Abstract
Progress is reported in the development of a computer program for modelling the process of microsegregation in multicomponent steels. The program is based on the single phase binary and ternary models described in the previous paper by Ogilvy and Kirkwood but has been extended to consider general, multicomponent alloys. The cooling rate required in the program formulation is currently determined according to a constant, set rate of heat extraction, but any, independently derivable rule could be employed. The peritectic reaction from ferritic to austenitic solidification encountered in a great many steels has been included in the formulation with the relevant, three-phase compositions decreed in pseudo-binary fashion by appropriate carbon equivalents. The onset of the austenite-cementite eutectic is similarly described. Manganese sulphide precipitation is described by removal of the elements from the residual liquid in appropriate ratio so as not to exceed a prescribed solubility product. Such devices can be fashioned similarly for other phase and precipitate developments as required.
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Abbreviations
- A :
-
Back diffusion term, m wt% s-1
- B :
-
Correction factor for fast — diffusing species
- C :
-
Concentration in the solid, wt%
- Cl :
-
Concentration in the liquid, wt%
- C 0 :
-
Bulk concentration, wt%
- C p :
-
Concentration in the liquid during the peritectic, wt%
- D :
-
Diffusivity in the solid, m2s-1
- f :
-
Fraction solid (= X/L)
- f :
-
Volumetric latent heat, Jm-3
- K :
-
Partition coefficient
- L :
-
Half dendrite arm spacing, m
- M :
-
Atomic weight, (a.m.u.)
- Q̇ :
-
Heat extraction rate, Jm-3s-1
- R :
-
Atomic weight ratio
- t :
-
time, s
- T :
-
Temperature, k
- W :
-
Cooling rate, ks-1
- x :
-
Distance coordinate normal to dendrite plate
- X :
-
Distance solidified, m
- Z :
-
Correction increment, wt%
- β :
-
Liquidus gradient, k wt% -1
- θ :
-
Heat capacity, Jm-3k-1
- c:
-
carbon
- i :
-
“i”th element
- Mn:
-
manganese
- S:
-
sulphur
- bcc:
-
body centred cubic delta ferrite
- fcc:
-
face centred cubic austenite
References
A.J.W. Ogilvy and D.H. Kirkwood: A model for the numerical computation of microsegrega-tion in alloys. Appl. Sci. Res. 44 (1987) 43–49.
A.J.W. Ogilvy: PhD Thesis, Sheffield University (1983).
H.T. Angus: Cast Iron, Butterworths (1976).
K. Schwerdtfeger: Arch. Eisenhutten. 41 (1970) 923–937.
A Guide to the Solidification of Steels, Jernkontoret, Stockholm (1977).
M.C.M. Cornelissen: paper presented at ‘Progress in Modelling of Solidification Processes’, Sheffield University (1986) (Inst. of Metals).
E. Schmidtmann and F. Rakoski: Stahl. u. Eisen 103 (18) (1983) 881–882.
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© 1987 Martinus Nijhoff Publishers, Dordrecht
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Howe, A.A. (1987). Development of a computer model of dendritic microsegregation for use with multicomponent steels. In: Smith, T.J. (eds) Modelling the Flow and Solidification of Metals. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3617-1_5
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DOI: https://doi.org/10.1007/978-94-009-3617-1_5
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