic recrystallization of polycrystalline aggregates

We present a general framework for the evolution of distribution functions of materials with internal variables based on thermodynamic extremum principles. The theory developed will be elaborated via the example of dynamic recrystallization in polycrystalline materials. Here, a distribution function is introduced to characterize the state of individual grains by grain size and dislocation density. Specifying free energy and dissipation within the polycrystalline aggregate we are able to derive evolution equations for the distribution function as well as for the internal variables using the approach introduced before. Once the distribution function is known macroscopic quantities like average strain and stress can be calculated. For distribution functions which are constant in time, describing a state of dynamic equilibrium, we obtain a partial differential equation in parameter space which we solve using a marching algorithm. Numerical results are presented and their physical interpretation is given.