On array models theoretical predictions versus measurements for the growth of cells and dendrites in the transient solidification of binary alloys

Abstract

Most of the theoretical studies of the growth of cells/dendrites in the literature are based on the assumption that it is a steady-state phenomenon. The analysis of cells/dendritic structures in the unsteady-state regime is very important, since it encompasses the majority of industrial solidification processes. The aim of the present investigation was to validate the predictions furnished by the cellular and primary dendritic growth models in the literature for unsteady-state conditions against a large spectrum of experimental data, which includes those for a variety of Al alloys (Al–Cu, Al–Si, Al–Fe, Al–Bi, Al–Ni, Al–Sn) and low thermal diffusivity alloys, such as Sn–Pb and Pb–Sb. The predictions furnished by the Hunt–Lu model do not match the cellular experimental scatter for any examined alloy system. However, this model matches well with the primary dendritic growth of Al alloys, with the exception of Al–Sn alloys, for which the Hunt–Thomas approach has to be applied. The primary dendritic predictions of Bouchard–Kirkaldy's model, performed with the originally suggested a ₁ calibration factors are, in most cases, located above the experimental points. Experimental growth laws relating cellular and dendritic spacings with the tip growth rate and the cooling rate, respectively, are established.

Keywords:

• solidification
• casting
• microstructure
• cell growth
• dendrite
• growth model

Acknowledgements

The authors acknowledge the financial support provided by FAPESP (The Scientific Research Foundation of the State of São Paulo, Brazil), CNPq (The Brazilian Research Council) and FAEPEX-UNICAMP.