Abstract
There have been many analytical and numerical studies on microsegregation and prediction of second phase in solidification structures of alloys, and they have both advantages and disadvantages especially on the applicability of variable partition ratio (k) of solute and diffusion coefficient (D) in the solid. In this paper, we propose and apply a new progressive-type solidification equation: CLi=CLi−1·[{1−(1−B·ki−1)fsi}⁄{1−(1−B·ki−1)fsi−1}](ki−1−1)⁄(1−B·ki−1), which has a parameter (B) including variable partition ratio (k) and D. A specific parameter B is given in each progressive solidification model: B=2α (Flemings model), B=2α(1−exp(−1⁄α))−exp(−1⁄2α) (Clyne-Kurz model), or B=2α⁄(1+2α) (Ohnaka model), where α=D·θf⁄L2, L: effective length of volume element (=s·d2⁄2, s: structure factor (=0.5∼1), d2: dendrite arm spacing), θf: local solidification time. The difference in B-values among the above models are small when D-value is relatively small. The solidification-paths of various Al-Ti-Cr alloys, which crystallize L12-type (Al,Cr)3Ti as the primary phase, are analyzed by the progressive-type solidification equation by using the above B values and the data of Al-Ti-Cr phase diagram including k-values (: functions of composition) and experimentally determined diffusion coefficient. The calculated results agree well with the solidification microstructures: the species and the amounts of non-equilibrium eutectic phases and the composition of primary phases.
