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J.R. Yang,

Taiwan National University,

Department of Materials Engineering,

Taipei, Taiwan.

H.K.D.H. Bhadeshia,

Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

Added to MAP: September 1999.

To calculate the one-dimensional parabolic thickening rate constant for diffusion-controlled growth of austenite from a mixture of bainitic ferrite and austenite.

Language: | FORTRAN |

Product form: | Source code |

Complete program.

Since both bainite and acicular ferrite are in the form of platelets, the movement of the planar austenite-ferrite interface can, during the early stages of reverse transformation, be modelled in terms of one-dimensional growth. For simplicity, it is assumed that growth is diffusion controlled by the equilibrium carbon concentrations at the gamma-alpha interface. It is also assumed that the tie-line (of the equilibrium phase diagram) which determines the interface compositions passes throught the bulk composition of the alloy (may be a good approximation if the alloy is dilute). Any effects due to soft impingement are not taken into account, since only the early stages of the transformation are being considered.

The one-dimensional diffusion-controlled thickening rate constant alpha_{1} is calculated by solving equations 21 and 22 from reference 1:

where

C^{1} is the carbon concentration in the austenite before the start of reaustenisation,

C^{{gamma alpha}} is the carbon concentration in the austenite phase at the gamma-alpha interface during reaustenitisation,

C^{{alpha gamma}} is the carbon concentration in the ferrite, which is assumed to remain the same before and during reaustenitisation, and

^{¯}D^{¯} is a weighted average value for the diffusivity of carbon.

The diffusivity is a function of temperature, the steel composition and carbon concentration. The weighted average value, ^{¯}D^{¯}, is calculated using equations 1-4 of reference 2.

- J.R. Yang and H.K.D.H. Bhadeshia, 1989,
*Materials Science and Engineering*,**A118**, 155-170. - H.K.D.H. Bhadeshia,
*Metal Science*, 1981,**15**, 477-479. - J.R. Yang and H.K.D.H. Bhadeshia, 1991,
*Materials Science and Engineering*,**A131**, 99-113. - J.R. Yang and H.K.D.H. Bhadeshia, 1987,
*Proc. Int. Conf on Welding Metallurgy of Structural Steels*, (Metallurgical Society of AIME), Ed. J.Y. Koo, 549-563. - J.R. Yang and H.K.D.H. Bhadeshia, 1988,
*Proc. Int. Conf.: Phase Transformations*, (Institute of Metals: London), Ed. G.W. Lorimer, 203-206. - K.R. Kinsman and H.I. Aaronson, 1967,
*Transformation and Hardenability in Steels*, (Climax Molybdenum: Ann Arbon, USA), 31-56.

**I6**- integer- I6 is the number of different steel compositions to be analysed.
**I8**- integer- I8 is the number of different temperature values (for each alloy) at which the parabolic rate constant is to be calculated.
**C**- real array of dimension 8- C(1) - C(7) are the concentrations (wt%) of the alloying components carbon, silicon, manganese, nickel, molybdenum, chromium and vanadium, in that order. (C(8) is used to hold the iron concentration, assumed to be the remaining wt%.)
**T**- real- T is the temperature (°C) at which the parabolic rate constant is to be calculated.
**XGAG**- real- XGAG is the equilibrium mole fraction of carbon in austenite at the austenite-ferrite interface.

**W**- real- W is the carbon-carbon interaction energy in austenite (J/mol).
**ALP**- real, 2-dimensional array- ALP contains the parabolic rate constant (cm/s
^{0.5}). **XXX**- real- XXX is 1/(parabolic rate constant)
^{2}(s/cm^{2}).

None.

No information supplied.

None.

Complete program.

Input number of different steel compositions: 1 Input C, Si, Mn, Ni, Mo, Cr, V wt%: 0.55 0.49 1.16 0.0 0.0 0.0 0.0 Input number of different temperatures: 3 Input temperature (deg.C) and equilibrium C mole fraction: 780 0.01 740 0.0176 700 0.0266

************************************************************************** Element: C Si Mn Ni Mo Cr V conc. wt%: 0.5500 0.4900 1.1600 0.0000 0.0000 0.0000 0.0000 mole frac: 0.0249 0.0095 0.0115 0.0000 0.0000 0.0000 0.0000 Carbon-carbon interaction energy in austenite = 8402.9 J/mol Starting mole fraction of carbon in austenite = 0.0249 Input temperature (deg.C) and equilibrium C mole fraction: 780 0.01 Temperature = 1053.00 K or 780.00 deg. C. Equilibrium mole fraction of C in austenite = 0.01000 Equilibrium mole fraction of C in ferrite = 0.00049 Parabolic rate constant (cm/s**0.5) = 0.1492D-03 Input temperature (deg.C) and equilibrium C mole fraction: 740 0.0176 Temperature = 1013.00 K or 740.00 deg. C. Equilibrium mole fraction of C in austenite = 0.01760 Equilibrium mole fraction of C in ferrite = 0.00059 Parabolic rate constant (cm/s**0.5) = 0.3944D-04 Input temperature (deg.C) and equilibrium C mole fraction: 700 0.0266 >>>> Equilibrium C concentration greater than starting conc. in austenite. >>>> Growth of austenite not possible. ************************************************************************** Alloy Temperature Parabolic rate constant 1/(p.r.c.)**2 (deg.C) (cm/s**0.5) (s/cm/cm) 1 740.00 0.3944D-04 0.6429D+09 1 780.00 0.1492D-03 0.4492D+08

Subroutines: | Functions: | |

MAP_STEEL_OMEGA | MAP_STEEL_CG | |

MAP_UTIL_TRAPE | MAP_STEEL_DCG | |

MAP_STEEL_XALPH |

parabolic rate constant, rate constant, parabolic, austenite, ferrite, diffusion, bainite, acicular, transformation, thickening

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