Materials Algorithms Project
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Subroutine MAP_STEEL_BAINTT

Provenance of code.
Purpose of code.
Specification.
Description of subroutine's operation.
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Auxiliary subroutines required.
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Provenance of Source Code

M. Takahashi
R & D Laboratories-2,
Nippon Steel Corporation,
Chiba 299-12,
Japan.

and

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

Added to MAP: May 1999.

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Purpose

For a given steel composition, MAP_STEEL_BAINTT calculates the C curve for the transformation from austenite to bainite.

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Specification

Language:	FORTRAN
Product form:	Source code

SUBROUTINE MAP_STEEL_BAINTT(KTEMP,SHEART,C,AC,JT,JTHIGH,JTLOW,T10,T20,W,W1,R,JN)

DOUBLE PRECISION KTEMP(100),SHEART(100),C(8),AC(8),T10,T20,W,W1,R
INTEGER JT,JTHIGH,JTLOW,JN

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Description

For a given steel composition, MAP_STEEL_BAINTT calculates the C curve for the transformation from austenite to bainite [1]. The free energy of transformation from austenite to ferrite, Delta G^{{gamma alpha}}, in pure iron is factorised into magnetic and non-magnetic components; Delta T_M and Delta T_NM represent the temperature changes, caused by unit concentration of substitutional solute, to the temperature at which Delta G^{{gamma alpha}} is calculated. These values, along with the carbon-carbon interaction energy in austenite, are also given as output parameters.

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References

M. Takahashi and H.K.D.H. Bhadeshia, 1991, Materials Transactions, J.I.M., 32, 689-696.

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Parameters

Input parameters

C - real array of dimension 8: The first seven elements are set to the C, Si, Mn, Ni, Mo, Cr, and V concentrations by percentage weight. The eighth element of the array is reserved for the calculation of iron concentration by difference (in the subroutine MAP_STEEL_OMEGA).
AC - real array of dimension 8: AC is used as workspace in subroutine MAP_STEEL_OMEGA.
JT - integer: JT is the temperature interval at which the calculations are to be performed (K).
JTHIGH - integer: JTHIGH is the highest temperature (Kelvin) for which calculations are to be performed.
JTLOW - integer: JTLOW is the lowest temperature (Kelvin) for which calculations are to be performed.
W1 - real: W1 is the carbon-carbon interaction energy in ferrite (Jmol^-1).
R - real: R is the universal molar gas constant (Jmol^-1K^-1).

Output parameters

JN - integer: JN is the number of temperatures for which calculations have been made.
KTEMP - real array of dimension JN <= 100.: KTEMP contains the temperature values (Kelvin).
SHEART - real array of dimension JN <= 100: SHEART contains the corresponding time values (seconds).
T10 - real: T10 = Delta T_M - Delta T_MN is the temperature change (Kelvin), due to the non-magnetic component, (caused by unit concentration of substitutional solute) to the temperature at which the free energy transformation from austenite to ferrite (delta G^{(gamma alpha)}) is calculated.
T20 - real: T20 = Delta T_M is the temperature change (Kelvin), due to the magnetic component, (caused by unit concentration of substitutional solute) to the temperature at which the free energy transformation from austenite to ferrite (delta G^{(gamma alpha)}) is calculated.
W - real: W is the carbon-carbon interaction energy in austenite (Jmol^-1).

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1. Program text

      DOUBLE PRECISION KTEMP(100),SHEART(100),C(8),AC(8),T10,T20
      DOUBLE PRECISION W,W1,R
      INTEGER JT,JTHIGH,JTLOW,JN,I
C
C  R is the molar gas constant (in Joules per mole per Kelvin, J/(mol K))
C
      R=8.31451D+00
C
      WRITE(*,*) 'Input C  Si  Mn  Ni  Mo  Cr  V  (wt%):'
      READ (*,*) (C(I), I=1,7)
      WRITE(*,*) 'Input T interval, lowest T, highest T (Kelvin):'
      READ (*,*) JT,JTLOW,JTHIGH
      WRITE(*,*) 'Input C-C interaction energy in ferrite (J/mol):'
      READ (*,*) W1
      CALL MAP_STEEL_BAINTT(KTEMP,SHEART,C,AC,JT,JTHIGH,JTLOW,
     &                      T10,T20,W,W1,R,JN)
      WRITE (*,1) W
      WRITE (*,2) T10,T20
      WRITE (*,3) JN
      WRITE (*,4)
      DO 100 I=1,JN
         WRITE (*,5) KTEMP(I),SHEART(I)
  100 CONTINUE
      STOP
    1 FORMAT(//'C-C interaction energy in austenite = 'F10.4,' J/mol')
    2 FORMAT('T10 = ',F10.5/'T20 =',F10.4)
    3 FORMAT('No. of temperature-time calculations made = ',I3)
    4 FORMAT(//' Temperature (K)    Time (seconds)')
    5 FORMAT(F10.1,11X,F10.4)
      END

2. Program data

 Input C  Si  Mn  Ni  Mo  Cr  V  (wt%):
     0.1 0.5  1   0    0   0  0
 Input T interval, lowest T, highest T (Kelvin):
          40          473      873
 Input C-C interaction energy in ferrite (J/mol):
        48570.0

3. Program results

C-C interaction energy in austenite =  8414.5574 J/mol
T10 =   -0.00965
T20 =   -0.4176
No. of temperature-time calculations made =  11


 Temperature (K)    Time (seconds)
     473.0           20713.3090
     513.0            1368.5975
     553.0             168.8970
     593.0              34.3657
     633.0              11.1622
     673.0               5.0913
     713.0               2.8674
     753.0               2.1947
     793.0               2.3621
     833.0               3.6943
     873.0               9.8318

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