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Due to its simplicity and efficiency, cluster dynamics modeling has been widely used to simulate microstructure evolution in materials, such as defect formation in metals. However, its computation cost becomes prohibitive when the clusters grow too large, so a particle-size-grouping method is often required. In this paper, three different size-grouping methods are compared with the exact solution of the ungrouped cluster dynamics model for Al3Sc precipitation in an Al-0.18 at.% Sc alloy. A new assumption of logarithmically-linear distribution of cluster number densities inside each size group is shown to be the most efficient way to match with all results of the ungrouped model. Finally, the calculated results are compared with the measured sizes and distributions of Al3Sc precipitates at different aging temperatures. The new size-grouping method is shown to have better accuracy for the chosen discretization and time-stepping method evaluated. This will enable significant computational savings, and the extension of time scales and cluster sizes to the ranges of realistic metallurgical systems, while preserving reasonable accuracy.

Grouping Methods of Cluster Dynamics Model for Precipitation Kinetics