Freckle criteria for the upward directional solidification of alloys

Yang, Wulin; Chang, Keh‐Minn; Chen, Wei; Mannan, S.; deBarbadillo, J.J.

doi:10.1007/s11661-001-0271-y

Cited by 60 publications

(38 citation statements)

References 34 publications

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“…These criteria are essentially based on a critical mushy zone size and thus a maximum local solidification time beyond which freckling occurs in the ingot. Recently, criteria involving the Rayleigh number have been proposed based on the studies in the area of directional solidification [29][30][31]. The Rayleigh number (Ra), which is the ratio of buoyancy-to-viscous force is defined as:…”

Section: Freckle Criteriamentioning

confidence: 99%

Modeling of Vacuum Arc Remelting of Alloy 718 Ingots

Patel¹,

Minisandram²,

Evans³

2004

Superalloys 2004 (Tenth International Symposium)

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Vacuum Arc Remelting (VAR) is typically the final melting process in the production of a wide range of alloys including superalloys, titanium, zirconium and specialty steels. During this process, a DC arc is struck under vacuum between a consumable electrode and a water-cooled copper crucible. The heat from the arc melts the electrode and molten metal droplets from the electrode solidify in the crucible to form an ingot. The purpose of VAR is to cast a sound, segregation free ingot. The soundness of the final structure and tendency for defect formation are determined by the pool profile and ingot solidification patterns during the process. These, in turn, depend on the melting parameters, which change as the ingot freezes. A carefully developed physics-based numerical model is useful in analyzing a priori the effect of melt parameters on the molten metal pool in the ingot. The purpose of this paper is to discuss the key features of such a model, and examine the effect of melting parameters on the pool profile. In addition, the effect of a molten metal pool perturbation during a power interruption and a melt rate cycle is examined for a 0.5m (20-inch) diameter ingot. Finally, the computed temperature distribution and flow field is used to predict the melting time for particles that fall into the molten pool and the likelihood of freckle formation in an alloy 718 VAR ingot.

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Section: Freckle Criteriamentioning

confidence: 99%

Modeling of Vacuum Arc Remelting of Alloy 718 Ingots

Patel¹,

Minisandram²,

Evans³

2004

Superalloys 2004 (Tenth International Symposium)

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“…Therefore, several attempts have been made to describe convection in terms of a nondimensional mushyzone Rayleigh number. [4,7,[23][24][25][26] The mushy-zone Rayleigh number proposed by Beckermann et al [26] (R aB ) has been successful in describing the freckle initiation in nickel-based superalloy castings. However, the critical Rayleigh number for the onset of freckling has not been tested against the extensive freckling data available in the literature on other alloy systems, such as Pb-Sn, [3][4][5][6][7]9] Pb-Sb, [4] and Al-Mg. [8] Describing convection through the mushy zone requires knowledge of the relationship between mushy-zone permeability (K) and its morphology, such as primary dendrite spacing ( 1 ), fraction of interdendritic liquid (), etc.…”

Section: Introductionmentioning

confidence: 99%

A mushy-zone rayleigh number to describe interdendritic convection during directional solidification of hypoeutectic Pb-Sb and Pb-Sn alloys

Tewari

Tiwari

2003

Metall Mater Trans A

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Based on measurements of the specific dendrite surface area (S v ), fraction of interdendritic liquid (), and primary dendrite spacing ( 1 ) on transverse sections in a range of directionally solidified hypoeutectic Pb-Sb and Pb-Sn alloys that were grown at thermal gradients varying from 10 to 197 K cm Ϫ1 and growth speeds ranging from 2 to 157 m s Ϫ1 , it is observed that S v ϭ 1 Ϫ1 S* Ϫ0.33 (3.38 Ϫ 3.29 ϩ 8.85 2 ), where S* ϭ D l G eff /V m 1 C o (k Ϫ 1)/k, with D l being the solutal diffusivity in the melt, G eff being the effective thermal gradient, V being the growth speed, m l being the liquidus slope, C o being the solute content of the melt, and k being the solute partition coefficient. Use of this relationship in defining the mushy-zone permeability yields an analytical Rayleigh number that can be used to describe the extent of interdendritic convection during directional solidification. An increasing Rayleigh number shows a strong correlation with the experimentally observed reduction in the primary dendrite spacing as compared with those predicted theoretically in the absence of convection.

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“…The Rayleigh number form is obtained by a similar method used by Yang 30 , with major differences being that in this work the gradient of the pressure is derived differently, the effect of the tilted solidification front is included without the need to know a priori the direction of the velocity vector and most importantly, the two dimensional anisotropic characteristic of the permeability tensor is preserved throughout the formulation. The simpler, but adequate 11 case of equilibrium between the solid dendrites and the interdendritic liquid was assumed in order to determine the solidification path, the composition and the density of the interdendritic liquid as functions of temperature using JMatPro® software.…”

Section: Development Of the Proposed Freckle Criterionmentioning

confidence: 99%

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

Valdés¹,

Cowen²,

Jablonski³

et al. 2010

7th International Symposium on Superalloy 718 and Derivatives (2010)

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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.

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Freckle criteria for the upward directional solidification of alloys

Cited by 60 publications

References 34 publications

Modeling of Vacuum Arc Remelting of Alloy 718 Ingots

Modeling of Vacuum Arc Remelting of Alloy 718 Ingots

A mushy-zone rayleigh number to describe interdendritic convection during directional solidification of hypoeutectic Pb-Sb and Pb-Sn alloys

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

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