The Columnar-Equiaxed Transition

"The columnar-equiaxed transition (CET) has been studied numerically under unsteady-state conditions using mathematical models that: (i) include a non-equilibrium undercooling at the columnar front;and(ii) describe the simultaneous evolution of the columnar and equiaxed zones.The results are discussed and compared with those produced by a steady-state analysis.IntroductionThe majority of the previous work on the columnar-equiaxed transition (CET) has concentrated on the production of equiaxed nuclei, regarding this as being the critical step in the formation of an equiaxed zone. Recently, the growth of equiaxed grains has been considered and this is not unreasonable because, for an equiaxed zone to be present, the grains must grow as well as nucleate. Since the growth rate of the grains will be determined by the thermal environment at and ahead of the columnar tips, it was decided to model the liberation and flow of heat during solidification to discover whether the various trends in the columnar range might be explained by their effect on the temperature profile throughout the casting. The models presented here for the solidification of a casting are the first to include the latent heat liberated ahead of the columnar front. Burden and Hunt (1) consider its effect only qualitatively, and although Lipton et al (2) adopt a criterion for the CET which is based on the thermal interaction of the columnar and equiaxed grains, they do not actually include the latent heat in their calculations.It can be argued that the latent heat liberated by the equiaxed grains in the bulk will retard the columnar dendrites in a casting: once the equiaxed grains are sufficiently well-established, the latent heat that they evolve could slow down the columnar growth to such an extent that the equi axed would dominate. Alternatively, the latent heat produced by the equiaxed grains might suppress further equiaxed solidification by raising the bulk temperature. The nature of the thermal interaction between columnar and equiaxed growth is not obvious, and because it is dependent on the material parameters and the dimensions of the system, it cannot be considered effectively in a qualitative way but has to be studied quantitatively: hence the need for the mathematical models discussed in the following pages. The results of the models are discussed in the light of a steady state analysis."