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Subroutine MAP_STEEL_AVOLF

  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.

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Provenance of Source Code

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

Added to MAP: March 1999



Purpose

To calculate the volume and area fractions of allotriomorphic ferrite formed
during continuous cooling transformation from austenite, for heterogeneous
nucleation.

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Specification

 Language:    FORTRAN
 Product form:Source code

 SUBROUTINE MAP_STEEL_AVOLF(AREA,ANS,VF,SV,BI,TIME,ETA,ALP1,ZETA,
&      XBAR,XAGA,XGAG)

 DOUBLE PRECISION ALP1,ANS,AREA,ARG,BI,ETA,SV,TIME,PHI,PI,VF
 DOUBLE PRECISION XAGA,XBAR,XGAG,ZETA
 DOUBLE PRECISION THETA(51),FUN(51)
 INTEGER IDUM,I


Description

The subroutine MAP_STEEL_AVOLF determines the extent of allotriomorphic
ferrite reaction, VOL, by numerical solution of equation 7 from reference 1:

                       [Equation 7 from reference 1.]


References

  1. H.K.D.H. Bhadeshia, L.-E. Svensson and B. Gretoft, Proc. Conf. on
     Welding Metallurgy of Structural Steels, ed. J.Y. Koo, Denver, (1987),
     ASM, pp 517-529.
  2. J.W. Cahn, Acta Metallurgica, 4, (1956), 449-459.


Parameters

Input parameters

 Name Type  Description

 SV   real  austenite grain boundary surface area per unit volume (in m-1).

 BI   real  allotriomorphic ferrite boundary nucleation rate per unit area
            (in m-2s-1).

 TIME real  time elapsed since the start of cooling (in seconds).

 ALP1 real  one-dimensional parabolic thickening rate constant
            perpendicular to the grain boundary (in ms-0.5).

 ETA  real  the ratio of the one-dimensional parabolic lengthening rate
            constant parallel to the grain boundary, to the 1-d parabolic
            thickening rate constant (ALP1). It is usually defined as 3.

 XBAR real  mole fraction of carbon in the bulk austenite.

 XAGA real  mole fraction of carbon in ferrite at the alpha/alpha+gamma
            boundary.

 XGAG real  mole fraction of carbon in austenite at the gamma/gamma+alpha
            boundary.

Output parameters

 Name Type  Description

 AREA real  fraction of austenite grain boundary covered by ferrite.

 ANS  real  value of the integral.

 VF   real  actual volume fraction of allotriomorphic ferrite formed.

 ZETA real  volume fraction of ferrite formed, divided by the equilibrium
            volume fraction of ferrite.
 

Error Indicators

None.
 

Accuracy

No information supplied
 

Further Comments

None.
 

Example

1. Program text

C Test program for the subroutine MAP_STEEL_AVOLF
C
      IMPLICIT NONE
      DOUBLE PRECISION ALP1,ANS,AREA,BI,ETA,SV,TIME,XBAR,XAGA,XGAG
      DOUBLE PRECISION VF,ZETA
C
      WRITE (*,*)
      WRITE (*,*) 'Input SV, BI, TIME, ALP1, ETA'
      READ  (*,*) SV,BI,TIME,ALP1,ETA
      WRITE (*,*) 'Input XBAR, XAGA, XGAG'
      READ  (*,*) XBAR,XAGA,XGAG
C
      CALL MAP_STEEL_AVOLF(AREA,ANS,VF,SV,BI,TIME,ETA,ALP1,ZETA,
     &                      XBAR,XAGA,XGAG)
      WRITE (*,1) ANS, ZETA, AREA, VF
      STOP
    1 FORMAT( //1H ,'Value of the integral = ',D12.5 // 1H ,
     & 'Zeta = ',D12.5 // 1H ,'Fraction of austenite grain boundary ',
     & 'covered by ferrite = ',D12.5 // 1H ,'Volume fraction of ',
     & 'allotriomorphic ferrite formed = ', D12.5 /)
      END

2. Program data

 Input SV, BI, TIME, ALP1, ETA
      1E4 1E4   10   3E-6   3
 Input XBAR, XAGA, XGAG
       0.02 0.0002 0.06

3. Program results

 Value of the integral =  0.10176D-03

 Zeta =  0.28866D-04

 Fraction of austenite grain boundary covered by ferrite =  0.12723D-03

 Volume fraction of allotriomorphic ferrite formed =  0.19308D-04
 

Auxiliary Routines

MAP_UTIL_TRAPE
 

Keywords

allotriomorphic ferrite, heterogeneous nucleation
 

Download

Download source code


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                        the University of Cambridge.

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