Advanced Solute Conservation Equations for Dendritic Solidification Processes Part I: Experiments and Theory

The macrosegregation formed in dendritic equiaxed structure during early stages of solidification of Al-4.5%Cu alloy has been studied by experimental work and by metallurgical study of cast samples taken from the experimental work. An experimental work was conducted to study the coupled effect of natural convection streams, interdendritic strain and mushy permeability of Al-4.5%Cu aluminum alloy solidified in horizontal rectangular parallelepiped cavity at different superheats. The metallurgical study includes macro-microstructure evaluation, measurements of grain size of equiaxed crystals and macrosegregation analysis. This study shows that the level of surface segregation exhibiting as positive segregation varies with superheat whereas the rest of inner ingot areas show the light fluctuation in segregation values. In addition to experimental work, there is a mathematical study which contains a complete derivation of local solute redistribution equations based on Fleming's approach under different solute diffusion mechanisms in the dendritic solid. This derivation includes also the effects of interdendritic strain and mushy permeability on the local solute redistribution distribution. Owing to the length of the study, it is presented in two parts. The first part describes the experimental work and its results as well as a detail derivation of solute conservation equations. This part also involves comparison and discussion between existing and proposed solute conservation equations. The second part contains the mathematical analyses of a two dimensional mathematical model of fluid flow, heat flow, solidification, interdendritic strain and macrosegregation. Also, this part also contains the numerical simulations by using finite difference technique FDT to create convection patterns, heat transfer, interdendritic strain, and macrosegregation distributions. This part also includes comparisons between the available measurements and model predications as well as full discussion of different model simulations. The mechanism of interdendritic strain generation and macrosegregation formation during solidification of dendritic equiaxed structure under different diffusion mechanisms in dendritic solid has also been explained and discussed.