Diffuse Grenzflächen thermodynamisch scharf: Ein voll physikalisch eingebettetes Multiphasenfeldmodell

Abstract

Motivated by the problem of distortion occuring during heat treatment of steel, the mutual influence of phase changes and stresses in metals is examined on the length scale of several grains, the mesoscopic length scale, using a multi phase field method. The metalurgical motivation of this work makes it necessary to derive governing equations from entropy maximization as well as from free energy minimization. The inner energy and the entropy of the system, thus the free energy, are as far as possible put together from well-known physical expressions. Commonly stated thermodynamical relations between the contributions are examined for their domain of validity, then this validities are proven between the chosen contributions to inner energy and entropy where they should account. New insights on the thermodynamics of phase changes are achieved. The phasefield itself is chosen such that one component of it symbolizes one phase in each grain, i.e. two components for each grain are needed. To deal with this amount of components and stresses and temperature, a FEM software with the capacity to deal with an arbitrary number of components is designed. Results of the simulations are presented.