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G.I. Rees,

Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

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.

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

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).

- 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

**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

**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).

None.

See [7].

None.

None supplied.

None supplied.

None supplied.

**Subroutines**:

MAP_STEEL_ALLSOL

MAP_STEEL_AVOLF

MAP_STEEL_PROGC

MAP_STEEL_RRAD

MAP_STEEL_TRIVSOL

**Functions**:

MAP_STEEL_NUCSOLVE

MAP_STEEL_CCTSOLVE

MAP_STEEL_WKINETIC

MAP_STEEL_WNSOLVE

MAP_STEEL_XALPH

MAP_STEEL_SOLVEFER

allotriomorphic ferrite, bainite, Widmanstätten ferrite, CCT curves

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