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Subroutine MAP_STEEL_PARAM2

  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

H.K.D.H. Bhadeshia and Sree Harsha Lalam,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

Added to MAP: July 1999

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Purpose

To calculate the carbon concentration and the lattice parameter of carbon-enriched austenite, at a specified temperature, after partial transformation to ferrite has occurred. Suitable for high carbon content steels.

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Specification

Language:FORTRAN
Product form:Source code

 SUBROUTINE MAP_STEEL_PARAM2(AGTX,AGT,AAT,VA,XBAR,XALPHA,XG,
& EXG,T,AV,RTEMP)

 DOUBLE PRECISION AGTX,AGT,AAT,VA,XBAR,XALPHA,XG,EXG,T,AV,RTEMP

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Description

This subroutine is used in the analysis of the transformation from austenite to ferrite by program MAP_STEEL_DILAT2. It obtains values for the carbon concentration and the lattice parameter of carbon-enriched austenite, at a temperature T, due to partial transformation of the austenite to ferrite, by solving iteratively equations 5 and 8 in reference 1:

ag = agT + Cc(wc-woc) . [1 + eg(T-TRT)]
and
wc = (woc - wac) . [Vapa/(1-Va)pg] + woc

where agT and ag are the austenite lattice parameters at temperature T before and after carbon enrichment; TRT is room temperature; woc and wc are the weight fractions of carbon in the austenite before and after enrichment; eg is the thermal expansion coefficient of austenite; Cc is the change in the austenite lattice parameter caused by the addition of unit concentration of carbon; wac is the carbon fraction in the ferrite; Va is the volume fraction of the ferrite; pa and pg are the densities of ferrite and austenite. A value of 3.3Å is used for Cc [2]. The densities are calculated from the lattice parameters, where it is assumed that all the atoms are Fe and no corrections are made for the compositional differences between the phases.

This subroutine is a slightly improved version of MAP_STEEL_PARAM; the iteration procedure in this routine continues until the absolute percentage in the calculated lattice parameter is less than 10-10, whereas for MAP_STEEL_PARAM a fractional change of less than 10-4 stipulates the convergence criterium.

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References

  1. H.K.D.H. Bhadeshia, S.A. David, J.M. Vitek, and R.W. Reed, 1991, Materials Science and Technology, 7, 686-698.
  2. D.J. Dyson and B. Holmes, 1970, J. Iron Steel Inst., 208, 469.

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Parameters

Input parameters

AGT - real
AGT (agT) is the austenite lattice parameter at temperature T containing woc (XBAR) amount of carbon.

AAT - real
AAT is the ferrite lattice parameter at temperature T.

VA - real
VA (Va) is the volume fraction of ferrite.

XBAR - real
XBAR (100woc) is the initial carbon concentration (wt%).

XALPHA - real
XALPHA is the concentration of carbon dissolved in ferrite (wt%).

EXG - real
EXG (eg) is the thermal expansion coefficient of austenite (K-1).

T - real
T is the temperature (°C).

AV - real
AV is the Avogadro constant (mol-1).

RTEMP - real
RTEMP (TRT) is room temperature (25 °C).

Output parameters

AGTX - real
AGTX (ag) is the carbon-enriched austenite lattice parameter at temperature T.

XG - real
XG (100wc) is the concentration of carbon in enriched austenite (wt%).

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Error Indicators

Execution of the program is halted and an error flagged if the number of iterations in subroutine MAP_STEEL_PARAM2 exceeds 1010.

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Accuracy

No information supplied.

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Further Comments

T and RTEMP may be given in either Kelvin or °C, provided that the same units are used for both parameters.

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Example

1. Program text

      DOUBLE PRECISION AGTX,AGT,AAT,VA,XBAR,XALPHA,XG
      DOUBLE PRECISION EXG,T,AV,RTEMP
C
C  AV is the Avogadro constant (in 1/(mole)
C
      AV=6.0221367D+23
C
      WRITE(*,*) 'Input AGT, AAT, VA, EXG:'
      READ (*,*) AGT,AAT,VA,EXG
      WRITE(*,*) 'Input XBAR, XALPHA, T:'
      READ (*,*) XBAR,XALPHA,T
      RTEMP = 25.0D+00
      CALL MAP_STEEL_PARAM2(AGTX,AGT,AAT,VA,XBAR,XALPHA,
     &                     XG,EXG,T,AV,RTEMP)
      WRITE (*,1) AGTX
      WRITE (*,2) XG
      STOP
    1 FORMAT ('Lattice parameter of carbon-enriched austenite = ',
     &         F8.4,' Angstroms')
    2 FORMAT ('Carbon concentration in the austenite          = ',
     &         F8.4,' wt%')
      END

2. Program data

 Input AGT, AAT, VA, EXG:
3.6448 2.8808   0.7 3.32E-5
 Input XBAR, XALPHA, T:
      0.968  0.02   349.0

3. Program results

Lattice parameter of carbon-enriched austenite =   3.7245 Angstroms
Carbon concentration in the austenite          =   3.3582 wt%

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Auxiliary Routines

None.

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Keywords

enriched, austenite, ferrite, lattice parameter, carbon, concentration

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Download

Download source code

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