H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.
Uses a finite difference method for the solution of the problem of X enrichment during the ageing of bainitic steels.
Complete program.
Language: | FORTRAN |
Product form: | Source code |
When cementite first forms in bainite or martensite, it grows by a paraequilibrium transformation mechanism, so substitutional solutes (such as chromium or manganese) do not partition during growth. The cementite therefore has a non-equilibrium composition when it first forms. In fact, the ratio of iron to X (substitutional solute) in the cementite is the same as that in the parent phase.
Since the cementite is not at equilibrium due to the slow diffusivity of X at low temperatures, there will be a tendency for solute to partition between the the cementite and matrix over time. MAP_STEEL_FINN calculates this redistribution by diffusion.
MAP_STEEL_FINN differs from MAP_STEEL_FINITE in reading in data on the normalised concentrations of X at the ferrite surface and the cementite surface for time not equal to zero.
Name | Type | Description |
---|---|---|
KTEMP | real | absolute temperature (in kelvin). |
EQFER | real | equilibrium weight percent of X in ferrite at the ageing temperature. |
EQCEM | real | equilibrium weight percent of X in cementite at the ageing temperature. |
EBAR | real | average weight percent of X in the alloy. |
TFER | real | thickness of ferrite (in metres). |
TCEM | real | thickness of cementite (in metres). |
J1 | integer | number of finite time increments. |
IFER | integer | number of finite dimension slices for ferrite. |
ICEM | integer | number of finite dimension slices for cementite. |
TIMH | real | time (in hours). |
IFER2 | integer | refers to number of slices for ferrite from previous run. |
ICEM2 | integer | refers to number of slices for cementite from previous run. |
J4,J5 | integers | related to the soft impingement detection subroutine. |
FREQ | real | pre-exponential factor for the diffusion coefficient. |
Q | real | activation free energy for the diffusion coefficient. |
JTEST | integer | adjusts mass balance condition once cementite has achieved its equilibrium condition at its surface. |
CFER | real array of dimension 1500 x 2. | CFER(x,1) is initial normalised ferrite concentration for slice h, where h is <=IFER2. |
CCEM | real array of dimension 20 x 2. | CCEM(x,1) is initial normalised cementite concentration for slice h, where h <=ICEM2. |
Name | Type | Description |
---|---|---|
CFER | real array of dimension 1500 x 2. | CFER(x,1) is final normalised ferrite concentration for slice h, where h<=IFER. |
CCEM | real array of dimension 20 x 2. | CCEM(x,2) is final normalised cementite concentration for slice h, where h<=ICEM. |
DFER | real | diffusion coefficient in ferrite, in m2s-1 |
DCEM | real | diffusion coefficient in cementite, in m2s-1 |
STFER | real | thickness per slice of ferrite, in m. |
STCEM | real | thickness per slice of cementite, in m. |
None.
No information supplied.
None.
Complete program
838.15 0.5D-03 39.0D+00 2.5D+00 1.0D-07 2.0D-06 1000 5 0.0003D+00 2.0D+00 43.2 6 5 2 2 2.53D-04 240580 0 1 0.7012D+01 (Cementite) 2 0.6998D+01 3 0.6988D+01 4 0.6983D+01 Slice number, normalised conc. 5 0.6982D+01 1 0.2205D-01 (Ferrite) 2 0.4387D-01 3 0.6565D-01 4 0.8737D-01 5 0.1090D+00 6 0.1306D+00
