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  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.


K. Ichikawa,
Nippon Steel Corporation,
Welding & Joining Research Center,
Steel Research Laboratories,
Technical Development Bureau,
20-1 Shintomi, Futtsu, Chiba,
293-8511 Japan.

Added to MAP: May 1999.

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To model the simultaneous transformation of allotriomorphic and Widmanstätten ferrite in a steel weld. Predicts values for the volume fractions of the different microstructures after cooling.

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The program is self-contained.

Product form:Source code

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Allotriomorphic ferrite is usually the first phase to form when austenite is cooled but its formation is frequently accompanied by that of Widmanstätten ferrite, which may grow directly from the allotriomorphic ferrite (secondary Widmanstätten ferrite) or from bare austenite grain surfaces (primary Widmanstätten ferrite). In the past such simultaneous transformations have been modelled by arbitrarily stopping one transformation to permit the next in the sequence to commence. Such a model is not realistic. In welding alloys it is the secondary Widmanstätten ferrite which predominates and inevitably interacts with the growth of allotriomorphic ferrite. This program uses a new model for calculating the volume fractions of Widmanstätten (primary & secondary) and allotriomorphic ferrite formed during cooling, as well as the volume fractions of bainite & acicular ferrite and retained austenite & martensite. It is based on a kinetic theory which is capable of handling several transformations together and is described in detail in reference 1. Both primary and secondary Widmanstätten ferrite nucleation events are, however, treated identically in this model; the two nucleation sites are assumed to have identical kinetic parameters.

In this program the solidification of the weld is divided up into 100 steps (segments), the ith segment corresponding to a change in the solidified fraction from (i-1)/100 to i/100. The solute concentration in the solid and liquid phases for this segment are calculated using Sheil's equation. The transformation behaviour is determined separately for each segment. The Widmanstätten start temperature is calculated using the theory in reference 2. The temperature, To', below which bainite forms by diffusionless transformation, is calculated as being the temperature at which austenite and ferrite of the same composition have identical free energy accounting for the stored energy of ferrite (here taken to be 350 Jmol-1). Cooling of the weld occurs in temperature steps of 5 °C; the time taken to reach each temperature is calculated using the cooling rate, which is obtained from the appropriate welding parameters [3]. The volume fractions of allotriomorphic and Widmanstätten ferrite which form at each temperature is determined. The processes are repeated at the next temperature until the temperature falls either below LOWT or below To'. If the temperature falls below To' the remaining matrix (austenite) is deemed to transform to bainite & acicular ferrite. Any remaining matrix at LOWT is assumed either to remain as austenite or form martensite. The volume fractions of each microstructure in the weld as a whole are then calculated by averaging over the contributions from all the segments.

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  1. K. Ichikawa and H.K.D.H. Bhadeshia, 1998, Mathematical Modelling of Weld Phenomena 4, Ed. H. Cerjak & H.K.D.H. Bhadeshia, IOM Communications, London, pp302.
  2. A. Ali and H.K.D.H. Bhadeshia, 1990, Materials Science and Technology, 6, 781.
  3. L.-E. Svensson, B. Gretoft and H.K.D.H. Bhadeshia, 1986, Scandinavian Journal of Metallurgy, 15, 97-103.
  4. A.P. Chakravati, R. Thibau. and S.R. Bala, 1985, Metal Constr., 17, 178R.
  5. Data obtained by Ed Metzbower, Naval Research Laboratory.
  6. Data obtained by K. Ichikawa, Nippon Steel Corporation, Japan.

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Input parameters

CARBON - real
carbon content (wt%).

SI - real
silicon content (wt%).

MN - real
manganese content (wt%).

NI - real
nickel content (wt%).

MO - real
molybdenum content (wt%).

CR - real
chromium content (wt%).

V - real
vanadium content (wt%).

SV - real
SV is the austenite grain surface per unit volume (m-1).

DUMM - real
DUMM is a fitting constant in the calculation of the nucleation rate (K2 in equation 24 of reference 1).

SITE - real
SITE is a multiplicative (fitting) factor for number density of nucleation sites (K1 in equation 23 of reference 1).

LOWT - real
LOWT is the lowest temperature at which the calculations are arbitrarily stopped (°C).

