Geometrical grounds of mean field solutions for normal grain growth
R. Darvishi Kamachali, A. Abbondandolo, K. F. Sieburg, I. Steinbach.
Acta Materialia, Elsevier, 90, 252-258, (2015)
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⁄⟨r²⟩ 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 in the light of new analytical results and found a value γ≈3.5–3.2 for the stable regime.
Keyword(s): grain growth; grain size distribution; self-similar regime; mean field theory; phase-field simulation