C.Capdevila-Montes and C.Garcia de Andres,
Departamento de Metalurgia Fisica,
Centro Nacional de Investigaciones Metalurgicas-
Consejo Superior de Investigaciones Cientificas,
Avenida Gregorio del Amo 8,
28040 Madrid Spain
H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.
Uses the the Gilmour et al approximation but with an analytical treatment (for alpha formation under NPLE mechanism) of the soft impingement problem in Fe-C-X alloys.
Complete Program.
Language: | FORTRAN |
Product form: | Source code |
The following calculations deal with the one-dimensional growth of planar grain boundary allotriomorphs from opposite side of grain.
This process may be considered in two stages: the first involves parabolic growth from both sides according to the earlier exact calculations; during the second stage of inmpingment, the driving force due to the carbon activity gradient is gradually reduced and the transformation rate correspondingly decreases to a value consistent with a uniform and equal carbon chemical potential in both phases [1].
The concentration of carbon in the middle of the austenite grain size is calculated by means of balancing the amount of carbon enrichment of the austenite against the carbon depletion of the ferrite [2]. At fixed time and temeprature, it is possible to study the volume fraction of pearlite formed. The pearlite appears when the carbon concentration in remaining austenite enriches the carbon concentration of the extrapolated tie-line austenite/austenite + cementite at this temperature [3], and when the moving interface is slower than maximum rate to allow nucleation in the interface [4].
All output is to STDOUT.
None.
If holding time at temperature close to Ae3 is higher than 10000 seconds, a problem with the convergence of data is obtained.
The nucleation time is incorporated according to [5-6], the effect of different alloying elements is taken into account.
The interface energy for nucleation of cementite in a moving interface is calculated according to [7-9].
Complete program.
0.37 0.56 1.45 0.000 0.025 0.04 0.110 0.000 0.140 0.020 0.000 70 640 1200 40
****Chemical composition**** Carbon=0.3700 Silicon=0.5600 Manganese=1.4500 Nickel=0.0000 Molibdenon=0.0250 Cromium=0.0400 Vanadium=0.1100 ********************************************************************* Isothermal temperature= 640.0 Holding time=1200.00 Austenite grain size ,in microns= 70.00 TIMESTEP in calculations= 10.00 C-C interaction energy in austenite in J/mol=8394.418 C-C interaction energy in ferrite in J/mol= 48570.000 ~~~~~~~MOLE FRACTION~~~~~~~~ Mole fraction of C in austenite=0.01680 Concentration of carbon in alfa/gama interface into ferrite=0.00074 Concentration of carbon in alfa/gama interface into austenite=0.04039958 ~~~~~WEIGHT PERCENTAGE~~~~~~ Carbon concentration