J - integer
Selects the type of welding process as follows:
  1. Shielded Metal Arc Welding (Manual Metal Arc).
  2. Metal Cored Wire, CO2 shielding.
  3. Metal Cored Wire, Fogon 20 shielding.
  4. Tandem Submerged Arc Welding.
  5. Single Submerged Arc Welding.
  6. Vertical-Up SMAW.
  7. Bead on Plate FCAW [4].
  8. Bead on Plate Self-Shielded [4].
  9. Bead on Plate SAW [4].
  10. Measured time-temperature Horizontal GMAW data. Interpass temperature 150 °C [5].
  11. Measured time-temperature Flat GMAW data. Interpass temperature 150 °C [5].
  12. Measured time-temperature Vertical GMAW data. Interpass temperature 150 °C.[5].
  13. Measured time-temperature Vertical GMAW data. Interpass temperature 93 °C [5].
  14. Computed time-temperature for laser weld: 117000 W, speed=5 mm/s, efficiency=0.50.
  15. Large heat input tandem Submerged Arc Welding (130kJ/cm) [6].
  16. Large heat input tandem Submerged Arc Welding (70kJ/cm) [6].
For further details see subroutine HFLOW in the program.
CURR - real
CURR is the welding current (Amps).

VOLT - real
VOLT is the welding voltage (Volts).

SPEED - real
SPEED is the welding speed (m/s).

TINT - real
TINT is the interpass temperature (°C).

Output parameters

FVFAW - real
FVFAW is the total volume fraction of allotriomorphic and Widmanstätten ferrite, averaged from 100 segregation segments.

FVFA - real
FVFA is the volume fraction of allotriomorphic ferrite, averaged over 100 segregation segments.

FVFW - real
FVFW is the volume fraction of Widmanstätten ferrite, averaged over 100 segregation segments.

FVFBAF - real
FVFBAF is the the total volume fraction of bainite and acicular ferrite, averaged over 100 segregation segments.

FVFRGM - real
FVFRGM is the volume fraction of retained austenite and martensite, averaged over 100 segregation segments.

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Error Indicators


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No information supplied.

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Further Comments

The program may take 15 minutes or more to run. In addition to the final results shown in the example below, some intermediate results are outputted during the calculations for each segment and can be used to monitor the progress of the computations.

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1. Program text

Complete program.

2. Program data

 Input C   Si   Mn   Ni   Mo   Cr   V (wt%)
    0.05  0.5    1    0    0    0   0
 Input austenite grain surface per unit volume (1/m):
 Input fitting factor for nucleation rate (K2):
 Input fitting factor for number of nucleation sites (K1):
 Input lowest temperature for calculations (degrees C):
 Input welding process:
 1 - SMAW; 2 - metal core wire CO2 shielding;
 3 - MCW Fogon 20 shielding; 4 - tandem SAW; 5 - single SAW
 Input welding current (Amps):
 Input welding voltage (Volts):
 Input welding speed (m/s):
 Input interpass temperature (degrees C):

3. Program results

                    Welding Current (amps) = 180.
                    Voltage (V) =34.
                    Welding Speed (m/s) = 0.400D-02
                    Welding Technique (SMAW:1, Tandem SAW:4, Single SAW:5)=    1
                    Interpass Temperature (Centigrade) = 200.

 *         Final Result of Calculations           *

 Total volume fraction of each microstructual component in the weld:

 Volume fraction of alpha + Widmanstatten =  0.90707
 Volume fraction of alpha                 =  0.12875
 Volume fraction of Widmanstatten         =  0.77832
 Volume fraction of bainite + acicular ferrite  =  0.06696
 Volume fraction of retained gamma + martensite =  0.02597

***************************** Details for each solidification segment ****************************

 Segment   Volume fraction  Volume fraction  Volume fraction    VF bainite &       VF retained
 number   alpha & Widmanst.    alpha Fe       Widmanstatten   acicular ferrite  gamma & martensite
    1          0.96978          0.13584          0.83394          0.00000            0.03022
    2          0.96976          0.13591          0.83385          0.00000            0.03024
    3          0.96971          0.13581          0.83390          0.00000            0.03029
    4          0.97009          0.13556          0.83453          0.00000            0.02991
    5          0.96964          0.13549          0.83416          0.00000            0.03036
    6          0.96992          0.13521          0.83471          0.00000            0.03008

(output for segments 7-94 omitted)

   95          0.42205          0.10437          0.31768          0.57795            0.00000
   96          0.38323          0.10140          0.28183          0.61677            0.00000
   97          0.35515          0.09930          0.25585          0.64485            0.00000
   98          0.30216          0.09511          0.20705          0.69784            0.00000
   99          0.21613          0.08692          0.12921          0.78387            0.00000
  100          0.11610          0.06948          0.04662          0.88390            0.00000

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Auxiliary Routines

All required subroutines and functions are supplied with the program.

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Widmanstatten, allotriomorphic, ferrite, bainite, martensite, welding, cooling, transformation, steel

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Download source code

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