Thermodynamics of Irreversible Processes in Material Systems
September 10, 2018 — September 14, 2018
- Franz Dieter Fischer (Montanuniversität Leoben, Austria)
Thermodynamics is an efficient tool for the description of the development of the microstructure of a solid material system as well as the motion of defects.
Within the framework of continuum mechanics a proper thermodynamic potential depending on external and internal state variables can be found to describe the state of a system. Internal state variables are assigned to properties, e.g., as concentrations of components, but can also be assigned to defects, e.g., cracks or dislocations. As a proper thermodynamic potential the Gibbs energy of a material system is introduced, relevant for systems under constant temperature and stresses.
A central role plays the dissipation and the associated dissipation function. The dissipation is derived from the rate of the Gibbs energy. Correspondingly, a dissipation function is introduced, in terms of thermodynamic fluxes (fluxes of matter, of heat, etc.). Finally, the dissipation and the dissipation function are used to derive evolution equations for the internal variables by applying an extremum principle for irreversible processes.
The Thermodynamic Extremal Principle (TEP) is demonstrated (related to prominent names such as Onsager, Prigogine, H. Ziegler et al.) yielding a variational formulation, which allows an explicit derivation of evolution equations for the internal variables. The according thermodynamic forces lead to the so-called configurational forces driving physico-chemical processes and defects. Applications to various fields of materials science are presented. For example, one can treat the development of the surface of a solid consisting of grains and interacting with the environment as grooving, together with its numerical realization. Systems characterized by distinct parameters, such as effective grain radii, as evolving quantities are dealt with, too. Particular emphasis is laid on phase transformations as diffusive transformations controlled by the interaction of chemical and mechanical processes. Martensitic (i.e. displacive) phase transformations are also investigated, based on the minimization of the mechanical energy contribution to the total energy of the system.
Also the Phase Field Method (PFM) is outlined for multiphysics problems (chemistry, diffusion, electricity, magnetism, mechanics) with respect to its mathematical foundation and demonstrated for practical applications.
A successful validation of the procedures, introduced for simulations, by numerical methods, applied in a wide field of actual problems, is a necessary condition for their practical usability. Therefore, also this topic will be dealt with in this course. Particularly, the implementation of the physical and mathematical framework into actual numerical codes shall be discussed in detail. Within this context also the concept of configurational forces is explained allowing an efficient numerical calculation of the driving forces on defects, such as cracks, dislocations and other objects.
In conclusion, this course shall offer an overall view on the subject of thermodynamics of irreversible processes in materials starting from physical principles and proceeding via their mathematical formulations and numerical solutions on the way to their application.