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Subroutine MAP_STEEL_ROUGH

  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

N.A. Chester,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

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Purpose

To make an initial (rough) search for the volume fraction of bainite for a given temperature.

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Specification

Language:FORTRAN
Product form:Source code

SUBROUTINE MAP_STEEL_ROUGH(TEMP, DGM, MAXVOL, ND, CD, XBAR,
& TTIME, VOL)

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

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Description

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 this subroutine is used. The volume fraction is increased by 0.01 steps from 0 until the calculated time is greater than the time required. The 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].

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References

  1. G.I. Rees and H.K.D.H. Bhadeshia, Materials Science and Technology, 8, (November 1992), 985-993.
  2. K. Rectorys, Survey of Applicable Mathematics, ILIFFE Books Ltd, London, 543, equation no. 410.
  3. H.K.D.H. Bhadeshia, J. Phys. (Orsay), 43, (C4), 443-448.

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Parameters

Input parameters

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).

Output parameters

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

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Error Indicators

None.

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Accuracy

No information supplied.

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Further Comments

None.

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Example

1. Program text

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

2. Program data

705.0      -1231.39   0.26   16.0
  1.72D-02   273.33

3. Program results

Volume fraction of bainite =   0.2401

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Auxiliary Routines

MAP_STEEL_FINE
MAP_STEEL_NEWF

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Keywords

bainite, kinetics, volume fraction

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Download

Download source code

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

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