of carbon at the bulk=0.37000 Concentration of carbon in alpha/gamma interface into austenite=0.90232597 Concentration of carbon in alpha/gamma interface into ferrite=0.01596 <<<<<< CRITICAL TEMPERATURES >>>>>> Ae3 temperature (C)= 726.85 Ae1 temperature (C)= 656.85 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ C diffusion coefficient into austenite(cm**/s)= 0.12011E-08 Parabolic-thickening rate constant (3-D) in cm/s**(1/2) = 0.10603E-03 Parabolic-thickening rate constant (1-D) in cm/s**(1/2) = 0.48376E-04 Half-thickness of the layer of ferrite in cm. NO INMPINGMENT = 0.16758E-02 Impingement began at 0.146436E-02 Maximum half-thickness in Fe-C system = 0.251849E-02 Maximum half-thickness in this system = 0.206482E-02 Time for nucleation = 25.71 seconds Time(s) Z-imp.(cm) Z-para.(cm) CL (%wt) Vol.Frac Migration Rate(m/s) ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ********Parabolic Growth******** 0.00 0.0000E+00 0.0000E+00 0.3700E+00 0.0000E+00 0.0000E+00 10.00 0.0000E+00 0.0000E+00 0.3700E+00 0.0000E+00 0.0000E+00 20.00 0.0000E+00 0.0000E+00 0.3700E+00 0.0000E+00 0.0000E+00 30.00 0.1002E-03 0.1002E-03 0.3700E+00 0.2864E-01 0.1167E-06 40.00 0.1829E-03 0.1829E-03 0.3700E+00 0.5226E-01 0.6398E-07 50.00 0.2384E-03 0.2384E-03 0.3700E+00 0.6813E-01 0.4907E-07 60.00 0.2833E-03 0.2833E-03 0.3700E+00 0.8094E-01 0.4130E-07 70.00 0.3220E-03 0.3220E-03 0.3700E+00 0.9199E-01 0.3634E-07 80.00 0.3565E-03 0.3565E-03 0.3700E+00 0.1018E+00 0.3283E-07 90.00 0.3879E-03 0.3879E-03 0.3700E+00 0.1108E+00 0.3017E-07 100.00 0.4170E-03 0.4170E-03 0.3700E+00 0.1191E+00 0.2806E-07 110.00 0.4441E-03 0.4441E-03 0.3700E+00 0.1269E+00 0.2634E-07 120.00 0.4698E-03 0.4698E-03 0.3700E+00 0.1342E+00 0.2491E-07 130.00 0.4940E-03 0.4940E-03 0.3700E+00 0.1412E+00 0.2368E-07 140.00 0.5172E-03 0.5172E-03 0.3700E+00 0.1478E+00 0.2262E-07 150.00 0.5393E-03 0.5393E-03 0.3700E+00 0.1541E+00 0.2170E-07 160.00 0.5606E-03 0.5606E-03 0.3700E+00 0.1602E+00 0.2087E-07 170.00 0.5811E-03 0.5811E-03 0.3700E+00 0.1660E+00 0.2014E-07 180.00 0.6009E-03 0.6009E-03 0.3700E+00 0.1717E+00 0.1947E-07 190.00 0.6201E-03 0.6201E-03 0.3700E+00 0.1772E+00 0.1887E-07 200.00 0.6387E-03 0.6387E-03 0.3700E+00 0.1825E+00 0.1832E-07 210.00 0.6567E-03 0.6567E-03 0.3700E+00 0.1876E+00 0.1782E-07 220.00 0.6743E-03 0.6743E-03 0.3700E+00 0.1927E+00 0.1735E-07 230.00 0.6914E-03 0.6914E-03 0.3700E+00 0.1976E+00 0.1692E-07 240.00 0.7082E-03 0.7082E-03 0.3700E+00 0.2023E+00 0.1652E-07 250.00 0.7245E-03 0.7245E-03 0.3700E+00 0.2070E+00 0.1615E-07 260.00 0.7405E-03 0.7405E-03 0.3700E+00 0.2116E+00 0.1580E-07 270.00 0.7561E-03 0.7561E-03 0.3700E+00 0.2160E+00 0.1548E-07 280.00 0.7714E-03 0.7714E-03 0.3700E+00 0.2204E+00 0.1517E-07 290.00 0.7864E-03 0.7864E-03 0.3700E+00 0.2247E+00 0.1488E-07 300.00 0.8012E-03 0.8012E-03 0.3700E+00 0.2289E+00 