Characterization of grain boundary migration and polygonization with the use of the postulate of global action

Incompressible polycrystalline materials are treated by the theory of mixtures with continuous diversity. Each species of the mixture is characterized by grain size and lattice orientation, that is assumed to be represented solely by one unit vector. Thus, the evolution of the distributions of grain sizes and of lattice orientations are modelled by the balance of mass, in which the specific production rate of mass "Gamma" has to be assigned constitutively. In this talk, I will present a method to assign a constitutive equation for "Gamma". The problem is that such a constitutive quantity must fulfil an integral restriction due to the conservation of mass. Thus, among the classical principles of determinism and local action, a new postulate is formulated, that is an extension of these two to take the variables belonging to the species assemblage into account and that is already known, in other forms, in the literature of mixtures with continuous diversity: The postulate of global action. The formulation of this axiom is general. However, it gives a simple method to assign "Gamma" coherently with the conservation of mass. In the second part of the talk, I will give a brief introduction of the concepts of grain boundary migration and polygonization. Besides, I will discuss their modelling through the specific production rate of mass "Gamma" and finally I will use the postulate of global action and give explicit constitutive equations for "Gamma" to model these phenomena within the application of the theory of mixtures with continuous diversity that is presented in the talk of Prof. K. Hutter.