Computer Simulation of Two-dimensional Grain Growth Using the Phase Field Model

Grain growth is one of the most basic microstructure evolution processes in polycrystalline materials. Investigation into the grain growth process is of both theoretical and practical significance. In recent years, computer simulation has become an effective means in the field of materials design and microstructure evolution. Simulation and analytical treatment of grain growth process helps to complete the verification and examination of theoretical model of grain growth and to establish foundation for materials design at microstructural level. Thus, this thesis simulated two-dimensional grain growth process using the phase field method. The quasi-steady state grain size distributions were examined so as to gain better understanding on grain growth process.In this dissertation, the algorithm based on the phase field model has been built up for the simulation of grain growth in two dimensions. The effectiveness of this method was primarily verified by modeling the shrinking of a circular grain embedded in an infinite matrix. Simulation of the two-dimensional grain growth process using this model was carried out. The results show that the simulated grain growth kinetics has a parabola form. The grain size distribution is time-dependent, which will arrive at the self-similar state after long time simulation. The quasi-steady state grain size distribution can be described by both the Weibull function and the Louat function. Comparing these two functions by graph and mathematics, it can be found that these two functions can replace each other approximately under certain conditions. Thus, the grain size distributions reported from different techniques is actuallconsistent. The side distribution obtained in this thesis has a Lognormal form. The correlation between grain size and side is non-linear. All these results agree with those from experiments and Monte Carlo simulation. Two main topology evolution mechanisms: neighbor switching and disappearing of small grains were recurred using the phase field simulation. Our observations show that before the total disappearing of small grains, a region of disordered material is formed, which cannot be seen using the sharp-interface models.

Keywords:grain growth; phase field method; quasi-stationary grain size distribution