0.1460E-07 310.00 0.8157E-03 0.8157E-03 0.3700E+00 0.2330E+00 0.1435E-07 320.00 0.8299E-03 0.8299E-03 0.3700E+00 0.2371E+00 0.1410E-07 330.00 0.8439E-03 0.8439E-03 0.3700E+00 0.2411E+00 0.1387E-07 340.00 0.8576E-03 0.8576E-03 0.3700E+00 0.2450E+00 0.1364E-07 350.00 0.8712E-03 0.8712E-03 0.3700E+00 0.2489E+00 0.1343E-07 360.00 0.8845E-03 0.8845E-03 0.3700E+00 0.2527E+00 0.1323E-07 370.00 0.8976E-03 0.8976E-03 0.3700E+00 0.2565E+00 0.1304E-07 380.00 0.9106E-03 0.9106E-03 0.3700E+00 0.2602E+00 0.1285E-07 390.00 0.9233E-03 0.9233E-03 0.3700E+00 0.2638E+00 0.1267E-07 400.00 0.9359E-03 0.9359E-03 0.3700E+00 0.2674E+00 0.1250E-07 410.00 0.9483E-03 0.9483E-03 0.3700E+00 0.2710E+00 0.1234E-07 420.00 0.9606E-03 0.9606E-03 0.3700E+00 0.2745E+00 0.1218E-07 430.00 0.9727E-03 0.9727E-03 0.3700E+00 0.2779E+00 0.1203E-07 440.00 0.9846E-03 0.9846E-03 0.3700E+00 0.2813E+00 0.1188E-07 450.00 0.9965E-03 0.9965E-03 0.3700E+00 0.2847E+00 0.1174E-07 460.00 0.1008E-02 0.1008E-02 0.3700E+00 0.2880E+00 0.1161E-07 470.00 0.1020E-02 0.1020E-02 0.3700E+00 0.2913E+00 0.1148E-07 480.00 0.1031E-02 0.1031E-02 0.3700E+00 0.2946E+00 0.1135E-07 490.00 0.1042E-02 0.1042E-02 0.3700E+00 0.2978E+00 0.1123E-07 500.00 0.1054E-02 0.1054E-02 0.3700E+00 0.3010E+00 0.1111E-07 510.00 0.1065E-02 0.1065E-02 0.3700E+00 0.3042E+00 0.1099E-07 520.00 0.1076E-02 0.1076E-02 0.3700E+00 0.3073E+00 0.1088E-07 530.00 0.1086E-02 0.1086E-02 0.3700E+00 0.3104E+00 0.1077E-07 540.00 0.1097E-02 0.1097E-02 0.3700E+00 0.3134E+00 0.1067E-07 550.00 0.1108E-02 0.1108E-02 0.3700E+00 0.3165E+00 0.1056E-07 560.00 0.1118E-02 0.1118E-02 0.3700E+00 0.3195E+00 0.1046E-07 570.00 0.1129E-02 0.1129E-02 0.3700E+00 0.3225E+00 0.1037E-07 580.00 0.1139E-02 0.1139E-02 0.3700E+00 0.3254E+00 0.1027E-07 590.00 0.1149E-02 0.1149E-02 0.3700E+00 0.3283E+00 0.1018E-07 600.00 0.1159E-02 0.1159E-02 0.3700E+00 0.3312E+00 0.1009E-07 610.00 0.1169E-02 0.1169E-02 0.3700E+00 0.3341E+00 0.1001E-07 620.00 0.1179E-02 0.1179E-02 0.3700E+00 0.3369E+00 0.9922E-08 630.00 0.1189E-02 0.1189E-02 0.3700E+00 0.3398E+00 0.9839E-08 640.00 0.1199E-02 0.1199E-02 0.3700E+00 0.3426E+00 0.9759E-08 650.00 0.1209E-02 0.1209E-02 0.3700E+00 0.3453E+00 0.9681E-08 660.00 0.1218E-02 0.1218E-02 0.3700E+00 0.3481E+00 0.9604E-08 670.00 0.1228E-02 0.1228E-02 0.3700E+00 0.3508E+00 0.9529E-08 680.00 0.1237E-02 0.1237E-02 0.3700E+00 0.3535E+00 0.9456E-08 690.00 0.1247E-02 0.1247E-02 0.3700E+00 0.3562E+00 0.9385E-08 700.00 0.1256E-02 0.1256E-02 0.3700E+00 0.3589E+00 0.9315E-08 710.00 0.1265E-02 0.1265E-02 0.3700E+00 0.3616E+00 0.9246E-08 720.00 0.1275E-02 0.1275E-02 0.3700E+00 0.3642E+00 0.9180E-08 730.00 0.1284E-02 0.1284E-02 0.3700E+00 0.3668E+00 0.9114E-08 740.00 0.1293E-02 0.1293E-02 0.3700E+00 0.3694E+00 0.9050E-08 750.00 0.1302E-02 0.1302E-02 0.3700E+00 0.3720E+00 0.8988E-08 760.00 0.1311E-02 