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A criterion for freckling prediction that includes the effect of a tilted solidification front was proposed and evaluated with experimental data available in the literature. The criterion is based on the maximum local Rayleigh number in the mush layer and was developed using Flemings' criterion and assuming that the interdendritic liquid flow is governed by the Darcy law. The proposed form preserves the anisotropic nature of the permeability tensor throughout the derivation and provides improved resolution on freckle prediction. A clear separation between the freckled and nonfreckled experiments was obtained for all compositions. The effect of the tilted solidification front over the freckling potential was corroborated, and the results suggested that the directionality of permeability affects the location within the mush layer of the potential nucleation sites for the channels leading to freckles. A threshold zone was determined from the enclosing experiments data, and the range contained one of the proposed critical values for superalloys, which previously was developed by a completely different method.

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In this article, a profile-fitting methodology was developed to measure the partition coefficients of solute elements during the solidification of Ni-base alloys. Better agreement with the theoretically calculated values is expected if the accuracy of the composition and the homogeneity of the model alloys are enhanced. Regular differential thermal analysis (DTA) measurements were consistently higher than the theoretical transition temperatures, and the differences were smaller when compared to the predictions performed with the thermodynamical database developed by Du et al. The better agreement between the experimental results and the theoretical predictions made with the newly developed database suggests that improvements in the accuracy of the theoretical predictions can still be obtained and are necessary for accurate freckling prediction. Quenching modified DTA (MDTA) experiments were proven to be appropriate for directly measuring the average partition coefficients of the solute elements. Regarding the cooling rate of the first stage of the quenching experiments, it was assumed successfully that the cooling rate prior to the quenching step of 0.083 Ks À1 was sufficiently slow to permit easy quenching, while being fast enough for the primary solidification reaction to depart from the equilibrium model and being closer to the Scheil model of segregation. The minimization of the error function defined from the Scheil equation was found to be an appropriate method for describing the segregation profiles of the quenched samples and permitted good estimations of the partition coefficients of the solute elements. The reliability of the methodology was found to be satisfactory given that the magnitudes calculated for the partition coefficients of the solutes in the multicomponent alloy 718 were found to be very close to the values reported in the literature.

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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.