Numerical modeling of microstructural evolution in metals, ceramics and rocks

Practically all metals, ceramics and rocks are polycrystalline materials which consist of a mixture of tiny grains (single crystals) which are “glued” together by interatomic forces. Polycrystals are intrinsically unstable. They undergo various changes with time, which, in turn, affect other physical and mechanical properties of the materials such as their strength and creep resistance. Therefore, understanding the microstructural evolution is very important in many practical and theoretical applications. Understanding the microstructural evolution in metals and ceramics helps to control the properties of these materials and enhance their performance in industrial applications. Understanding the microstructural evolution in rocks is also essential to theories of the dynamics of solid interior of the Earth. Computational methods proved to be very useful for studying microstructural evolution. Furthermore, this is, perhaps, the only way to study microstructural evolution on geological time scales. This work develops the Monte Carlo Potts model to investigate microstructural evolution of polycrystalline materials. The emphasis is on coarsening of two-phase systems. In particular, the model is applied to investigate the microstructural evolution of a two-phase system in which both phases coarsen simultaneously. It is shown that a two-phase system with initially small grains eventually reaches an asymptotic regime in which grain growth in both phases is coupled due to Zener pinning and obeys a power-law scaling relationship. This conclusion is valid in a broad parameter range and is in agreement with theoretical predictions and laboratory experiments. The Monte Carlo Potts model is also shown to be successful in simulating the degeneration of lamellar structures formed upon eutectoid phase transformations. We find that an isotropic lamellar structure degenerates via edge spheroidization and termination migration into nearly equiaxed grains with a diameter which is 2 to 3 times larger than the initial lamellar spacing. The duration of this process is comparable with the time it would take Ostwald ripening to produce grains of the same size. Eventually grain growth reaches the asymptotic regime of coarsening described by a power-law function of time. Lamellae with anisotropic grain boundaries coarsen more slowly and via a different mechanism, discontinuous coarsening. This produces larger grains upon degeneration of lamellae. It is also shown that coarsening of two-phase systems under variable conditions, such as continuous cooling, can approximately be described by a differential form of the grain growth equation.