Materials Algorithms Project
Program Library
- Provenance of code.
- Purpose of code.
- Specification.
- Description of subroutine's operation.
- References.
- Parameter descriptions.
- Error indicators.
- Accuracy estimate.
- Any additional information.
- Example of code
- Auxiliary subroutines required.
- Keywords.
- Download source code.
- Links.
G.I. Rees,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.
Top |
Next
Determines the parabolic thickening constant for the growth of allotriomorphic ferrite, under carbon diffusion control.
Top |
Next |
Prev
Language: | FORTRAN
|
Product form: | Source code |
SUBROUTINE MAP_STEEL_ALLSOL(XMAX, XGCURR, XALPHA, DCOEFFA,TCC, ALPHA, CC, CC0, IFAIL)
DOUBLE PRECISION CC(6), XAMAX, XGCURR, XALPHA, DCOEFFA, TCC,ALPHA, CC0
INTEGER IFAIL
Top |
Next |
Prev
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/(2D0.5) and Omega), a good approximation to the parabolic rate constant is obtained. An approximate
solution is used to speed up the calculation.
Top |
Next |
Prev
- J.W. Christian, Theory of Transformation in Metals and Alloys,
Part 1, Pergamon Press, Oxford, (1975).
- H.K.D.H. Bhadeshia, Progress in Materials Science, 29,
(1985), 321-386.
- R. Trivedi, Metall. Trans. A, 1A, (1970), 921-927.
Top |
Next |
Prev
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.
Top |
Next |
Prev
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.
Top |
Next |
Prev
If yp = alpha/(2D0.5), and ya is the true value, then the error resulting from the approximation is :-
Top |
Next |
Prev
None.
Top |
Next |
Prev
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
Top |
Next |
Prev
MAP_STEEL_XALPH
Top |
Next |
Prev
parabolic thickening, allotriomorphic ferrite, carbon diffusion control
Top |
Next |
Prev
Download source code
Top |
Prev