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Subroutine MAP_STEEL_MUCG

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Provenance of Source Code

N.A. 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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This subroutine calculates an initial value for the chemical driving force for the bainite reaction, the carbon concentration at the To' line, where the bainite transformation is no longer thermodynamically possible, and the average carbon content of the alloy in mole fractions.

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Specification

Language:	FORTRAN
Product form:	Source code

None supplied.

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Description

This subroutine uses the steel composition and the temperature to calculate the initial value for the chemical driving force for the bainite reaction using the equation:

G_max = RT ln( a_cf / a_ca )

a_cf is the activity of carbon in ferrite and is calculated by calling subroutine MAP_STEEL_GMAAX; a_ca is the activity of carbon in austenite and is calculated by function MAP_STEEL_CG.

The routine calls MAP_STEEL_OMEGA to calculate the carbon-carbon interaction energy in austenite and the average carbon content of the alloy in mole fractions; MAP_STEEL_ENERGY gives a value for the free energy change for the transformation of austenite to ferrite of the same chemical composition; subroutine MAP_STEEL_AXTO calculates the carbon concentration at the T_o' line, where the bainite transformation is no longer thermodynamically possible; function MAP_STEEL_AFEG gives a value for the natural logarithm of the activity of iron in austenite.

The excess partial molar enthalpy of solution and entropy of solution of carbon in austenite are taken to be 38575 J/mol and 13.48 J/mol respectively. The excess partial molar enthalpy of solution and entropy of solution of carbon in ferrite are taken to be respectively 111918 J/mol and 51.44 J/mol (T<1000K) or 105525 J/mol and 45.34521 J/mol (T>1000K). The carbon-carbon interaction energy in ferrite is assumed to be 48570 J/mol. A value of 400 J/mol is used for the stored energy in bainite.

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References

N.A. Chester, unpublished work.
See the references sections of the webpages for the auxiliary routines.

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Parameters

Input parameters

C - real array of dimension 8: C contains the composition of the steel (in mole fraction), corresponding to the alloying elements C, Si, Mn, Ni, Mo, Cr, V, Fe.
K - real array of dimension 8: K contains the composition of the steel (wt.%).
T - real: T is the isothermal holding temperature (degrees centigrade).
ND - real: ND is the austenite grain size (microns).

Output parameters

GMAX - real: GMAX is the initial value of the maximum nucleation free energy change (Jmol^-1).
XTO400 - real: XTO400 is the carbon concentration (for a given temperature) at the To' line, where the bainite transformation is no longer thermodynamically possible.
XBAR - real: XBAR is the average carbon content of the alloy (mole fraction).