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Subroutine MAP_STEEL_BSMS

  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,
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

To calculate the martensite and bainite start-temperatures.

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Specification

Language:FORTRAN
Product form:Source code

SUBROUTINE MAP_STEEL_BSMS(T10,T20,W,W1,JTLOW,JTHIGH,JT,BS,MS,X1,
& XTOSL,XTOCN,XTOSL2,XTOCN2,R)

DOUBLE PRECISION T10,T20,W,W1,BS,MS,X1,XTOSL,XTOCN,XTOSL2,XTOCN2,R

INTEGER JTLOW,JTHIGH,JT

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Description

MAP_STEEL_BSMS calculates the martensite-start and bainite-start temperatures. The bainite-start temperature is calculated on the growth condition alone. It is defined by the point where the driving force for diffusionless transformation exceeds the stored energy of bainite. A linear regression of the free energy change, for the transformation of austenite to ferrite of the same chemical composition, as a function of the temperature is obtained. From this the bainite start energy is calculated, assuming that the stored energy is 400 J/mol [3]. The calculation of the martensite start temperature is based on the thermodynamics of martensitic transformations in plain carbon steels given in references 4 and 5. Also given are the slopes and intercepts of the To and To' lines in the phase diagram. The To line is the locus of all temperatures at which austenite and ferrite of the same composition have identical free energies. The To' line is the same as the To line except that the stored energy of ferrite is increased by a specified amount, in this case 400 J/mol.

If the free energy of transformation from austenite to ferrite, Delta G{gamma alpha}, in pure iron is factorised into magnetic and non-magnetic components, then Delta TM and Delta TNM represent the temperature changes, caused by unit concentration of substitutional solute, to the temperature at which Delta G{gamma alpha} is calculated. These quantities are functions of the substitutional solute content of the alloy and can be calculated using subroutine MAP_STEEL_OMEGA

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References

  1. G.J. Shiflet, J.R. Bradley and H.I. Aaronsson, Metallurgical Transactions, 9A, (1978), 999.
  2. J.A. Lobo and G.H. Geiger, Metallurgical Transactions, 7A, (1976), 1347 & 1359.
  3. H.K.D.H. Bhadeshia, Bainite in Steels, Institute of Materials, London, (1992), 1-454.
  4. H.K.D.H. Bhadeshia, Metal Science, 15, (1981), 175-177.
  5. H.K.D.H. Bhadeshia, Metal Science, 15, (1981), 178-180.

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Parameters

Input parameters

T10 - real
T10 = Delta TM - Delta TMN 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 TM 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).

W1 - real
W1 is the carbon-carbon interaction energy in ferrite (Jmol-1).

JTLOW - integer
JTLOW is the lowest temperature (Kelvin) for which calculations are to be performed.

JTHIGH - integer
JTHIGH is the highest temperature (Kelvin) for which calculations are to be performed.

JT - integer
JT is the temperature interval at which the calculations are to be performed (K).

X1 - real
X1 is the carbon concentration (in mole fraction).

R - real
R is the universal molar gas constant (Jmol-1K-1).


Output parameters

BS - real
BS is the bainite-start temperature (degrees centigrade).

MS - real
MS is the martensite-start temperature (degrees centigrade).

XTOSL - real
XTOSL is the slope of the To line (the locus of all temperatures at which austenite and ferrite of the same composition have identical free energies).

XTOCN - real
XTOCN is the intercept of the To line.

XTOSL2 - real
XTOSL2 is the slope of the To' line. The To' line is the same as the To line except that the stored energy of ferrite is increased by a specified amount, in this case 400 J/mol.

XTOCN2 - real
XTOCN2 is the intercept of the To' line.

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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 T10,T20,W,W1,X1,BS,MS,XTOSL,XTOCN,XTOSL2,XTOCN2
      DOUBLE PRECISION R
      INTEGER JTLOW,JTHIGH,JT
C
C  R is the molar gas constant (in joules per mole per kelvin, J/(mol K))
C
      R=8.31451D+00
C
      WRITE(*,*)
      WRITE(*,*) 'Input T10,   T20,   W,   W1,   X1:'
      READ (*,*) T10,T20,W,W1,X1
      WRITE(*,*)
      WRITE(*,*) 'Input lowest T, highest T, T interval (K):'
      READ (*,*) JTLOW, JTHIGH, JT
      CALL MAP_STEEL_BSMS(T10,T20,W,W1,JTLOW,JTHIGH,JT,
     &                    BS,MS,X1,XTOSL,XTOCN,XTOSL2,XTOCN2,R)
      WRITE (*,10) BS
      WRITE (*,20) MS
      WRITE (*,30) XTOSL, XTOCN
      WRITE (*,40) XTOSL2, XTOCN2 
      STOP
   10 FORMAT (//'Bainite-start temperature    = ',F8.2, ' deg. C')
   20 FORMAT ('Martensite-start temperature = ',F8.2, ' deg. C')
   30 FORMAT (/'To line:       slope = ',D12.5,',  intercept = ',D12.5)
   40 FORMAT ('To-prime line: slope = ',D12.5,',  intercept = ',D12.5/)
      END

2. Program data

 Input T10,   T20,   W,   W1,   X1:
    -0.0097 -0.42 8414.5 48570 0.032
 
 Input lowest T, highest T, T interval (K):
         473       873           40

3. Program results

Bainite-start temperature    =   386.47 deg. C
Martensite-start temperature =   213.62 deg. C

To line:       slope = -0.15081D-03,  intercept =  0.10355D+00
To-prime line: slope = -0.13788D-03,  intercept =  0.85872D-01

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Auxiliary Routines

Subroutines
MAP_UTIL_ANALY
MAP_STEEL_AXTO

Functions
MAP_STEEL_ENERGY
MAP_STEEL_FTO1 (called by MAP_STEEL_AXTO)
MAP_STEEL_G91 (called by MAP_STEEL_AXTO)

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Keywords

martensite, bainite, start-temperature

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Download

Download source code

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