Abstract
The dendrite tip kinetics model accuracy relies on the reliability of the stability constant used, which is usually experimentally determined for 3D situations and applied to 2D models. The paper reports authors` attempts to cure the situation by deriving 2D dendritic tip scaling parameter for aluminium-based alloy: Al-4wt%Cu. The obtained parameter is then incorporated into the KGT dendritic growth model in order to compare it with the original 3D KGT counterpart and to derive two-dimensional and three-dimensional versions of the modified Hunt’s analytical model for the columnar-to-equiaxed transition (CET). The conclusions drawn from the above analysis are further confirmed through numerical calculations of the two cases of Al-4wt%Cu metallic alloy solidification using the front tracking technique. Results, including the porous zone-under-cooled liquid front position, the calculated solutal under-cooling, the average temperature gradient at a front of the dendrite tip envelope and a new predictor of the relative tendency to form an equiaxed zone, are shown, compared and discussed for two numerical cases. The necessity to calculate sufficiently precise values of the tip scaling parameter in 2D and 3D is stressed.
Highlights
Dendritic crystal structures which form during solidification of metallic alloys have their enormous influence on the mechanical properties of solid alloys, the dendritic growth problem has been a topic of long-term interest within the academia and metal industry
The obtained parameter is incorporated into the KGT dendritic growth model in order to compare it with the original 3D KGT counterpart and to derive two-dimensional and three-dimensional versions of the modified Hunt’s analytical model for the columnar-to-equiaxed transition (CET)
Results show that for the same G value, the CET shifts to a higher V value for the 3D σ* stability parameter proving that there is a significant difference in 2D and 3D representation of the CET effect
Summary
Dendritic crystal structures which form during solidification of metallic alloys have their enormous influence on the mechanical properties of solid alloys, the dendritic growth problem has been a topic of long-term interest within the academia and metal industry. Rebow and Browne [12] estimated dendritic tip stability parameters σ* of two aluminium alloys, namely Al-4wt%Cu and Al-2wt%Si, based on measured values of their crystal-melt surface energy anisotropy strength ε and a simple linear scaling law of microscopic solvability theory. They showed that the stability parameter has the significant influence on columnar dendritic growth models and on a columnar to equiaxed transition with help of modified Hunt’s analytical maps and meso-scale front tracking simulations. Results show that for the same G value, the CET shifts to a higher V value for the 3D σ* stability parameter proving that there is a significant difference in 2D and 3D representation of the CET effect
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