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Subroutine MAP_STEEL_BAINCA

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

Calculates the volume fractions of bainitic ferrite, martensite and retained austenite which form in a steel weld on cooling.

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Specification

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Description

MAP_STEEL_BAINCA predicts the volume fractions of the microstructures formed in a steel weld on cooling [1]. It calculates the volume fraction of bainitic ferrite, and uses two different methods to obtain the volume fractions of martensite and retained austenite (see references 2 and 3 for further details).

The subroutine is designed for welding problems involving continuous cooling transformations, the cooling curves being determined by the parameters C₁ and C₂, the welding current, voltage, speed and arc transfer efficiency, and the interpass temperature. All of these are required as inputs to this subroutine. C₁ and C₂ are heat flow constants which depend on the welding process and are derived from equation 1(b) of reference [4]:

where dT/dt is the cooling rate, Q is the heat input (Jm^-1), eta is the arc weld efficiency, and T_i is the interpass temperature.

This subroutine calls MAP_STEEL_BAINTT to calculate a series of C curves for bainite for a range of austenite carbon concentrations. MAP_STEEL_BSMS is used to obtain values for the bainite and martensite start temperatures and to calculate the T_o and T_o' curves of the temperature versus carbon plot on the paraequilibrium phase diagram. For each C curve MAP_STEEL_XALPH gives the carbon concentration of the bainitic ferrite, and the volume fraction formed is obtained from the T_o and T_o' curves using the lever rule. Scheil's rule [5] is then used to obtain the total volume fraction of bainite formed during cooling. Given the martensite start temperature, the ambient temperature (assumed to be 20 °C) and the remaining volume fraction of austenite, the volume fraction of retained austenite and the volume fraction of martensite are determined by calling subroutines MAP_STEEL_MART (Khan & Bhadeshia method) and MAP_STEEL_MART2 (Koistinen & Marburger method).

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References

1. M. Takahashi and H.K.D.H. Bhadeshia, 1991, Materials Transactions of the Japan Institute of Metals, 32, 689-696.
2. S.A. Khan and H.K.D.H. Bhadeshia, 1990, Materials Science and Engineering, A129, 257-272.
3. D.P. Koistinen and R.E. Marburger, 1959, Acta Metallurgica, 7, 59.
4. L.-E. Svensson, B. Gretoft and H.K.D.H. Bhadeshia, Scandinavian Journal of Metallurgy, 15, (1986), 97-103.
5. E. Scheil, 1935, Arch. Eisenhuttenwesen, 12, 565; Review by J.W. Christian, 1975, Theory of Transformations in Metals and Alloys, Part 1, 2nd edn., Pergamon Press, Oxford.

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Parameters

Input parameters

CC - real array of dimension 8

The first seven elements of CC 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).

TINT - real

TINT is the interpass or preheat temperature (°C).

C1 - real

C1 is the heat flow constant C₁ described above.

C2 - real

C2 is the heat flow constant C₂ described above.

CURR - real

CURR is the welding current (Amps).

VOLT - real

VOLT is the welding voltage (Volts).

EFF - real

EFF is the arc transfer efficiency.

SPEED - real

SPEED is the welding speed (ms^-1).

VOLFRA - real

VOLFRA is the volume fraction of allotriomorphic ferrite.

VOLW - real

VOLW is the volume fraction of Widmanstätten ferrite.

W1 - real

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

JRICH - integer

Set JRICH = 1 if the residual austenite is enriched due to a prior reaction (i.e. if VOLFRA > 0 and/or VOLW > 0).

Output parameters

AVOLB - real

AVOLB is the volume fraction of bainitic ferrite.

VMART - real

VMART is the volume fraction of martensite (Khan & Bhadeshia method).

VAUSTR - real

VAUSTR is the volume fraction of retained austensite (Khan & Bhadeshia method).

VMART2 - real

VMART2 is the volume fraction of martensite (Koistinen & Marburger method).

VAUST2 - real

VAUST2 is the volume fraction of retained austenite (Koistinen & Marburger method).

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Error Indicators

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Accuracy

The variable JT in the subroutine is the temperature interval at which calculations are made (currently 40 °C). The accuracy can be improved by using a smaller value.

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Further Comments

The variable TCAMB in the subroutine is set equal to the ambient temerature, which is assumed to be 20 °C, and is used for the calculation of the amount of retained austenite.

If VOLFRA+VOLW>0.99 no calculations are carried out as there is then no austenite present to transform.

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Example

1. Program text

      DOUBLE PRECISION CC(8),TINT,C1,C2,CURR,VOLT,EFF,SPEED,VOLFRA
      DOUBLE PRECISION AVOLB,VMART,VAUSTR,VMART2,VAUST2,VOLW,W1
      INTEGER I
C
      W1 = 48570D0
      WRITE(*,*) 'Input C  Si  Mn  Ni  Mo  Cr  V  (wt%):'
      READ (*,*) (CC(I), I=1,7)
      WRITE(*,*) 'Input welding parameters:'
      WRITE(*,*) 'Interpass T (deg. C), C1, C2, Efficiency:'          
      READ (*,*) TINT,C1,C2,EFF
      WRITE(*,*) 'Current (A), Voltage (V), Speed (m/s):'
      READ (*,*) CURR,VOLT,SPEED
      WRITE(*,*) 'Input initial volume fraction of allotriomorphic',
     &           ' ferrite:'
      READ (*,*) VOLFRA
      WRITE(*,*) 'Input initial volume fraction of Widmanstatten ',
     &           'ferrite:'
      READ (*,*) VOLW
      JRICH = 0
      IF (VOLFRA.GT.0.0 .OR. VOLW.GT.0.0 ) JRICH = 1
      CALL MAP_STEEL_BAINCA(CC,TINT,C1,C2,CURR,VOLT,EFF,SPEED,AVOLB,
     &               VMART,VAUSTR,VMART2,VAUST2,VOLFRA,VOLW,W1,JRICH)
      WRITE (*,1) AVOLB
      WRITE (*,2) VMART,VAUSTR
      WRITE (*,3) VMART2,VAUST2
      STOP
    1 FORMAT (/'Volume fraction of bainite             = ',F8.5/)
    2 FORMAT ('Khan and Bhadeshia:'/
     &        'Volume fraction of martensite          = ',F8.5/
     &        'Volume fraction of retained martensite = ',F8.5/)
    3 FORMAT ('Koistinen and Marburger:'/
     &        'Volume fraction of martensite          = ',F8.5/
     &        'Volume fraction of retained martensite = ',F8.5/)
      END

2. Program data

 Input C  Si  Mn  Ni  Mo  Cr  V  (wt%):
    0.05 0.5 1.0   0   0   0  0
 Input welding parameters:
 Interpass T (deg. C), C1, C2, Efficiency:
        200   1325   1.6   0.775
 Current (A), Voltage (V), Speed (m/s):
        180     34     0.004
 Input initial volume fraction of allotriomorphic ferrite:
 0.39
 Input initial volume fraction of Widmanstatten ferrite:
 0.25

3. Program results

Volume fraction of bainite             =  0.30576

Khan and Bhadeshia:
Volume fraction of martensite          =  0.03361
Volume fraction of retained martensite =  0.02063

Koistinen and Marburger:
Volume fraction of martensite          =  0.04772
Volume fraction of retained martensite =  0.0065

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Auxiliary Routines

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Keywords

bainite, martensite, retained austenite, steel, weld, cooling

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Download

Download source code

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