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C.Garcia de Andres and C.Capdevila-Montes,
CENIM-CSIC,
Departamento de Metalurgia Fisica,
Avda. Gregorio del Amo 8,
Madrid 28040
Spain
H.K.D.H. Bhadeshia and S.S Babu*,
Phase Transformations Group,
Department of Materials Science and Metallurgy
University of Cambridge
Cambridge CB23QZ
*Dr Suresh Babu is now with the Oak Ridge National Laboratory, Oak Ridge, TN, USA
Uses a finite difference method for the solution of the problem of the diffusion profile collapse during heat treatment at temperature T.
Complete program
| Language: | FORTRAN |
| Product form: | Source code |
The carbon composition profile build up ahead of the allotriomorphic ferrite/austenite interface in the residual austenite, is examined here using a finite difference method to stimulate any homogenisation of concentration. The main advantage of the application of finite difference method to this problem is that it can handle the changing boundary conditions during the homogenisation process.
The finite difference method is based on the technique discussed by Crank [6]. The model assumes one dimensional diffusion process ahead of a planar allotriomorphic-austenite interface. The initial profile set up at time t=0.0, is given by analytical equation calculated by Coates [3,4,5]. The composition profile is then subjected to finite difference method after normalising the variables to dimensionless quantities suitable for this method.
a) Output to the screen:
b) Output to the OUT file:
None.
A good accuracy is maintained if NSLI is higher than 200 slices.
The coefficient R=D*t/x**2 of the general finite difference equation described by Cranck [3,4,5] is taken to be 0.1. This particular value was assumed after checking that variation of R coefficient from 0.1 - 0.3 made negligible difference to the results.
Complete program.
0.053 0.510 1.410 0.030 0.010 1.59 0.000 0.000 0.000 0.000 0.000 70 600 120 0.1e-02 10 470 Chemical composition C,Si,Mn,Ni,Mo,Cr,V,Co,Cu,Al,W Prior austenite grain size (in microns) Temperature (in centigrade) Time at this temperature (in seconds) Half-thickness of allotriomorphic ferrite (in centimeters) Time required to form allotriomorphic ferrite of previous half thickness Anealing temperature (in centigrade)
a) Output to STDOUT:
****Chemical composition****
Carbon= .0530 Silicon= .5100
Manganese=1.4100 Nickel= .0300
Molybdenum= .0100 Chromium=1.5900
Vanadium= .0000
****************************************************************
Isothermal temperature= 600.0
Holding time= 120.00
Austenite grain size in microns= 70.00
+++++++Initial Profile Calculation is over+++++++
Area under the normalised curve= .5430652E+03
****************************************************************
/////-Finite difference method starts-/////
INTERFACE CONCENT. TIME
.4578793E-01 .0000000E+00
.4422596E-01 .1962215E-01
.4285907E-01 .6543451E+00
.4164919E-01 .1306012E+01
.4056746E-01 .1971883E+01
.3959168E-01 .2651476E+01
.3870459E-01 .3343907E+01
.3789258E-01 .4044720E+01
.3714478E-01 .4758699E+01
.3645246E-01 .5480714E+01
.3580847E-01 .6211984E+01
.3520693E-01 .6950158E+01
.3464294E-01 .7696216E+01
.3411238E-01 .8451103E+01
.3361178E-01 .9211989E+01
.3313815E-01 .9979625E+01
.3268895E-01 .1075474E+02
.3226195E-01 .1153805E+02
.3185522E-01 .1232622E+02
.3146707E-01 .1311980E+02
.3109601E-01 .1391933E+02
.3074072E-01 .1472533E+02
.3040001E-01 .1553403E+02
.3007286E-01 .1634583E+02
.2975830E-01 .1716550E+02
.2945549E-01 .1798906E+02
.2916366E-01 .1881689E+02
.2888212E-01 .1964934E+02
.2861023E-01 .2048677E+02
.2834743E-01 .2132484E+02
.2809317E-01 .2216853E+02
.2784697E-01 .2301816E+02
.2760840E-01 .2386924E+02
.2737704E-01 .2472199E+02
.2715251E-01 .2558157E+02
