Numerical Simulation of Three-Dimensional Mesoscopic Grain Evolution: Model Development, Validation, and Application to Nickel-Based Superalloys

The mesoscopic grain model is a multiscale model which takes into account both the dendrite growth mechanism and the vast numerical computation of the actual castings. Due to the pursuit of efficient computation, the mesoscopic grain calculation accuracy is lower than that of dendrite growth model. Improving the accuracy of mesoscopic grain model is a problem to be solved urgently. In this study, referring to the calculation method of solid fraction in microscopic dendrite growth model, a cellular automata model of 3D mesoscopic grain evolution for solid fraction calculated quantitatively at the scale of cell is developed. The developed model and algorithm validation for grain growth simulation is made by comparing the numerical results with the benchmark experimental data and the analytical predictions. The results show that the 3D grain envelopes simulated by the developed model and algorithm are coincident with the shape predicted by the analytical model to a certain extent. Then, the developed model is applied to the numerical simulation of solidification process of nickel-based superalloys, including equiaxed and columnar dendritic grain growth. Our results show good agreement with the related literature.