[MAP Logo]

Materials Algorithms Project
Program Library

Subroutine MAP_STEEL_MICRO

Provenance of code.
Purpose of code.
Specification.
Description of subroutine's operation.
References.
Parameter descriptions.
Error indicators.
Accuracy estimate.
Any additional information.
Example of code
Auxiliary subroutines required.
Keywords.
Download source code.
Links.

Provenance of Source Code

G.I. Rees,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

Top | Next

To calculate the volume fraction of the phases of allotriomorphic ferrite, bainite, and Widmanstätten ferrite in steel microstructures as a function of the cooling rate from the austenite phase. It also calculates the temperatures and times at which 5%, 25%, 50%, and 70% transformation is achieved for different cooling rates.

Top | Next | Prev

Specification

Language:	FORTRAN
Product form:	Source code

SUBROUTINE MAP_STEEL_MICRO(TEMPC, XEQ, XT0, X44, SHT, DIFFT,
& GMAX, DELTC, ICOOL, IL, STOR, XBAR, VGAM, RET1, RET2, RETBOR,
& WINTER, SV, MS, ITOT)

DOUBLE PRECISION TEMPC(1000), XEQ(1000), XT0(1000), X44(1000),
& SHT(1000), DIFFT(1000), GMAX(1000), STOR(12,20), DELTC,
& XBAR, VGAM, RET1, RET2, RETBOR, WINTER, SV, MS

INTEGER ICOOL, IL, ITOT

Top | Next | Prev

Description

An estimate is made of the microstructure of a steel of given grain size subjected to a given cooling rate. The calculation is based on data on the thermodynamics of austenite transformation to various forms of ferrite (i.e. allotriomorphic ferrite, Widmanstätten ferrite, and bainite) and on the the calculated time-temperature transformation diagram `incubation times' for the onset of these reactions.

The growth rate of allotriomorphic ferrite is assumed to follow carbon diffusion controlled growth with nucleation at the grain boundary [1, 2]. This is calculated by the routine MAP_STEEL_AVOLF2, with the effective nucleation rate calculated by MAP_STEEL_NUCSOLVE in accordance with the calculated incubation time for ferrite formation [3]. The effect of niobium on the kinetics of ferrite nucleation is treated in accordance with the findings of [4].

Widmanstätten ferrite and bainite are distinguished by the temperature at which they form [5]. Their growth kinetics are modelled by the same relationship [6,7] and are calculated by the function MAP_STEEL_WKINETIC, while the effective nuceation rate is calculated by MAP_STEEL_WNSOLVE.

The output of the subroutine contains the estimated microstructure volume fractions for each phase, as well as the temperature and time at which, during continuous cooling transformation, the overall transformation reaches 5%, 25%, 50%, and 70% (i.e. the time-temperature values of the CCT curve are calculated for each cooling rate).

Top | Next | Prev

References

J.W. Christian, Theory of Transformation in Metals and Alloys, Part 1, 2nd ed., Pergamon Press, Oxford, 1975.
H.K.D.H. Bhadeshia, L-E Svensson, and B. Gretoft, Proc. Conf. Welding Metallurgy and Structural Steels, ed. J.Y. Koo, TMS AIME, Warrendale, Penn., (1987), 517-530.
H.K.D.H. Bhadeshia, Metal Science, 16, (1982), 156-165.
M.H. Thomas and G.M. Michal, Proc. Int. Conf. `Solid-Solid Transformations', eds. H.I. Aaronson et al., TMS AIME, Warrendale, Penn., (1981), 469-473.
H.K.D.H. Bhadeshia, Acta Metall., 29, (1981), 1117-1130.
M. Umemoto, A. Hiramatsu, A. Moriya, T. Watanabe, S. Nanba, N. Nakajima, G. Anan, and Y. Higo, I.S.I.J, 32, (1992), 306-315.
G.I. Rees, H.K.D.H. Bhadeshia, and T. Maurickx, Progress Report for SOLLAC, August 1995.
A. Ali and H.K.D.H. Bhadeshia, Materials Science and Technology, 5, (1990), 398-402.
Pickering

Top | Next | Prev

Parameters

Input parameters

TEMP - real array: TEMP contains a range of temperature values (in centigrade) from Ae'₃ to 115 degrees below M_s.
XEQ - real array: XEQ contains values of the equilibrium austenite composition x^{gamma alpha} as a function of temperature [5], (in mole fraction).
XT0 - real array: XT0 contains the x^(T'₀) composition (in mole fraction) for which austenite and ferrite with a stored energy of 400 Jmol^-1 have the same free energy [5].
X44 - real array: X44 contains the composition (in mole fraction) for which Delta G_m = G_N, as a function of temperature [3].
SHT - real array: SHT contains the incubation times (in seconds) for the lower C-curve, as a function of temperature [3].
DIFFT - real array: DIFFT contains the incubation times (in seconds) for the upper C-curve, as a function of temperature [3].
GMAX - real array: GMAX contains the values of Delta G_m (in joules per mole), as a function of temperature [3, 8].
ICOOL - integer: ICOOL = 0 if linear cooling is used, = 1 if natural cooling is used.
XBAR - real: XBAR is the mean carbon concentration x of the bulk alloy (in mole fraction).
WINTER - real: WINTER is the carbon-carbon interaction parameter w for austenite.
SV - real: SV is the austenite grain boundary surface area per unit volume S_v (in m^-1).
RET1 - real: RET1 is the calculated retardation factor of the upper C-curve, depending on the austenite grain size and the amount of niobium and boron in solid solution in austenite [7].
RET2 - real: RET2 is the calculated retardation factor of the lower C-curve, depending on the austenite grain size [7].
RETBOR - real: RETBOR is the retardation effect of boron calculated from the reported effect of boron addition on 0.1C-0.5Mo steel [9], assuming a grain size of 50 microns.
MS - real: MS is the calculated martensite-start temperature, M_s, of the alloy.
VGAM - real: VGAM is set to 1.0

Output parameters

STOR - real array of dimension 12 x IL
STOR contains the output:-: STOR(1, ) contains the volume fraction of ferrite.; STOR(2, ) contains the volume fraction of Widmanstätten ferrite.; STOR(3, ) contains the volume fraction of bainite.; STOR(4, ) contains the time for 5% transformation (in seconds).; STOR(5, ) contains the temperature for 5% transformation (in centigrade).; STOR(6, ) contians the time for 25% transformation (in seconds).; STOR(7, ) contains the temperature for 25% transformation (in centigrade).; STOR(8, ) contains the time for 50% transformation (in seconds).; STOR(9, ) contains the temperature for 50% transformation (in centigrade).; STOR(10, ) contains the time for 70\% transformation (in seconds).; STOR(11, ) contains the temperature for 70\% transformation (in centigrade).