Materials Algorithms Project
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Subroutine MAP_STEEL_ALLSOL

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

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Purpose

Determines the parabolic thickening constant for the growth of allotriomorphic ferrite, under carbon diffusion control.

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Specification

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Description

The equation linking the parabolic thickening constant for ferrite with the austenite supersaturation is:-

where :-

Omega is the supersaturation,

alpha is the parabolic thickening constant, and

D is the weighted average diffusion coefficient of carbon in austenite.

By fitting a polynomial curve to the accurately determined master solution (which lies between alpha/(2D^0.5) and Omega), a good approximation to the parabolic rate constant is obtained. An approximate solution is used to speed up the calculation.

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References

1. J.W. Christian, Theory of Transformation in Metals and Alloys, Part 1, Pergamon Press, Oxford, (1975).
2. H.K.D.H. Bhadeshia, Progress in Materials Science, 29, (1985), 321-386.
3. R. Trivedi, Metall. Trans. A, 1A, (1970), 921-927.

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Parameters

Input parameters

XMAX - real

XMAX is the carbon concentration x^{{gamma alpha}} (mole fraction) of the austenite at the alpha/gamma boundary.

XGCURR - real

XGCURR is the carbon concentration (mole fraction) far away from the alpha/gamma interface.

XALPHA - real

XALPHA is the carbon concentration x^{{alpha gamma}} (mole fraction) of the ferrite.

DCOEFFA - real

DECOEFFA is the weighted average diffusion coefficient D of carbon in austenite (in cm²s^-1).

TCC - real

TCC is the temperature (in kelvin).

CC - real array of dimension 6

CC contains the coefficients for the polynomial approximation of the function.

CC0 - real

CC0 is the constant term in the polynomial approximation of the function.

Output parameters

ALPHA - real

ALPHA is the parabolic thickening rate constant alpha (in cms^-0.5).

IFAIL - integer

IFAIL is set to 1 if the calculation falls outside the fitting range, it is 0 otherwise.

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Error Indicators

Fitting accuracy deteriorates for very high supersaturation. If OMEGA is greater than 0.985, it is outside the fitting range and IFAIL is set to 1.

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Accuracy

If yp = alpha/(2D^0.5), and ya is the true value, then the error resulting from the approximation is :-

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Further Comments

None.

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Example

1. Program text

       DOUBLE PRECISION XMAX, XGCURR, XALPHA, DCOEFFA, TCC, ALPHA, CC(6), CCO
       DATA (CC(J),J=1,6)/0.7297D+01,-0.7808D+01,-0.3581D+02,
&      0.1262D+03,-0.1434D+03,0.5624D+02/
       CC0=-1.8893
       READ (5,*) XMAX, XGCURR, XALPHA
       READ (5,*) DCOEFFA, TCC
       IFAIL = 0
       CALL MAP_STEEL_ALLSOL(XMAX, XGCURR, XALPHA, DCOEFFA, TCC,
&      ALPHA, CC, CC0, IFAIL)
       IF (IFAIL .EQ. 1) THEN
          WRITE (6,5)
          FORMAT ('Warning - outside fitting range')
       ENDIF
       WRITE (6,10) ALPHA
       FORMAT('Parabolic thickening constant = ',D13.5)
       STOP
       END

2. Program data

0.27278D-01   0.10200D-01   0.67211D-03
0.37760D-08   0.97115D+03

3. Program results

Parabolic thickening constant = 0.84710D-04

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Auxiliary Routines

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Keywords

parabolic thickening, allotriomorphic ferrite, carbon diffusion control

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Download

Download source code

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