Program Library

- Provenance of code.
- Purpose of code.
- Specification.
- Description of subroutine's operation.
- References.
- Parameter descriptions.
- Error indicators.
- Accuracy estimate.
- Any additional information.
- Example of code
- Auxiliary subroutines required.
- Keywords.
- Download source code.
- Links.

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.

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

Language: | FORTRAN |

Product form: | Source code |

SUBROUTINE MAP_STEEL_BAINCA(CC,TINT,C1,C2,CURR,VOLT,EFF, | |

& | SPEED,AVOLB,VMART,VAUSTR,VMART2,VAUST2,VOLFRA,VOLW,W1,JRICH) |

| |

DOUBLE PRECISION AVOLB,CC(8),C1,C2,CURR,EFF,SPEED,TINT | |

DOUBLE PRECISION VAUSTR,VAUST2,VMART,VMART2,VOLFRA,VOLW | |

DOUBLE PRECISION W1,VOLT | |

INTEGER JRICH |

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 C_{1} and C_{2}, the welding current, voltage, speed and arc transfer efficiency, and the interpass temperature. All of these are required as inputs to this subroutine. C_{1} and C_{2} 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).

- M. Takahashi and H.K.D.H. Bhadeshia, 1991,
*Materials Transactions of the Japan Institute of Metals*,__32__, 689-696. - S.A. Khan and H.K.D.H. Bhadeshia, 1990,
*Materials Science and Engineering*,__A129__, 257-272. - D.P. Koistinen and R.E. Marburger, 1959,
*Acta Metallurgica*,__7__, 59. - L.-E. Svensson, B. Gretoft and H.K.D.H. Bhadeshia,
*Scandinavian Journal of Metallurgy*,__15__, (1986), 97-103. - 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.

**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 C
_{1}described above. **C2**- real- C2 is the heat flow constant C
_{2}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).

**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).

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.

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.

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

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

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

Subroutines | Functions
| ||||

MAP_STEEL_BAINTT | MAP_STEEL_CULRAT | ||||

MAP_STEEL_BSMS | MAP_STEEL_XALPH | ||||

MAP_STEEL_MART | |||||

MAP_STEEL_MART2 |

Called by MAP_STEEL_BAINTT:

Subroutines | Functions
| ||||

MAP_STEEL_GMAAX | MAP_STEEL_AFEG | ||||

MAP_STEEL_OMEGA | MAP_STEEL_CG | ||||

MAP_STEEL_TTTT | MAP_STEEL_ENERGY |

Called by MAP_STEEL_BSMS:

Subroutines | Functions
| ||||

MAP_UTIL_ANALY | MAP_STEEL_ENERGY | ||||

MAP_STEEL_AXTO |

Called by MAP_STEEL_MART:

Subroutines | Functions
| ||||

None. | MAP_STEEL_GMART | ||||

MAP_STEEL_GMDASH |

Called by MAP_STEEL_AXTO:

Subroutines | Functions
| ||||

None. | MAP_STEEL_FTO1 | ||||

MAP_STEEL_G91 |

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

**
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
**