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.
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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
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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
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DOI: https://doi.org/10.1007/BF00412005