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G.I. Rees,

Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

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

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

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 V_{alpha} formed after time t is given by
[1, 2, 3]:

where V_{max} is the maximum amount of ferrite that can form at the reaction
temperature, S_{v} 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.

- J.W. Christian, Theory of Transformation in Metals and Alloys, Part 1, 2nd ed., Pergamon Press, Oxford (1975).
- H.K.D.H. Bhadeshia, Progress in Materials Science,
__29__, (1985), 321-386. - 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.

**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
S
_{v}(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.
V
_{alpha}/V_{max}. **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).

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

None.

See reference [3].

Nucleation rate `BI` may be calculated using the function MAP_STEEL_NUCSOLVE.

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

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

Time = 0.79239D+02

ferrite, volume fraction

**
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
**