.2693446E-01 .2644331E+02
.2672258E-01 .2730742E+02
.2651655E-01 .2817413E+02
.2631609E-01 .2904364E+02
.2612095E-01 .2991615E+02
.2593089E-01 .3079189E+02
.2574567E-01 .3167104E+02
.2556508E-01 .3255380E+02
.2538892E-01 .3344039E+02
.2521701E-01 .3433099E+02
.2504917E-01 .3522035E+02
.2488523E-01 .3611407E+02
.2472503E-01 .3701233E+02
.2456844E-01 .3790974E+02
.2441530E-01 .3881203E+02
.2426550E-01 .3971372E+02
.2411890E-01 .4062061E+02
.2397538E-01 .4152714E+02
.2383485E-01 .4243919E+02
.2369718E-01 .4335110E+02
.2356228E-01 .4426886E+02
.2343006E-01 .4518671E+02
.2330042E-01 .4610474E+02
.2317327E-01 .4702307E+02
.2304855E-01 .4794780E+02
.2292615E-01 .4887303E+02
.2280602E-01 .4979885E+02
.2268808E-01 .5072536E+02
.2257227E-01 .5165884E+02
.2245851E-01 .5259321E+02
.2234674E-01 .5352856E+02
.2223691E-01 .5446498E+02
.2212896E-01 .5540256E+02
.2202283E-01 .5634137E+02
.2191847E-01 .5728152E+02
.2181583E-01 .5822307E+02
.2171486E-01 .5916611E+02
.2161552E-01 .6011073E+02
.2151776E-01 .6105701E+02
.2142154E-01 .6200502E+02
.2132681E-01 .6295486E+02
.2123355E-01 .6390659E+02
.2114170E-01 .6486031E+02
.2105123E-01 .6581608E+02
.2096212E-01 .6677400E+02
.2087431E-01 .6773413E+02
.2078779E-01 .6869656E+02
.2070251E-01 .6966136E+02
.2061846E-01 .7062169E+02
.2053559E-01 .7158451E+02
.2045388E-01 .7254989E+02
.2037331E-01 .7351791E+02
.2029384E-01 .7448866E+02
.2021545E-01 .7546221E+02
.2013812E-01 .7643149E+02
.2006182E-01 .7740368E+02
.1998652E-01 .7837885E+02
.1991221E-01 .7935708E+02
.1983887E-01 .8033118E+02
.1976647E-01 .8130844E+02
.1969499E-01 .8228894E+02
.1962441E-01 .8327276E+02
.1955471E-01 .8425256E+02
.1948588E-01 .8523578E+02
.1941790E-01 .8622250E+02
.1935074E-01 .8720529E+02
.1928440E-01 .8819168E+02
.1921885E-01 .8918174E+02
.1915408E-01 .9016796E+02
.1909007E-01 .9115796E+02
.1902681E-01 .9215180E+02
.1896428E-01 .9314187E+02
.1890247E-01 .9413590E+02
.1884137E-01 .9512621E+02
.1878096E-01 .9612056E+02
.1872122E-01 .9711904E+02
.1866215E-01 .9811388E+02
.1860374E-01 .9911293E+02
.1854596E-01 .1001084E+03
.1848882E-01 .1011082E+03
.1843229E-01 .1021123E+03
.1837636E-01 .1031130E+03
.1832103E-01 .1041181E+03
.1826629E-01 .1051198E+03
.1821212E-01 .1061260E+03
.1815851E-01 .1071288E+03
.1810546E-01 .1081363E+03
.1805295E-01 .1091404E+03
.1800098E-01 .1101493E+03
.1794953E-01 .1111548E+03
.1789860E-01 .1121652E+03
.1784817E-01 .1131805E+03
.1779825E-01 .1141925E+03
.1774882E-01 .1152096E+03
.1769987E-01 .1162234E+03
.1765139E-01 .1172424E+03
.1760339E-01 .1182581E+03
.1755584E-01 .1192707E+03
.1750874E-01 .1202884E+03
b) Output to file out:
Profile corresponding at time of 21.32 seconds
INTERFACE CONCENTRATION DISTANCE (cm)
.2834743E-01 .1000000E-02
.2204003E-01 .1083333E-02
.1524192E-01 .1166667E-02
.9650050E-02 .1250000E-02
.5939514E-02 .1333333E-02
.3898470E-02 .1416667E-02
.2951983E-02 .1500000E-02
.2577544E-02 .1583333E-02
.2450031E-02 .1666667E-02
.2412389E-02 .1750000E-02
.2402702E-02 .1833333E-02
.2400520E-02 .1916667E-02
.2400089E-02 .2000000E-02
.2400013E-02 .2083333E-02
.2400002E-02 .2166667E-02
.2400000E-02 .2250000E-02
.2400000E-02 .2333333E-02
.2400000E-02 .2416667E-02
.2400000E-02 .2500000E-02
.2400000E-02 .2583333E-02
.2400000E-02 .2666667E-02
.2400000E-02 .2750000E-02
.2400000E-02 .2833333E-02
.2400000E-02 .2916667E-02
.2400000E-02 .3000000E-02
.2400000E-02 .3083333E-02
.2400000E-02 .3166667E-02
.2400000E-02 .3250000E-02
.2400000E-02 .3333333E-02
.2400000E-02 .3416667E-02
Subroutines:
MAP_STEEL_DIFFUS
Functions:
MAP_STEEL_AFEG
MAP_STEEL_CG
MAP_STEEL_DAFEG
MAP_STEEL_DCG
MAP_STEEL_XALPH
finite difference, allotriomorphic ferrite, profile collapse
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
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