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G.I. Rees,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.
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Calculates the effective nucleation rate which, in a given time, results in a specified Widmanstätten ferrite or bainite volume fraction.
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Language: | FORTRAN
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Product form: | Source code |
DOUBLE PRECISION FUNCTION MAP_STEEL_WNSOLVE(GBN, V, G, RADIUS, VM,
& SV, TIME)
DOUBLE PRECISION GBN, V, G, RADIUS, VM, SV, TIME
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The function uses the previously calculated value for the nucleation rate (GBN) as
a starting point. It sets bounds for the nucleation rate required to form volume
fraction V in time TIME, and then solves for it. The solution method is
bisection [2].
If there is no previously calculated value for the nucleation rate, GBN may be set to
1.0.
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- H.K.D.H. Bhadeshia, Metal Science, 16, (1982), 156-165.
- W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling,
Numerical Recipes, Cambridge University Press, Cambridge, U.K., (1986).
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Input parameters
- GBN - real
- GBN is the previously calculated value of MAP_STEEL_WNSOLVE. If the
function is being called for the first time, the value of GBN is set to
1.0.
- V - real
- V is the volume fraction assumed to have formed by time TIME.
- G - real
- G is the growth rate of a plate under carbon diffusion control(in
ms-1).
- RADIUS - real
- RADIUS is the critical radius of curvature rhoc of a ferrite
plate tip which gives zero growth rate (in metres).
- VM - real
- VM is the maximum allowable volume fraction Vmax of either
bainite or Widmanstätten ferrite that can form at the temperature
concerned.
- SV - real
- SV is the surface area Sv of austenite grain boundary per unit
volume (in m-1).
- TIME - real
- TIME is the incubation period at the given temperature [1] (in
seconds).
Output parameters
- MAP_STEEL_WNSOLVE - real
- MAP_STEEL_WNSOLVE is the nucleation rate (in ms-1).
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None.
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The successful solution gives a nucleation rate for which the predicted volume fraction
matches the target value V with a maximum error of |Delta| so that:
|(Delta V/V)| < 0.015
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None.
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1. Program text
DOUBLE PRECISION GBN, V, G, RADIUS, VM, SV, TIME
DOUBLE PRECISION MAP_STEEL_WNSOLVE, NRATE
READ (5,*) GBN, V, G, RADIUS
READ (5,*) VM, SV, TIME
NRATE = MAP_STEEL_WNSOLVE(GBN, V, G, RADIUS, VM, SV, TIME)
WRITE (6,10) NRATE
10 FORMAT ('Nucleation rate = ', D13.5,' m/s')
STOP
END
2. Program data
0.40294D-01 0.10000D-01 0.10447D-04 0.19331D-08 0.18303D+00 0.20000D+05 0.12204D+02
3. Program results
Nucleation rate = 0.47849D-01 m/s
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MAP_STEEL_WKINETIC
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nucleation rate, Widmanstatten, bainite, volume fraction
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Download source code
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