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Function MAP_STEEL_SOLVEFER

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of subroutine's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary subroutines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

G.I. Rees,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

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Purpose

Gives the time taken to reach a volume fraction, V, of ferrite.

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Specification

Language:FORTRAN
Product form:Source code

DOUBLE PRECISION FUNCTION MAP_STEEL_SOLVEFER(AREA, ANS,
& V, SV, BI, ALP, VOL, XBAR, XAGA, XGAG, TPRE)

DOUBLE PRECISION AREA, ANS, V, SV, BI, ALP, VOL, XBAR,
& XAGA, XGAG, TPRE

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Description

The subroutine MAP_STEEL_AVOLF is used to determine the volume fraction of ferrite formed in a given time, and this is used in an iterative calculation to find the time needed to form a given fraction of ferrite.

If the nucleation rate of grain boundary allotriomorphs is I, and the parabolic thickening rate is alpha, the volume fraction Valpha formed after time t is given by [1, 2, 3]:

Equation

where Vmax is the maximum amount of ferrite that can form at the reaction temperature, Sv is the surface area of austenite grain boundary per unit volume, alpha is the parabolic thickening constant for ferrite growth normal to the austenite grain boundary, with (eta alpha) being the parabolic lengthening constant for ferrite in the plane of the boundary.

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References

  1. J.W. Christian, Theory of Transformation in Metals and Alloys, Part 1, 2nd ed., Pergamon Press, Oxford (1975).
  2. H.K.D.H. Bhadeshia, Progress in Materials Science, 29, (1985), 321-386.
  3. H.K.D.H. Bhadeshia, L.-E. Svensson, and B. Gretoft, Proc. Conf. Welding Metallurgy and Structural Steels, ed. J.Y. Koo, TMS AIME, Warrendale, Penn., (1987), 515-530.

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Parameters

Input parameters

AREA - real
AREA is the fractional coverage of the austenite grain boundary surface (given by the intercept of a test plane with the growing allotriomorphs at the austenite boundary), corrected for the effect of `extended' areas [1, 3].

ANS - real
ANS is the integral of the extended area over all space, corrected for extended volume effects [1, 3].

V - real
V is the volume fraction of ferrite.

SV - real
SV is the austenite grain boundary surface area per unit volume Sv (in m-1).

BI - real
BI is the nucleation rate required for a given allotriomorphic ferrite fraction.

ALP - real
ALP is the parabolic thickening rate alpha for ferrite allotriomorphs (in ms-0.5).

VOL - real
VOL is the normalised fraction of ferrite i.e. Valpha/Vmax.

XBAR - real
XBAR is the mean carbon content of the austenite (in mole fraction).

XAGA - real
XAGA is the carbon content of ferrite at the alpha/gamma interface (in mole fraction).

XGAG - real
XGAG is the carbon content of austenite at the gamma/alpha interface (in mole fraction).

TPRE - real
TPRE is the previous value for the time (in seconds).

Output parameters

MAP_STEEL_SOLVEFER - real function.
MAP_STEEL_SOLVEFER is the time taken to reach a volume fraction of ferrite.

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Error Indicators

None.

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Accuracy

See reference [3].

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Further Comments

Nucleation rate BI may be calculated using the function MAP_STEEL_NUCSOLVE.

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Example

1. Program text

       DOUBLE PRECISION AREA, ANS, V, SV, BI, ALP, VOL, XBAR, XAGA,
&      XGAG, TPRE, XSOLVE, MAP_STEEL_SOLVEFER
       READ (5,*) AREA, ANS, V, SV
       READ (5,*) BI, ALP, VOL, TPRE
       READ (5,*) XBAR, XAGA, XGAG
       XSOLVE = MAP_STEEL_SOLVEFER(AREA, ANS, V, SV, BI, ALP, VOL,
&      XBAR, XAGA, XGAG, TPRE)
       WRITE (6,10) XSOLVE
10     FORMAT('Time =',D13.5)
       STOP
       END

2. Program data

0.10000D+01   0.98971D+00   0.23103D+00    0.20000D+05   0.89889D+09
0.82867D-06   0.38638D+00   0.79239D+02    0.91643D-02   0.63701D-03
0.21846D-01

3. Program results

Time =   0.79239D+02

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Auxiliary Routines

MAP_STEEL_AVOLF

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Keywords

ferrite, volume fraction

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Download

Download source code

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