Abstract
A development of the Brody-Flemings model for the prediction of dendritic microsegregation in alloys is proposed. The original model considered one-dimensional back diffusion into thickening platelike dendrite arms of fixed spacing. The present modification allows for the dendrite arm coarsening which is observed to occur during solidification and considers microsegregation in both binary and multi-component alloy systems. It is shown that numerical calculations of microsegregation using finite difference techniques based on this model give good agreement with experiment.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
Abbreviations
- B=(1−f)/(1−(1−k)f):
-
correction factor for fast diffusing species
- c :
-
concentration in solid, wt.%
- c 0 :
-
average concentration, wt.%
- c l :
-
concentration in liquid, wt.%
- D :
-
diffusion coefficient in solid
- f :
-
fraction solid (=X/L)
- k :
-
equilibrium partition coefficient
- L :
-
half dendrite arm spacing
- t :
-
time
- W :
-
cooling rate
- x :
-
direction coordinate normal to dendrite plate
- X :
-
distance solidified
- β :
-
liquidus gradient
- i :
-
refers to the ith solute element
References
G.H. Gulliver: Metallic Alloys, Charles Griffin, London, (1922).
E. Scheil: Z. Metallk. 34 (1942) 70.
H.D. Brody and M.C. Flemings: Trans AIME 236 (1966) 615.
T.W. Clyne and W. Kurz: Metall. Trans. 12A (1981) 965.
T.F. Bower, H.D. Brody and M.C. Flemings: Trans. AIME 236 (1966) 624.
M.C. Flemings: Solidification Processing, McGraw-Hill, New York (1974).
C.J. Smithells, Metals Reference Book, 5th edn., Butterworths, London (1976)
B.A. Rickinson and D.H. Kirkwood: Proc. Conf. on Solidification and Casting of Metals, Sheffield, July 1977, Metals Society, London (1979), p. 44.
T.Z. Kattamis, J.C. Coughlin and M.C. Flemings: Trans. Metall. Soc. AIME 239 (1967) 1504.
K.H. Chien and T.Z. Kattamis: Z. Metallkunde 61 (1970) 475
K.P. Young and D.H. Kirkwood: Metall. Trans. 6A (1975) 197.
D.H. Kirkwood: Mat. Sci. and Eng. 65 (1984) 101.
J. Crank: Quart. J. Mech. App. Math. 10 (1957) 220.
D.H. Kirkwood and D.J. Evans: Conf. on ‘The Solidification of Metals’, Iron and Steel Inst., London (1978) ISI P110.
A.A. Howe: Appl. Sci. Res. 44 (1987) 51–59.
G.D. Smith: Numerical Solution of Partial Differential Equations, 2nd edn., Clarendon Press, Oxford (1978).
D.A. Bennett: Ph.D. thesis, Univ. of Sheffield (1978).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Ogilvy, A.J.W., Kirkwood, D.H. A model for the numerical computation of microsegregation in alloys. Applied Scientific Research 44, 43–49 (1987). https://doi.org/10.1007/BF00412005
Issue Date:
DOI: https://doi.org/10.1007/BF00412005