Mathematical modeling of phase transformations in steels in frameworks of diffuse interface description

In steels all known solid state phase transformations are observed: polymorphic transformation with wide spectrum of morphological and kinetics features, eutectoid decomposition (pearlite transformation), decomposition of supersaturated solid solutions, short- and long - range ordering in austenite and martensite. The important feature of these systems is different diffusion mobility of metal and carbon atoms. Therefore, reorientation of the crystal lattice may occur simultaneously with the diffusion redistribution of carbon and alloying elements. In this paper in the context of diffuse interface description is investigated microstructure evolution in steels during thermo-mechanical loading. In the frameworks of diffuse interface model the shape and mutual distribution of the grains is represented by functions that are continuous in space and time, the phase-field variables. Therefore, the evolution of the shape of the grains, or in other words the position of the interfaces, as a function of time, is implicitly given by the evolution of the phase-field variables. The temporal evolution of the phase- field variables is described by a set of kinetic equations, which are received in terms of thermodynamics of irreversible processes. Phase is thought as a labeling device for identifying regions with different state functions, and in this work the definition of a phase is taken to be a region of microstructure characterized by a homogeneous state function that differs from the functions of the other phases. Phase fraction variables are introduced for the purpose of associating regions of the system with different state functions. Also features of solid state are taken into account. Strong inter-atomic transformation is the causes of elastic stress and various relaxation mechanisms that influence on shape, orientation and structure of new phase. In the article the algorithm of the considered problem decision and results of the isothermal martensite transformation numerical experiments are submitted.