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.
MAP_STEEL_CONCDIF uses a numerical solution for the problem of the growth of a planar interface under the conditions of volume diffusion control and a diffusion coefficient in the matrix which varies with concentration, to obtain a value for the one-dimensional parabolic thickening rate constant for the growth of ferrite in austenite.
Language: | FORTRAN |
Product form: | Source code |
Complete program.
The problem of a planar boundary growing under conditions of volume diffusion control, with a diffusion coefficient in the matrix phase which varies with concentration, is solved numerically to provide a value for the growth rate constant [1,2]. This numerical method is more rigorous than using a weighted average value of the diffusivity, as has been done in other programs [3] and gives more realistic results when the velocity is not constant. The model is relevant for the growth of precipitates from solid solution and is used in this program to find the parabolic rate constant for the growth of ferrite from austenite in a low alloy steel. The program solves equations 5 and 6 from reference 2:
and
where
C_{n} is the carbon concentration in the austenite, well away from the interface (at infinity).
C_{o} is the carbon concentration in the austenite at the interface.
C_{1} is the carbon concentration in the ferrite at the interface.
D_{o} is the carbon diffusion coefficient, D, at the interface.
x is the distance from the interface in the direction of motion of the interface.
t is the time.
alpha is the parabolic growth rate constant for ferrite in austenite.
For a given steel composition, temperature and carbon concentration at the interface in the austenite, C_{o}, the program calls MAP_STEEL_OMEGA to calculate C_{n}, MAP_STEEL_XALPH to obtain a value for C_{1}, and MAP_STEEL_DIFFUS to calculate D_{o} and an initial value for D. In the numerical analysis the concentration profile is split up into N sections. The calculations are carried out using different values of N. An initial estimate for alpha is obtained with N=10. Subsequent evaluations are made for N=60, 110 and 160. Further details of the numerical method used are given in reference [2].
None.
The iteration procedure is iterated until RESDU1 is less than 10^{-4} and RESDU2 is less than 10^{-6}.
i.e.
For further details see reference [2].
None.
Complete program.
Input C, Si, Mn, Ni, Mo, Cr, V wt%: 0.12 0.49 1.16 0.0 0.0 0.0 0.0 Input temperature (deg.C) and C mole fraction in austenite at the interface: 780 0.01 Repeat calculations for another set of data (y/n)? y Input temperature (deg.C) and C mole fraction in austenite at the interface: 700 0.0266 Repeat calculations for another set of data (y/n)? n
************************************************************************** Element: C Si Mn Ni Mo Cr V conc. wt%: 0.1200 0.4900 1.1600 0.0000 0.0000 0.0000 0.0000 mole frac: 0.0055 0.0096 0.0117 0.0000 0.0000 0.0000 0.0000 Carbon-carbon interaction energy in austenite = 8402.7 J/mol Starting mole fraction of carbon in austenite = 0.0055 Temperature = 780.00 deg. C Equ. C conc. in austenite at the interface = 0.0100 mole fractions Equ. C conc. in ferrite at the interface = 0.4859D-03 mole fractions Diffusivity of carbon in austenite (Do) = 0.1250D-07 squ.cm/s No. steps Rate constant (cm/s**0.5) Residue 1 Residue 2 10 0.7350D-04 0.481D-04 0.000D+00 60 0.8405D-04 0.581D-04 0.657D-06 110 0.8511D-04 0.431D-04 0.300D-06 160 0.8551D-04 0.498D-04 0.545D-06 Temperature = 700.00 deg. C Equ. C conc. in austenite at the interface = 0.0266 mole fractions Equ. C conc. in ferrite at the interface = 0.6691D-03 mole fractions Diffusivity of carbon in austenite (Do) = 0.5162D-08 squ.cm/s No. steps Rate constant (cm/s**0.5) Residue 1 Residue 2 10 0.1163D-03 0.738D-04 0.000D+00 60 0.1484D-03 0.176D-04 0.845D-06 110 0.1522D-03 0.277D-04 0.848D-06 160 0.1536D-03 0.322D-04 0.764D-06
Subroutines | Functions | |
MAP_STEEL_OMEGA | MAP_STEEL_CG | |
MAP_UTIL_TRAPE | MAP_STEEL_DCG | |
MAP_STEEL_DIFFUS | MAP_STEEL_XALPH |
parabolic, thickening, diffusion, planar, growth, concentration dependent, diffusion controlled, diffusion coefficient
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
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