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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
To calculate the volume and area fractions of allotriomorphic ferrite formed during continuous cooling transformation from austenite, for heterogeneous nucleation.
| 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
The subroutine MAP_STEEL_AVOLF determines the extent of allotriomorphic ferrite reaction, VOL, by numerical solution of equation 7 from reference 1:
| 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. |
| 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. |
None.
No information supplied
None.
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
Input SV, BI, TIME, ALP1, ETA
1E4 1E4 10 3E-6 3
Input XBAR, XAGA, XGAG
0.02 0.0002 0.06
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
allotriomorphic ferrite, heterogeneous nucleation
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