The thermal, mechanical and chemical properties of metals are strongly coupled by their microstructure. At elevated temperatures, grain coarsening and refinement as well as recrystallization may occur and influence the mechanical response during forming. In addition, due to alloying, second phase particles may be present and interact with the grain boundaries. Therefore, a predictive description of thermomechanically coupled processes requires taking the underlying microstructural phenomena into account. In order to ensure that all constitutive relations are consistent and physically meaningful, the material model should be derived out of a thermodynamic framework.
In this work, we use the procedure of Rational Extended Thermodynamics to derive a material model based on a mean-field microstructure description. The state of the material is characterised by its free energy as a thermodynamic potential describing various energy storage mechanisms. In the present approach, the choice of constitutive relations is restricted by an entropy principle, which is evaluated using the method of Lagrange multipliers.
We apply the framework to derive a model for the microstructure evolution in a polycrystalline material including a distribution of second phase particles. We study the applicability of the theory by means of numerical simulations. Dependent on the particle content and their sizes, grain boundary motion is affected by drag forces. An extension of the model to deformation and stress as well as recrystallization is straightforward.