Solidification Front Tilt Angle Effect on Potential Nucleation Sites for Freckling in the Remelt of Ni-Base Superalloys

Abstract

By considering the mushy layer as a porous media with variable permeability, a Rayleigh number based freckling criterion was developed from the Flemings ratio between the magnitude of the interdendritic flow velocity and the solidification rate. The proposed form includes the effect of the tilt angle by preserving the anisotropic nature of the permeability tensor throughout the derivation and uses Poirier's experimentally determined functional forms for the parallel and perpendicular components. The proposed form of Rayleigh number criterion was found to provide better resolution when evaluated against available experimental data in the literature.Especially, it showed that the nucleation of channels in the mushy layer leading to freckles is equally probable in the proximity of the tips of the dendrites or deeper in the mushy layer, for example at approximately 0.7 liquid fraction and 0.4 liquid fraction respectively, depending on the angle of tilt of the solidification front.