![[MAP Logo]](../../maplogo1.gif)
H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.
Added to MAP: July 1999.
To calculate the volume fractions of the microstructures formed in low-alloy steel weld deposits during cooling. Also given are values for the allotriomorphic ferrite half-thickness and the time available for unrestricted Widmanstätten ferrite growth.
| Language: | FORTRAN |
| Product form: | Source code |
SUBROUTINE MAP_STEEL_AN2(X,Y,HIGHT,LOWT,L,VMAX,C1,C2,TINT,CURR, & VOLT,EFF,VELOC,JI3,VACIC,VOLW,VOLFRA,Q,TIMC,PPMBSL,JBOR,FBORW) DOUBLE PRECISION C1,C2,CURR,EFF,FBORW,FHIGHT,L,LOWT,PPMBSL,Q DOUBLE PRECISION TIMC,TINT,VACIC,VELOC,VMAX,VOLFRA,VOLT,VOLW DOUBLE PRECISION X(6),Y(6) INTEGER JI3,JBOR
The model, used here to calculate the volume fractions of the microstructures formed during cooling in weld deposits, is described in reference 1. The austenite is assumed to form columnar grains which are hexagonal in cross-section with sides of length L/2. The allotriomorphic ferrite grows inwards from the grain boundaries to form a layer of thickness q (half-thickness). The subroutine requires, as input, values for the parabolic thickening rate constant of allotriomorphic ferrite as a function of temperature. (Suitable values can be obtained using subroutine MAP_STEEL_RATE2.) These values are fitted to a 3rd order polynomial in temperature. The equation is re-expressed as a function of time by substituting into it an expression for temperature using equation (1b) of reference 2:
(Further details and values for C1 and C2 can be obtained by referring to subroutine MAP_STEEL_COOLCU.) The half thickness of allotriomorphic ferrite, q, obtained by continuous cooling from the temperature at which ferrite formation starts to the temperature at which it ceases and Widmanstätten ferrite starts, can then be calculated from equation 5 of reference 1:
where the integration is made over time t as the weld cools from the allotriomorphic ferrite start temperature at t=0 to the stop temperature at tl, and 
is the parabolic thickening rate constant as a function of temperature.
The volume fraction, Va, of allotriomorphic ferrite is obtained using equations 6(a) and 6(b) of reference 1:
The second equation is an empirical correction to the calculated volume fraction. The half thickness of ferrite is then recalculated from the volume fraction using equation 6(c) of reference 1:
If the flag JI3 is set to 5, however, no empirical corrections are made and the volume fraction of allotriomorphic ferrite is read into the subroutine as an input.
The volume fraction of Widmanstätten ferrite formed, Vw, is calculated from equation 8 of reference 1:
where Vmax is the lengthening rate of a Widmanstätten ferrite plate, t2 is the time available for Widmanstätten ferrite to grow without interference from the formation of acicular ferrite and C4 is a factor which depends only on the concentration of boron in solution. The time t2 is set equal to the time required for a Widmanstätten ferrite plate to grow unhindered across an austenite grain, t3, given by equation 11 of reference 1:
unless it is greater than a critical time, tc, after which the formation of acicular ferrite interferes with the growth of Widmanstätten ferrite. In this case the time t2 is set equal to tc, which is taken to be 2.11 seconds.
The factor C4 is defined as 6.8717 unless the flag JBOR=1. In this case the effect of soluble boron in the austenite of concentration xB (in parts per million) is taken into account and C4 is calculated using the equation:
FBORW defines the strength of the interaction and is an input to the subroutine. A value of 5.0 for FBORW is generally used [3].
The volume fraction of acicular ferrite formed, Vaf, is taken to be equal to the volume fraction of the remaining untransformed austenite:
None.
No information supplied.
None.
IMPLICIT NONE
DOUBLE PRECISION L,C1,C2,CURR,EFF,FBORW,HIGHT,LOWT,PPMBSL,Q
DOUBLE PRECISION TIMC,TINT,VOLT,VELOC,VACIC,VMAX,VOLFRA
DOUBLE PRECISION VOLW,X(6),Y(6)
INTEGER I,JBOR,JI3
C
WRITE(*,*) 'Input 6 temperature values:'
READ (5,*) (X(I), I=1,6)
WRITE(*,*) 'Input 6 values for the parabolic thicknening rate:'
READ (5,*) (Y(I), I=1,6)
WRITE(*,*) 'Input HIGHT,LOWT,L,VMAX:'
READ (5,*) HIGHT,LOWT,L,VMAX
WRITE(*,*) 'Input C1,C2,TINT:'
READ (5,*) C1,C2,TINT
WRITE(*,*) 'Input CURR,VOLT,EFF,VELOC:'
READ (5,*) CURR,VOLT,EFF,VELOC
WRITE(*,*) 'Input JBOR,PPMBSL,FBORW:'
READ (5,*) JBOR,PPMBSL,FBORW
JI3 = 0
CALL MAP_STEEL_AN2(X,Y,HIGHT,LOWT,L,VMAX,C1,C2,TINT,CURR,
& VOLT,EFF,VELOC,JI3,VACIC,VOLW,VOLFRA,Q,TIMC,PPMBSL,JBOR,FBORW)
WRITE (6,1) VOLFRA,VOLW,VACIC,Q,TIMC
STOP
1 FORMAT('Volume fraction allotriomorphic ferrite = ',F7.3/
& 'Volume fraction Widmanstatten ferrite = ',F7.3/
& 'Volume fraction acicular ferrite = ',F7.3/
& 'Half thickness of allotriomorphic ferrite = ',F7.3,
& ' microns'/
& 'Duration of Widmanstatten ferrite growth = ',F7.3,
& ' seconds')
END
Input 6 temperature values: 640.0 680.0 720.0 760.0 800.0 840.0 Input 6 values for the parabolic thicknening rate: 3.02E-04 3.32E-04 3.32E-04 3.06E-04 2.22E-04 5.54E-05 Input HIGHT,LOWT,L,VMAX: 722.0 621.0 168.0 1.98E-04 Input C1,C2,TINT: 1325.0 1.6 200.0 Input CURR,VOLT,EFF,VELOC: 180.0 34.0 0.775 4.0E-03 Input JBOR,PPMBSL,FBORW: 1 1.0 5.0
Volume fraction allotriomorphic ferrite = 0.338 Volume fraction Widmanstatten ferrite = 0.080 Volume fraction acicular ferrite = 0.582 Half thickness of allotriomorphic ferrite = 13.538 microns Duration of Widmanstatten ferrite growth = 0.211 seconds
steel welds, acicular, Widmanstatten, allotriomorphic, ferrite, volume fraction
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
MAP Website administration / map@msm.cam.ac.uk