0.1311E-02 0.3700E+00 0.3745E+00 0.8926E-08 770.00 0.1320E-02 0.1320E-02 0.3700E+00 0.3771E+00 0.8866E-08 780.00 0.1329E-02 0.1329E-02 0.3700E+00 0.3796E+00 0.8807E-08 790.00 0.1337E-02 0.1337E-02 0.3700E+00 0.3821E+00 0.8749E-08 800.00 0.1346E-02 0.1346E-02 0.3700E+00 0.3846E+00 0.8692E-08 810.00 0.1355E-02 0.1355E-02 0.3700E+00 0.3871E+00 0.8637E-08 820.00 0.1363E-02 0.1363E-02 0.3700E+00 0.3895E+00 0.8582E-08 830.00 0.1372E-02 0.1372E-02 0.3700E+00 0.3920E+00 0.8529E-08 840.00 0.1380E-02 0.1380E-02 0.3700E+00 0.3944E+00 0.8476E-08 850.00 0.1389E-02 0.1389E-02 0.3700E+00 0.3968E+00 0.8425E-08 860.00 0.1397E-02 0.1397E-02 0.3700E+00 0.3992E+00 0.8374E-08 870.00 0.1406E-02 0.1406E-02 0.3700E+00 0.4016E+00 0.8324E-08 880.00 0.1414E-02 0.1414E-02 0.3700E+00 0.4040E+00 0.8275E-08 890.00 0.1422E-02 0.1422E-02 0.3700E+00 0.4063E+00 0.8227E-08 900.00 0.1430E-02 0.1430E-02 0.3700E+00 0.4087E+00 0.8180E-08 910.00 0.1439E-02 0.1439E-02 0.3700E+00 0.4110E+00 0.8134E-08 920.00 0.1447E-02 0.1447E-02 0.3700E+00 0.4133E+00 0.8088E-08 930.00 0.1455E-02 0.1455E-02 0.3700E+00 0.4156E+00 0.8043E-08 940.00 0.1463E-02 0.1463E-02 0.3700E+00 0.4179E+00 0.7999E-08 ********Impingement begins******** 950.00 0.1463E-02 0.1471E-02 0.3700E+00 0.4179E+00 0.4983E-08 960.00 0.1469E-02 0.1479E-02 0.3727E+00 0.4196E+00 0.4963E-08 970.00 0.1474E-02 0.1487E-02 0.3764E+00 0.4213E+00 0.4943E-08 980.00 0.1480E-02 0.1494E-02 0.3801E+00 0.4230E+00 0.4922E-08 990.00 0.1486E-02 0.1502E-02 0.3838E+00 0.4246E+00 0.4901E-08 1000.00 0.1492E-02 0.1510E-02 0.3875E+00 0.4263E+00 0.4880E-08 1010.00 0.1498E-02 0.1518E-02 0.3913E+00 0.4280E+00 0.4859E-08 1020.00 0.1504E-02 0.1525E-02 0.3951E+00 0.4296E+00 0.4837E-08 1030.00 0.1510E-02 0.1533E-02 0.3989E+00 0.4313E+00 0.4815E-08 1040.00 0.1515E-02 0.1541E-02 0.4027E+00 0.4330E+00 0.4792E-08 1050.00 0.1521E-02 0.1548E-02 0.4065E+00 0.4346E+00 0.4769E-08 1060.00 0.1527E-02 0.1556E-02 0.4104E+00 0.4363E+00 0.4746E-08 1070.00 0.1533E-02 0.1563E-02 0.4143E+00 0.4379E+00 0.4723E-08 1080.00 0.1539E-02 0.1571E-02 0.4182E+00 0.4396E+00 0.4699E-08 1090.00 0.1544E-02 0.1578E-02 0.4221E+00 0.4413E+00 0.4675E-08 1100.00 0.1550E-02 0.1586E-02 0.4260E+00 0.4429E+00 0.4650E-08 1110.00 0.1556E-02 0.1593E-02 0.4300E+00 0.4446E+00 0.4625E-08 1120.00 0.1562E-02 0.1600E-02 0.4339E+00 0.4462E+00 0.4600E-08 1130.00 0.1568E-02 0.1608E-02 0.4379E+00 0.4479E+00 0.4574E-08 1140.00 0.1573E-02 0.1615E-02 0.4419E+00 0.4495E+00 0.4548E-08 1150.00 0.1579E-02 0.1622E-02 0.4460E+00 0.4512E+00 0.4522E-08 1160.00 0.1585E-02 0.1629E-02 0.4500E+00 0.4528E+00 0.4495E-08 1170.00 0.1591E-02 0.1636E-02 0.4541E+00 0.4544E+00 0.4468E-08 1180.00 0.1596E-02 0.1644E-02 0.4582E+00 0.4561E+00 0.4441E-08 1190.00 0.1602E-02 0.1651E-02 0.4623E+00 0.4577E+00 0.4413E-08 1200.00 0.1608E-02 0.1658E-02 0.4664E+00 0.4594E+00 0.4385E-08 ~~~~~~~~~~~~~~~~~Carbon Profile ahead interface~~~~~~~~~~~~~~~~~~~~~~~~~~ Number of particles per unit area = 0.2810D+11 DALPHA = 0.9399D-05 m DGAMMA = 0.7000D-04 m Isothermal temperature= 640.0 Holding time at this temperature= 40.00 Carbon concen.