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Subroutine MAP_STEEL_AUSGROW

  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

D. Gaude-Fugarolas,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge CB2 3QZ, U.K.

E-mail:dg241@cam.ac.uk
 
 

Added to MAP: 2006.

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Purpose

This program predicts the reverse transformation to austenite from a ferrite/pearlite structure.

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Specification

 
Language:  FORTRAN 
Product form:  Source code. 
    Complete program.

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Description

One or more stages of any steel component manufacturing process often involve raising the temperature of the material until its microstructure transforms totally or partially into austenite. The ability to be able to predict or model quantitatively the progress of such phase transformation taking into account prior microstructure and composition is so very desirable.

MAP_AUSGROW considers a hypoeutectoid equilibrium starting microstructure. It was developed originally to deal with the sort of heavily banded microstructures usually found in rolled steel, but it has been adapted to be used in any hypoeutectoid steel which contains only ferrite and pearlite.

Starting information is loaded into the program using a text input file ('inputfile'. It includes the composition of the steel (wt.% of C, Si, Mn, Cr, Ni, Mo and V), microstructural description of the steel (Lalpha, Lh, Lp Le and Lcol - semi thickness of ferrite grains/layers, 1/2(Lalpha + Lp)*, semithickness of pearlite conglomerates/layers*, 1/2 pearlite interlamelar spacing (defined as thickness of ferrite lamella + thickness of cementite lamella), and average diameter of pearlite colonies (measured by mean linear intersection).  The third line of the input file contains the Ac1 temperature in degrees Celsius for that composition. The last line of such file contains two fitting parameters for nucleation.

(*) Some of these parameters had geometrical meaning when the model was only applied to heavily banded microstructures. On the present version Lp allows to define the volume fraction of pearlite relative to allotriomorphic ferrite (Lalpha).

The temperature evolution is supplied to the program in a file called 'temperature' that contains two columns (time (/seconds), temperature (/grades Celsius), ending with a line in which the time is lower than zero. Other auxiliary files are needed for the use of the program during the calculations ('weightfile', 'minmaxfile'). The output is saved in another file called 'outputfile' (the names of the input and output files can be modified if the need arises). The temperature cycle can follow a complex path (and not simply a heating ramp and going back to temperatures under the lower critical temperature).

The output file gives for each time instant the temperature and the corresponding volume fraction of each phase (austenite, pearlite, ferrite and total).  In this version of the program the output file includes two extra columns (Vpfr and Vpcm) that are not in use.

The process of austenitisation follows several stages. First, nuclei of austenite are formed at the boundaries of the pearlite colonies. These nuclei grow until they reach the right size to start a stage of steady growth that finishes when all the pearlite had become austenite. When that happens, the last stage of the process, the transformation of allotriomorphic ferrite, starts.
 

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References

  1. Gaude-Fugarolas, D. "A model for austenitisation of  hypoeutectoid steels". (unpublished) Cambridge University, Cambridge, 2001.
  2. Brooks, C.R. "Principles of the austenitisation of steels". Elsevier applied science, London, 1992.
  3. Christian, J.W. "Theory of transformations in metals and alloys, part I". Pergamon Press, Oxford, 1975.
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Parameters

Input parameters

COMP(8)- double precision array of dimension 8
            COMP contains in its 7 first positions the composition of the steel: wt.% C, wt.% Si, wt.% Mn, wt.% Cr, wt.% Ni, wt.% Mo and wt.% V.
LALPHA- double precision
            2*LALPHA contains, in metres, the thickness (modal value or averaged value) of ferrite grains. In a banded structure, the thickness of ferrite bands.
LHYPO- double precision
            LHYPO contains, in metres, the sum of LALPHA and LPEARL.
LPEARL- double precision
            2*LPEARL contains, in metres, the proportional thickness of pearlite relative to ferrite. In a banded structure, the thickness of pearlite bands.
LEUT- double precision
            2*LEUT contains, in metres, characteristic spacing of the pearlite, .measured as the thickness of one lamina of ferrite and one lamina of cementite
LCOL- double precision
            LCOL contains, in metres, the averaged diameter (measured by mean linear intersection) of pearlite colonies.
NEXTTIME- double precision
            NEXTTIME contains, in seconds, the next time step in the thermal history.
NEXTTEMP- double precision
            NEXTTEMP contains, in degrees Celsius, the next temperature in the thermal history.
AC1- double precision
            AC1 contains, in degrees Celsius, the lower critical temperature of a steel of the given composition.
IZERO- double precision
            IZERO contains a fitting factor for nucleation.
Q- double precision
            Q contains a constant for nucleation.

