A Phenomenological Analysis of Freckling in Directional Solidification of NiBase Superalloy: The Role of Edge and Curvature in Casting Components
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Abstract
The geometrical factor in freckle formation has rarely been taken into account. In this work, freckle formation in superalloy components is examined. It is found that freckle formation is subject to the effects of the edge and curvature. In polygonal casting sections, freckles are formed preferably on the convex edges. In the components with a curved contour, freckles are exclusively formed on the outwardcurving surface having positive curvature.
Freckles remain as one of main casting defects in singlecrystal (SC) or directionally solidified (DS) Nibase components.[1, 2, 3, 4] They appear to be long trails of equiaxed grains aligning roughly parallel to the direction of gravity and are often found on the surface of SC or DS superalloy castings.[5, 6, 7] It is generally acknowledged that freckles are formed as a consequence of thermossolutal convection, which is driven by density inversion in the mushy zone.[1,8, 9, 10, 11] The interdendritic liquid in the mushy zone tends to “jet” upward from the mush zone. Along the way, these jets erode dendrites and break them apart. Thereafter, the eroded dendrites redissolve into the liquid or act as nuclei for equiaxed grains.[12, 13, 14, 15, 16, 17]

Above a critical thermal gradient, the mushy zone becomes too small to accommodate the convective currents for freckles to form.

With an increasing solidification velocity, the local solidification time will be shorter than the minimum one required to form freckles, resulting in a frecklefree structure.

In addition, larger casting size leads to severe freckling.[1, 4, 5, 26, 27, 28] This is because an increased cross section of a casting has a wider mushy zone, providing a sufficient reservoir for the interdendritic convection, and the convention favors the freckle formation.[29, 30, 31, 32] In contrast, freckles are normally not found in components with small crosssectional area.[1] This is commonly referred to as the size effect of freckle formation.
In recent work,[16,24, 25, 26, 27] a series of SC and DS experiments with a relatively complex geometry was carried out under industrial conditions, and a number of interesting phenomena related to freckle formation were observed, such as the shadow,[33] step,[33,34] orientation,[35] slopping[23] and edge effects.[33,36]
Recently, we observed that freckles prefer to form on the edges of components instead of on the plane surface despite the higher cooling rate on the edges, which is unfavorable for freckle formation. In this article, the edge and curvature effect on freckle formation will be reported.
Compositions of NiBase Superalloy CMSX4 (Wt Pct)
Co  Cr  Mo  W  Al  Ti  Ta  Hf  Re  C  

CMSX4  9.0  6.5  0.6  6.0  5.6  1.0  6.5  0.1  3.0  0.12 
A solidified structure is revealed in the decanted mushy zone because of the insufficient feeding. The decanted mushy zone can be easily recognized as the dark zone ahead of the fully solidified solid zone, which appears much brighter, as shown in convex blade side A in Figure 2. In the exposed freckling channels in the mushy zone, growing dendrite and broken dendrite arms can be observed. At the locations corresponding to the freckling channels, the mushy zone is wider because of the delayed solidification processing. Under each channel in the mushy zone, a freckle chain can be found in the solid zone. It is then evidently confirmed that the freckle formation resulted from the channelshaped segregation and convection in the mushy zone. The molten alloy in the freckling channels was seriously segregated, significantly lowering the solidus temperature. As a result, the residual melt in the channels was exhausted by the neighboring dendrites, leaving open grooves on the surface of convex side A.
On the middle part of convex side A, as shown in Figure 2, the most serious freckles were observed, although the local curvature effect was relatively small. The thickness of the crosssectional mold must be an important promoting factor, i.e., the size factor, to provide a sufficient reservoir to support the interdendritic convection and hence the onset of freckling. On the other side, regardless of the favorable size factor and thermal condition of concave side B, no freckles were observed. The interpretation for this important phenomenon is proposed as the curvature effect of the component cross section. The negative curvature of site B diverges and weakens the surface effect compared with positive curvature, which will strengthen the surface effect owing to the overlapping effect.
The result of edge and curvature effects on freckle formation is schematically illustrated in Figure 4(c). In the figure the blade contour is simplified as a polygonal section to illustrate the surface effect on freckle formation in complex components. Edges A, C and D are convex edges with different angles, whereas concave edge B presents an angle > 180 deg. Surface effect zones and overlapping zones are marked on Figure 4(c). At edges A, C and D, the surface effect zones of the neighboring sides are overlapped for an angle < 180 deg. As illustrated in the figure, the effect of the convection condition on freckle formation in the overlapping region is doubled compared with the effect at the flat side, leading to the socalled “edge effect” on freckle formation (Figures 1 and 2). To some extent, the overlapping effect of the neighboring sides is more pronounced if the included angle becomes smaller according to the observations of freckles on the trailing edges of turbine blades. At concave edge B in Figure 4(c) where an included angle > 180 deg occurs inside of the polygonal, there is a gap in the wedge shape. No freckle forms in concave edge B.
 (1)
Fluid permeability near the wall is much higher than that inside of the casting, promoting thermalsolutal convection and freckle formation on the component surface.
 (2)
On the edges of the components, the surface effects on convection overlap each other, providing a more favorable freckling condition than that on the flat surfaces, leading to the socalled “edge effect,” promoting freckle formation.
 (3)
The edge effect can be extended to the curvature effect. The convex side has a positive curvature, and the surface effect can be overlapped and then strengthened, while the concave side has a negative curvature, and the surface effect will diverge and then weaken. Therefore, freckles are observed more frequently on the convex surface than on the concave ones of castings.
 (4)
The insertion of ceramic cores into casting components provides an internal wall, which promotes freckle formation on the convex surface.
Notes
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