(%wt) at gamma/theta interf. in austenite= 0.58919E+00 Position of interface at this temperature= 0.18290E-03 Migration rate of alpha/gamma boundary (m/s)= 0.6398E-07 Highest rate of alpha/gamma to allow nucleation (m/s)= 0.5740E-07 Volume fraction of allotromorphic ferrite= 0.52257E-01 Position(cm) C(%wt) Vpearlite Vtot -------------------------------------------------------------- No impingement takes place 0.18290E-03 0.9023E+00 0.0000E+00 0.5226E-01 0.28290E-03 0.6835E+00 0.0000E+00 0.5226E-01 0.38290E-03 0.4647E+00 0.0000E+00 0.5226E-01 0.48290E-03 0.3700E+00 0.0000E+00 0.5226E-01 0.58290E-03 0.3700E+00 0.0000E+00 0.5226E-01 0.68290E-03 0.3700E+00 0.0000E+00 0.5226E-01 0.78290E-03 0.3700E+00 0.0000E+00 0.5226E-01 0.88290E-03 0.3700E+00 0.0000E+00 0.5226E-01 0.98290E-03 0.3700E+00 0.0000E+00 0.5226E-01 0.10829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.11829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.12829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.13829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.14829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.15829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.16829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.17829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.18829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.19829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.20829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.21829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.22829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.23829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.24829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.25829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.26829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.27829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.28829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.29829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.30829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.31829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.32829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.33829E-02 0.3700E+00 0.0000E+00 0.5226E-01 0.34829E-02 0.3700E+00 0.0000E+00 0.5226E-01
Subroutines :-
MAP_STEEL_DIFFUS
MAP_STEEL_GMAAX
Functions :-
MAP_STEEL_CG
MAP_STEEL_DCG
MAP_STEEL_AFEG
MAP_STEEL_DAFEG
MAP_STEEL_XALPH
ferrite growth kinetics, allotriomorphic ferrite, soft impingement
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
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