Materials Algorithms Project
Program Library

Subroutine MAP_STEEL_COOL

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 calculate the kinetics of formation of bainitic ferrite during continuous cooling.

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Specification

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Description

The Scheil method [1] is used to calculate the volume fraction of bainite formed during continuous cooling by dividing the cooling curve into fifty isothermal steps. For each temperature step the time to form the already formed volume fraction is added to the time for the step, and the new volume fraction is then calculated.

The isothermal bainite formation is found by solving equation 28 of [2] by integration. The integration uses a standard method from [3].

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References

1. J.W. Christian, The Theory of Transformations in Metals and Alloys, Second edition, Pergamon Press, Oxford, 545.
2. G.I. Rees and H.K.D.H. Bhadeshia, Materials Science and Technology, 8, (November 1992), 985-993.
3. K. Rectorys, Survey of Applicable Mathematics, ILIFFE Books Ltd, London, p543, equation 410.
4. H.K.D.H. Bhadeshia, J. Phys. (Orsay), 43, (C4), 443-448.

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Parameters

Input parameters

K - real array of dimension 8

K contains the composition of the steel (in weight percent) corresponding to the alloying elements C, Si, Mn, Ni, Mo, Cr, V, Fe.

ND - real

ND is the grain size of the parental austenite (in micrometres).

CD - real array of dimension 4

CD is an array of four constants optimised for the isothermal equation with experimental data from [4] :-

CD(1) = 0.34458D+02

CD(2) = 0.14750D+03

CD(3) = 0.20980D+05

CD(4) = 0.30327D+02

FF - real

FF is a factor by which all calculated volume fractions are multiplied, to allow for the presence of allotriomorphic ferrite. If none of this phase exists the FF is set to 1.

ST - real

ST is the start temperature for the cooling (in kelvin).

FT - real

FT is the finish temperature for the cooling (in kelvin).

TIME - real

TIME is the time taken to cool from ST to FT (in seconds).

ICALC - integer

ICALC is the number of temperature steps (< 100).

Output parameters

V - real array of dimension <= 100.

V(I) contains the volume fraction at temperature T(I).

TEMP - real array of dimension <= 100.

TEMP contains the temerature values at which the volume fraction is calculated.

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Error Indicators

None.

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Accuracy

No information provided.

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Further Comments

None.

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Example

1. Program text

       DOUBLE PRECISION K(8), ND, CD(4), FF, FT, ST, TIME, V(100), TEMP(100)
       INTEGER ICALC
       READ (5,*) K(1), K(2), K(3), K(4)
       READ (5,*) K(5), K(6), K(7), ND
       READ (5,*) FF, ST, FT, TIME
       ICALC = 50
       CD(1) = 0.34458D+02
       CD(2) = 0.14750D+03
       CD(3) = 0.20980D+05
       CD(4) = 0.30327D+02
       CALL MAP_STEEL_COOL(K,ND,CD,FF,ICALC,FT,ST,TIME,V,TEMP)
       DO 20 1,ICALC
        WRITE (6,*) V(I), T(I)
20     CONTINUE
       STOP
       END

2. Program data

0.38     1.29      1.73     0.0
   0.0     0.0     0.0     16.0
   1.0   500.0   300.0   2000.0

3. Program results

  0.0000   500.00
  0.0000   496.00
  0.0000   492.00
  0.0000   488.00
  0.0000   484.00
  0.0118   480.00
  0.0276   476.00
  0.0472   472.00
  0.0691   468.00
  0.0919   464.00
  0.1144   460.00
  0.1359   456.00
  0.1563   452.00
  0.1754   448.00
  0.1925   444.00
  0.2090   440.00
  0.2249   436.00
  0.2401   432.00
  0.2546   428.00
  0.2668   424.00
  0.2771   420.00
  0.2834   416.00
  0.2931   412.00
  0.3045   408.00
  0.3166   404.00
  0.3288   400.00
  0.3409   396.00
  0.3526   392.00
  0.3640   388.00
  0.3750   384.00
  0.3856   380.00
  0.3959   376.00
  0.4058   372.00
  0.4168   368.00
  0.4267   364.00
  0.4358   360.00
  0.4445   356.00
  0.4527   352.00
  0.4617   348.00
  0.4712   344.00
  0.4712   340.00
  0.4856   336.00
  0.4971   332.00
  0.5071   328.00
  0.5162   324.00
  0.5247   320.00
  0.5247   316.00
  0.5368   312.00
  0.5462   308.00
  0.5543   304.00

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Auxiliary Routines

Functions:
MAP_STEEL_MV
MAP_STEEL_NEWF

Subroutines:
MAP_STEEL_ROUGH
MAP_STEEL_MUCG

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Keywords

bainitic ferrite, continuous cooling, Scheil method

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Download

Download source code

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