The Interdependence Model: An Improved Predictor of Grain Size

The newly developed Interdependence Theory is described by the Interdependence equation that is able to predict grain size on a more rigorous basis than has previously been possible. In this paper the theory is briefly introduced and then the Interdependence equation is used to predict the experimentally determined grain size for a broad range of aluminium alloy compositions, each cast with a range of AlTi and AlTiB master alloy additions. It is shown that the Interdependence equation provides reasonable prediction of grain size when using literature values for the diffusion coefficient, nucleation undercooling and interface growth velocity. Insights into the effect of the distribution of the added TiB₂ particle size on the efficacy of master alloys are revealed illustrating why so few added particles become successful nucleants. Implications of the Interdependence model for further research are also discussed.