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

Abstract

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.

EBSD Study of Delta-Processed Ni-Based Superalloy

“…The highest percentage of average angle misorientation of the γ-phase of 80% corresponds to angles < 1° (blue), as illustrated in Figure 11b, and the δ-phase presents a percentage on average of 12% angle misorientation < 1° (red tones), as shown in Figure 11c. This reveals that both phases are mostly a necessary ratio of less than one for a reference frame transformation of a crystalline network to another [34,[45][46][47], i.e., the orientation distance in space between two different orientations. For the local change of crystalline orientations produced inside the grains, a dispersion of crystalline orientations was found, which increases with a random distribution and deformation in the crystallographic orientation, irrespective of the axis, Z0, Y0, and X0.…”

“…Some researchers have already used EBSD analysis for nickel-based superalloys. For instance, the flow behavior of IN718 by hot compression tests conducted at several conditions in connection with the grain boundary misorientation angle distribution at different temperatures, microstructural evolution, and twinning formation during dynamic recrystallization has been analyzed [21,[31][32][33][34]. It has also been found that twin boundaries are particularly resistant to precipitate formation, and no clear evidence has been found for a special relationship between boundary misorientation and precipitation [35].…”

GPU-Accelerated Cellular Automaton Model for Grain Growth during Directional Solidification of Nickel-Based Superalloy

“…To simulate grain growth in superalloy solidification, a CA model [32] was adopted. A continuous nucleation model proposed by Rappaz and Gandin et al [33] was used to describe the heterogeneous nucleation.…”

“…Moore neighborhoods of cell A were considered for cell capture. The extension of the capture rule to 3D is straightforward, which can be referred to [32].…”