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N.A. Chester,

Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

Searches for the volume fraction of bainite for a given temperature. Search is more fine than MAP_STEEL_ROUGH.

Language: | FORTRAN |

Product form: | Source code |

SUBROUTINE MAP_STEEL_FINE(TEMP, DGM, MAXVOL, ND, CD, XBAR, TTIME,

& VHIGH, VOL)

DOUBLE PRECISION TEMP, DGM, MAXVOL, ND, CD(4), XBAR, TTIME, VHIGH, VOL

An equation is in the form: time equals a function of volume fraction of bainite. To calculate the volume fraction of bainite for a given time the subroutine MAP_STEEL_ROUGH is used to find the value to an accuracy of 0.01 volume fraction. This subroutine MAP_STEEL_FINE is then called to calculate the volume fraction to an accuracy of 0.0001.

The equation used (in function MAP_STEEL_NEWF) is a solution of equation (28) in [1] which has been integrated correctly. The integration uses a standard solution found in [2].

- G.I. Rees and H.K.D.H. Bhadeshia, Materials Science and Technology,
__8__, (November 1992), 985-993. - K. Rectorys, Survey of Applicable Mathematics, ILIFFE Books Ltd, London, 543, equation no. 410.
- H.K.D.H. Bhadeshia, J. Phys. (Orsay),
__43__, (C4), 443-448.

**TEMP**- real- TEMP is the temperature (in kelvin).
**DGM**- real- DGM is the initial value of the maximum nucleation free energy change (in
joules per mole).
**MAXVOL**- real- MAXVOL is the maximum volume fraction of bainite, taken to be that at which
the carbon concentration of the austenite reaches the To' line.
**ND**- real- ND is the grain size of the parental austenite (in micrometres).
**CD**- real array of dimension 4- CD is an array of 4 constants optimised for this equation with experimental data from [3], the values being :-
- CD(1) = 0.34458D+02
- CD(2) = 0.14750D+03
- CD(3) = 0.20980D+05
- CD(4) = 0.30327D+02
**XBAR**- real- XBAR is the mole fraction of carbon in the alloy.
**TTIME**- real- TTIME is the isothermal holding time for which the volume fraction bainite
is being calculated (in seconds).
**VHIGH**- real- VHIGH is the volume fraction found by MAP_STEEL_ROUGH to be the first to take longer
than time TTIME.

**VOL**- real- VOL is the volume fraction of bainite calculated, rounded up to the nearest
0.0001 volume fractions.

None.

No information supplied.

None.

DOUBLE PRECISION TIME, DGM, MAXVOL, ND, CD(4), XBAR, TTIME, & VHIGH, VOL READ (5,*) TEMP, DGM, MAXVOL, ND READ (5,*) XBAR, TTIME, VHIGH CD(1) = 0.34458D+02 CD(2) = 0.14750D+03 CD(3) = 0.20980D+05 CD(4) = 0.30327D+02 CALL MAP_STEEL_FINE(TEMP, DGM, MAXVOL, ND, CD, XBAR, & TTIME, VHIGH, VOL) WRITE (6,10) VOL 10 FORMAT ('Volume fraction of bainite = ',D12.6) STOP END

705.0 -1231.39 0.26 16.0 1.72D-02 273.33 0.25

Volume fraction of bainite = 0.2401

bainite, kinetics, volume fraction

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