Geometrical grounds of mean field solutions for normal grain growth

Abstract The classical mean field approach for normal grain growth in polycrystalline materials is revisited. We re-drive and study possible self-similar solutions and show that the grain size distribution can be determined only by the geometry of neighbouring grains for any given configuration. In three dimensions, it is shown that a single index 〈 R 〉 2 〈 R 2 〉 can represent the geometrical characteristic of grains and has a one-to-one relationship with the mean field parameter γ . We reinvestigate the results of our recent phase-field study [Darvishi Kamachali R, Steinbach I. Acta Mater 2012;60:2719] in the light of new analytical results and found a value γ ≈ 3.5 – 3.2 for the stable regime.