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Austenite and ferrite are two different allotropes of iron, with face-centered and body-centered cubic structure respectively. The transformation of austenite to ferrite is therefore accompanied by a change in density, and causes the external dimensions of a piece of solid austenite/ferrite to change (dilatation). These changes can be measured, enabling the transformation itself to be monitored as it progresses, using a dilatometer.

The program MAP_STEEL_DILAT2 calculates the volume fraction of transformed austenite to ferrite from the measured dilatations. The ferrite lattice parameter is obtained for the given solute concentrations by subroutine MAP_STEEL_FERR. An iterative procedure is used to calculate the volume fraction of ferrite. For a given volume fraction, subroutine MAP_STEEL_PARAM2 evaluates the lattice parameter and carbon content of the austenite [1,2]. The expected density change of the material, as calculated from the lattice parameters and volume fractions of the two components, is then compared with the measured dilatation using subroutine MAP_STEEL_FPARAM, which gives a measure of the error in the calculated dilation. The derivative of the dilatation error with respect to the volume fraction is then calculated and used to find a new value for the volume fraction. The size of the change made with each iteration is modified by the parameter SENS in the main program, and is currently set to 0.1.

This method of iteration is an improvement on the method used by MAP_STEEL_DILAT, and allows data from steels with high carbon content (greater 0.5wt%) and low dilatation to be successfully analysed. Subroutine MAP_STEEL_PARAM2 is a slightly improved version of MAP_STEEL_PARAM, called by MAP_STEEL_DILAT; the iteration procedure in this routine continues until the absolute percentage in the calculated lattice parameter is less than 10^-10, whereas for MAP_STEEL_PARAM a fractional change of less than 10^-4 stipulates the convergence criterium.

Sample input and output data files (LENGTH.DAT and OUT.DAT) are provided with the program.

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References

H.K.D.H. Bhadeshia, S.A. David, J.M. Vitek, and R.W. Reed, 1991, Materials Science and Technology, 7, 686-698.
D.J. Dyson and B. Holmes, 1970, Journal of the Iron and Steel Institute, 208, 469.

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Parameters

Input parameters

Name	Type	Description
IDATA	integer	Number of L,T pairs to be read in.
XBAR	real	Carbon concentration (weight percent).
SI	real	Silicon concentration (wt%).
MN	real	Manganese concentration (wt%).
NI	real	Nickel concentration (wt%).
MO	real	Molybdenum concentration (wt%).
CR	real	Chromium concentration (wt%).
VAN	real	Vanadium concentration (wt%).
XALPHA	real	Amount of carbon trapped in ferrite (wt%). This can be calculated using MAP_STEEL_XALPH.
EXA	real	Linear expansion coefficient of ferrite (K^-1).
EXG	real	Linear expansion coefficient of austenite (K^-1).
IPARAM	integer	Set IPARAM to 1 if the user wishes the program to read in values for the ferrite and the pure austenite lattice parameters (GG0 and PP). Otherwise if IPARAM to 0, PP is calculated using subroutine MAP_STEEL_FERR and GG0 is set to 3.573x10^-10m.
GG0	real	Lattice parameter for pure austenite at room temperature (metres).
PP	real	Lattice parameter for the ferrite in the steel at room temperature (metres).
L	real array of dimension IDATA	Fractional change in length, as measured by the dilatometer.
T	real array of dimension IDATA	Temperature (°C).
TIME	real array of dimension IDATA	Time since start of transformation (incubation time) (seconds).

The input parameters are read in by the program from a file called LENGTH.DAT and should be arranged as follows:

IDATA  XBAR  SI  MN  NI  MO  CR  VAN
XALPHA  EXA  EXG IPARAM
PP  GG0 
L(1)  T(1)  TIME(1)
L(2)  T(2)  TIME(2)
L(3)  T(3)  TIME(3)  etc.

Line 3 (PP and GG0) should only be included if IPARAM is not set to 0.

Output parameters

Name	Column label	Description
T	Ctemp	Temperature (°C).
L	Del-L	Fractional change in length.
TIME	Time(s)	Incubation time (seconds).
VA	V-alpha	Volume fraction of ferrite.
XG	Xg-wt%	Carbon concentration in carbon-enriched austenite (wt%).
XGM	Xg-Mfrc	Mole fraction of carbon in carbon-enriched austenite.
AAT	AAT Ang	Ferrite lattice parameter (Å) at temperature T.
AGT	AGT Ang	Lattice parameter (Å) of austenite containing the initial amount of carbon (XBAR) at temperature T.
AGTX	AGTX Ang	Lattice parameter (Å) of the carbon enriched austenite (containing XG amount of carbon) at temperature T.
AA	AA	Ferrite lattice parameter at 298K.