G.I. Rees,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.
Calculates the growth rate (as a function of the supersaturation) of a plate in the shape of a parabolic cylinder growing under carbon diffusion control.
Language: | FORTRAN |
Product form: | Source code |
A fitted polynomial is used to approximate the relationship between the Peclet number p and the supersaturation Omega for a plate in the shape of a parabolic cylinder growing under carbon diffusion control [1]:
where x[gamma alpha] is the carbon concentration in the austenite, rhoc is the critical plate-tip radius (for zero growth rate), and S2 is a function of p displayed graphically in Trivedi's original paper [1].
The plate tip radius rho is also approximated from a solution given by Trivedi, and hence the growth rate G is calculated using :-
where D is the weighted average coefficient [2] of carbon for austenite between the mean alloy composition and the capillarity-affected tip radius carbon concentration [3, 4].
The fit deteriorates for large OMEGA, and the program terminates if OMEGA is greater than 0.995.
If ps represents the series approximation of the Peclet number, and pa is the true solution to Trivedi's equation, the error in the approximation of the Peclet number is given by:-
Called by the routine MAP_STEEL_MICRO.
DOUBLE PRECISION XMAX, XBAR, DCOEFFW, TCC, RADIUS, G, & C(6), C0, PI, R INTEGER J INCLUDE 'map_constants_pi.f' INCLUDE 'map_constants_gas.f' DATA (C(J), J=1,6)/-20.15, 174.0, -562.3, 912.4, -732.9, 232.4/ C0 = -1.8756 READ (5,*) XMAX, XBAR, DCOEFFW READ (5,*) TCC, RADIUS CALL MAP_STEEL_TRIVSOL(XMAX, XBAR, DCOEFFW, TCC, RADIUS, & G, C, C0, PI, R) WRITE (6,10) G 10 FORMAT ('Plate growth velocity = ',D13.5,' m/s') STOP END
0.39994D-01 0.11871D-01 0.21860D-08
Plate growth velocity = 0.63712D-05 m/s
Trivedi, carbon, diffusion, plate, growth rate, carbon diffusion control, supersaturation
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
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