Output parameters

TIME- double precision
            NEXTTEMP contains, in seconds, the actual time step in the thermal history.
TEMP- double precision
            TEMP contains, in degrees Celsius, the actual temperature in the thermal history.
VAUS- double precision
            VAUS contains the actual volume fraction of austenite.
VPER- double precision
            VPER contains the actual volume fraction of pearlite.
VFER- double precision
            VFFR contains the actual volume fraction of  allotriomorphic ferrite.
VPFR- double precision
            VPFR is not used in this version of the model.
VPCM- double precision
            VPCM is not used in this version of the model.
VTOT- double precision
            VTOT contains the sum of the volume fractions of all phases present. It should equal to unity at all times.
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Error Indicators

None.

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Accuracy

This is a simplified model of some very complex physical phenomena. The result is as accurate as the assumptions of the model are realistic and as the computer calculations allow using double precision. However, the accuracy of the input parameters, (e.g. microstructure) may affect the accuracy of the results.
 

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Further Comments

None.

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Example

1. Program text

    Complete program.

2. Program data

    Example of input file:
  
 0.54 0.20 0.74 0.20 0.17 0.05 0.001
 0.5E-5 2.5E-5 0.5E-6 2.0E-5 2.9E-5
 711.0 
 1.3E-2  5.334
Example of fragment of 'temperature' file: 
0       700
0.06275 706.275
0.1255  712.55
0.1882  718.82
0.251   725.1
0.3137  731.37
0.3765  737.65
0.4392  743.92
0.502   750.2
0.5647  756.47
0.6275  762.75
0.6902  769.02
0.753   775.3
0.8157  781.57
0.8784  787.84
0.9412  794.12
1.004   800.4
1.067   806.7
1.129   812.9
1.192   819.2
1.255   825.5
1.318   831.8
1.38    838
1.443   844.3

...

3. Program results

Example of fragment of output file: 
 Time /s  Temp./C  Vaus   Vpearl   Vfer    Vpfr    Vpcm     Total
   0.00   -273.0  0.0000  0.8000  0.2000  0.0000  0.0000    1.0000
   0.00    700.0  0.0000  0.8000  0.2000  0.0000  0.0000    1.0000
   0.06    706.3  0.0000  0.8000  0.2000  0.0000  0.0000    1.0000
   0.13    712.5  0.0000  0.8000  0.2000  0.0000  0.0000    1.0000
   0.19    718.8  0.0000  0.8000  0.2000  0.0000  0.0000    1.0000
   0.25    725.1  0.0001  0.7999  0.2000  0.0000  0.0000    1.0000
   0.31    731.4  0.0002  0.7998  0.2000  0.0000  0.0000    1.0000
   0.38    737.6  0.0007  0.7993  0.2000  0.0000  0.0000    1.0000
   0.44    743.9  0.0017  0.7983  0.2000  0.0000  0.0000    1.0000
   0.50    750.2  0.0038  0.7962  0.2000  0.0000  0.0000    1.0000
   0.56    756.5  0.0082  0.7918  0.2000  0.0000  0.0000    1.0000
   0.63    762.8  0.0789  0.7211  0.2000  0.0000  0.0000    1.0000
   0.69    769.0  0.2329  0.5671  0.2000  0.0000  0.0000    1.0000
   0.75    775.3  0.4869  0.3131  0.2000  0.0000  0.0000    1.0000
   0.82    781.6  0.7181  0.0819  0.2000  0.0000  0.0000    1.0000
   0.88    787.8  0.8000  0.0000  0.2000  0.0000  0.0000    1.0000
   0.94    794.1  0.8237  0.0000  0.1763  0.0000  0.0000    1.0000
   1.00    800.4  0.8356  0.0000  0.1644  0.0000  0.0000    1.0000
   1.07    806.7  0.8462  0.0000  0.1538  0.0000  0.0000    1.0000
   1.13    812.9  0.8569  0.0000  0.1431  0.0000  0.0000    1.0000
   1.19    819.2  0.8680  0.0000  0.1320  0.0000  0.0000    1.0000
   1.25    825.5  0.8798  0.0000  0.1202  0.0000  0.0000    1.0000
   1.32    831.8  0.8924  0.0000  0.1076  0.0000  0.0000    1.0000

...
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Auxiliary Routines

MAP_STEEL_OMEGA
MAP_STEEL_DIFFUS
MAP_STEEL_CG
MAP_STEEL_DCG

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Keywords

austenitisation, reverse transformation, austenitization, phase transformation, banded structure, austenite, hypoeutectoid steel

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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.

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

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