Materials Algorithms Project
Program Library

Function MAP_STEEL_NEWF2

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

N. Chester,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

E-mail: Naomi_Chester@technology.britishsteel.co.uk

Added to MAP: November 1999

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Purpose

To calculate the time required to form a given volume fraction of bainitic ferrite.

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Specification

 DOUBLE PRECISION FUNCTION 
&                 MAP_STEEL_NEWF2 (TK,GM0,PSI,THETA,ND,CD,XB,U)

 DOUBLE PRECISION TK,GM0,PSI,THETA,ND,CD(4),XB,U

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Description

This program finds the time required for a given volume fraction of bainitic ferrite to form during an isothermal transformation in a steel alloy. Reference 1 describes the theory and gives an expression for the overall transformation rate of bainite (equation 28). However the final solution for the time required which is given in reference 1 contains an error. A correct analytical solution was obtained using equation 410 in reference 2, giving the result expressed by equation 4.35 in reference 4. This latter equation contains 4 fitting parameters; values for these parameters were obtained by fitting the equation to experimental data values for low alloy steels [4]. These values must be passed to the function from the calling routine in the array CD:

Calculations using equation 4.35 [4] were found to give correct predictions only for a temperature of 405 deg. C, which was attributed to a change in plate volume with transformation temperature. This program incorporates a temperature dependent expression for the plate width u_w [5] given by:

subject to a minimum value of 0.05 microns and with temperature T in Centigrade.

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References

1. G.I. Rees and H.K.D.H. Bhadeshia, 1992, Materials Science and Technology, 8, 985-993.
2. K. Rektorys, 1969, Survey of Applicable Mathematics, ILIFFE Books Ltd, London, p543.
3. H.K.D.H. Bhadeshia, J. Phys. (Orsay), 43, (C4), 443-448.
4. N.A. Chester, 1997, PhD Thesis, University of Cambridge, Mathematical Modelling of Microstructural Development in Continuously Annealed High-Strength Steels.
5. L.C. Chang, 1995, PhD Thesis, University of Cambridge, Bainite Transformation and Novel Bainitic Rail Steels.
6. N.A. Chester and H.K.D.H. Bhadeshia, 1997, IV European Symposium on Martensitic Transformation (Esomat '97) Conference Proceedings, Enschede, The Netherlands.

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Parameters

Input parameters

TK - real

TK is the temperature at which bainite is to form (Kelvin).

GM0 - real

GMO is the initial value of the maximum nucleation free energy change (Jmol^-1).

PSI - real

PSI is the normalised volume fraction of bainitic ferrite, i.e. the actual volume fraction divided by the maximum volume fraction.

THETA - real

THETA is the maximum volume fraction of bainite, taken to be that at which the carbon concentration of the austenite reaches the T₀' line.

ND - real

ND is the grain size of the parental austenite (microns).

CD - real array of dimension 4

CD must contain the four fitting parameters:

CD(1) = 0.57919D-06

CD(2) = 0.14750D+03

CD(3) = 0.20980D+05

CD(4) = 0.30327D+02

XB - real

XB is the mole fraction of carbon in the alloy.

Output parameters

MAP_STEEL_NEWF2 - real

MAP_STEEL_NEWF2 is the time taken to form the given volume fraction of bainite (seconds).

U - real

U is the volume of the bainite plates used in the calculations (mm³).

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Error Indicators

None.

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Accuracy

No information supplied.

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Further Comments

None.

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Example

1. Program text

      IMPLICIT NONE
      DOUBLE PRECISION TK,GM0,PSI,THETA,ND,CD(4),XB,NEWFX,U
      DOUBLE PRECISION MAP_STEEL_NEWF2
C
      WRITE(*,*) 'Input T(K), GM0, norm. vol. fraction:'
      READ (*,*) TK, GM0, PSI
      WRITE(*,*) 'Max. vol. fraction, grain size, C mole fraction:'
      READ (*,*) THETA, ND, XB
      CD(1) = 0.57919D-06
      CD(2) = 0.14750D+03
      CD(3) = 0.20980D+05
      CD(4) = 0.30327D+02
      NEWFX = MAP_STEEL_NEWF2(TK,GM0,PSI,THETA,ND,CD,XB,U)
      U = U * 1D9
      WRITE (*,1) NEWFX,U
      STOP
    1 FORMAT(' Time for bainite formation        = ',F7.2,' seconds'/
     & ' Plate volume used in calculations = ',F7.2,' cubic microns')
      END

2. Program data

 Input T(K), GM0, norm. vol. fraction:
     653.0  -1523.03  0.2015
 Max. vol. fraction, grain size, C mole fraction:
   0.397  16.0  0.0172

3. Program results

 Time for bainite formation        =   93.24 seconds
 Plate volume used in calculations =   14.12 cubic microns

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Auxiliary Routines

Utility Functions:
MAP_UTIL_FUNCT
MAP_UTIL_FACT (Called by MAP_UTIL_FUNCT)

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Keywords

bainite, kinetics, volume fraction, bainitic ferrite, time

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Download

Download source code

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