Evaluation of a rayleigh-number-based freckle criterion for Pb-Sn alloys and Ni-base superalloys
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20/6/03
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Evaluation of a Rayleigh-Number-Based Freckle Criterion for Pb-Sn Alloys and Ni-Base Superalloys J.C. RAMIREZ and C. BECKERMANN A criterion for predicting the formation of freckles for Pb-Sn and Ni-base superalloys is evaluated using available experimental data. The criterion is based on a maximum value of the Rayleigh number, which indicates that the magnitude of buoyancy forces is largest with respect to the retarding frictional forces. The definition of the Rayleigh number involves a characteristic length scale. The two options explored in this study are the distance from the liquid mush interface and the scale represented by the ratio of thermal diffusivity to the casting speed. Additionally, two alternative ways of computing the mushy-zone permeability are explored. Only two of the possible combinations of length scales and permeability relations provide a maximum value within the mush that can be chosen as a representative value for the given conditions. It is found that the Rayleigh number that uses the ratio of thermal diffusivity to the casting speed as a length scale provides the best separation between freckled and nonfreckled data. Critical values for the Rayleigh number are in the range of 38 to 46 for vertically solidified Pb-Sn and within the range of 30 to 33 for Ni-base superalloys. Although not exactly the same, the proximity of these intervals indicates that the critical Rayleigh number is not very sensitive to alloy-specific system parameters. The influence of sample pulling inclination angle on this critical value is assessed for Ni-base superalloys. A preliminary relationship between the critical Rayleigh number and the inclination angle is developed.
I. INTRODUCTION
FOR unidirectional solidification of castings, where the objective is to obtain a columnar structure, the presence of chains of small equiaxed grains (i.e., freckles) is to be avoided. This concern is of chief importance for directionally solidified superalloy single-crystal parts, where the presence of freckles renders the part defective. For Pb-Sn alloys, there is admittedly no concern over the practical implications of the presence of freckles; however, simple binary alloys such as Pb-Sn are popular with experimental researchers because they provide insight into the same complicated phenomena that would be expected in more complex systems. During upward directional solidification, the interdendritic liquid in the mushy zone is held by the frictional forces stemming from the presence of the dendrite arms, which essentially act as a solid boundary. However, due to microsegregation, light alloy elements will be rejected into the melt if the partition ratio is less than unity, or heavy elements will preferentially be incorporated into the solid, for partition ratios larger than unity. Under either of these two circumstances, the density of the liquid decreases and in some circumstances it may do so by a factor large enough so that the induced buoyant forces overcome the frictional resistance offered b
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