Diffusion coefficient in ferrite, m**2/s = 0.2570D-18 Diffusion coefficient in cementite, m**2/s, = 0.2570D-18 Half thickness of ferrite, m = 0.2000D-05 Thickness of cementite, m = 0.1000D-06 Eq. conc. of X at interface, in ferrite, wt.% = 0.5000D-03 Eq. conc. of X at interface, in cementite, wt.% = 0.3900D+02 Absolute Temperature = 838.15 ICEM, IFER = 5 200 STCEM (m) = 0.1000D-07 STFER (m) = 0.1000D-07 Time 0, slice 1, cementite and ferrite norm conc 7.0120 0.0221 HOURS CEM FERRITE AVERAGE X FERS CEMS 47.5 19.8213 2.3745 2.8000 0.0005 20.0940 51.8 21.6400 2.3304 2.8014 0.0005 21.8438 56.1 23.0851 2.2954 2.8025 0.0005 23.2546 60.5 24.3204 2.2655 2.8035 0.0005 24.4684 64.8 25.4169 2.2390 2.8043 0.0005 25.5499 69.1 26.4128 2.2149 2.8051 0.0005 26.5347 73.4 27.3316 2.1927 2.8059 0.0005 27.4447 77.8 28.1889 2.1720 2.8065 0.0005 28.2949 82.1 28.9954 2.1525 2.8072 0.0005 29.0955 86.4 29.7594 2.1340 2.8078 0.0005 29.8545 No Norm. Conc. wt.%X in Cementite 1 0.1192D+02 29.8079 2 0.1191D+02 29.7725 3 0.1190D+02 29.7482 4 0.1189D+02 29.7352 5 0.1189D+02 29.7333 No Norm. Conc. wt.%X in Ferrite 1 0.2180D-01 0.0545 2 0.4338D-01 0.1085 3 0.6492D-01 0.1623 4 0.8639D-01 0.2160 5 0.1078D+00 0.2695 6 0.1291D+00 0.3228 7 0.1503D+00 0.3758 8 0.1714D+00 0.4286 9 0.1924D+00 0.4810 10 0.2132D+00 0.5330 11 0.2339D+00 0.5846 12 0.2543D+00 0.6358 13 0.2746D+00 0.6865 14 0.2947D+00 0.7368 15 0.3146D+00 0.7865 16 0.3342D+00 0.8356 17 0.3537D+00 0.8841 18 0.3728D+00 0.9321 19 0.3917D+00 0.9793 20 0.4104D+00 1.0260 21 0.4287D+00 1.0719 22 0.4468D+00 1.1171 23 0.4646D+00 1.1616 24 0.4821D+00 1.2053 25 0.4993D+00 1.2482 26 0.5162D+00 1.2904 27 0.5327D+00 1.3317 28 0.5489D+00 1.3723 29 0.5648D+00 1.4120 30 0.5804D+00 1.4509 31 0.5956D+00 1.4889 32 0.6104D+00 1.5261 33 0.6250D+00 1.5624 34 0.6391D+00 1.5979 35 0.6530D+00 1.6325 36 0.6665D+00 1.6662 37 0.6796D+00 1.6990 38 0.6924D+00 1.7310 39 0.7048D+00 1.7621 40 0.7169D+00 1.7923 41 0.7287D+00 1.8217 42 0.7401D+00 1.8502 43 0.7511D+00 1.8778 44 0.7619D+00 1.9046 45 0.7722D+00 1.9306 46 0.7823D+00 1.9558 47 0.7920D+00 1.9801 48 0.8014D+00 2.0036 49 0.8105D+00 2.0263 50 0.8193D+00 2.0482 51 0.8278D+00 2.0694 52 0.8359D+00 2.0898 53 0.8438D+00 2.1094 54 0.8513D+00 2.1284 55 0.8586D+00 2.1466 56 0.8656D+00 2.1641 57 0.8724D+00 2.1809 58 0.8788D+00 2.1970 59 0.8850D+00 2.2125 60 0.8910D+00 2.2274 61 0.8967D+00 2.2416 62 0.9021D+00 2.2553 63 0.9073D+00 2.2683 64 0.9123D+00 2.2808 65 0.9171D+00 2.2927 66 0.9216D+00 2.3041 67 0.9260D+00 2.3150 68 0.9301D+00 2.3253 69 0.9341D+00 2.3352 70 0.9379D+00 2.3446 71 0.9414D+00 2.3536 72 0.9448D+00 2.3621 73 0.9481D+00 2.3702 74 0.9512D+00 2.3779 75 0.9541D+00 2.3852 76 0.9569D+00 2.3921 77 0.9595D+00 2.3987 78 0.9620D+00 2.4049 79 0.9643D+00 2.4108 80 0.9666D+00 2.4164 81 0.9687D+00 2.4217 82 0.9707D+00 2.4267 83 0.9725D+00 2.4314 84 0.9743D+00 2.4358 85 0.9760D+00 2.4400 86 0.9776D+00 2.4439 87 0.9791D+00 2.4477 88 0.9805D+00 2.4512 89 0.9818D+00 2.4545 90 0.9830D+00 2.4576 91 0.9842D+00 2.4605 92 0.9853D+00 2.4632 93 0.9863D+00 2.4658 94 0.9873D+00 2.4682 95 0.9882D+00 2.4704 96 0.9890D+00 2.4725 97 0.9898D+00 2.4745 98 0.9905D+00 2.4763 99 0.9912D+00 2.4781 100 0.9919D+00 2.4797 101 0.9925D+00 2.4812 102 0.9930D+00 2.4826 103 0.9935D+00 2.4839 104 0.9940D+00 2.4851 105 0.9945D+00 2.4862 106 0.9949D+00 2.4873 107 0.9953D+00 2.4883 108 0.9957D+00 2.4892 109 0.9960D+00 2.4900 110 0.9963D+00 2.4908 111 0.9966D+00 2.4915 112 0.9969D+00 2.4922 113 0.9971D+00 2.4928 114 0.9974D+00 2.4934 115 0.9976D+00 2.4939 116 0.9978D+00 2.4944 117 0.9980D+00 2.4949 118 0.9981D+00 2.4953 119 0.9983D+00 2.4957 120 0.9984D+00 2.4961 121 0.9986D+00 2.4964 122 0.9987D+00 2.4967 123 0.9988D+00 2.4970 124 0.9989D+00 2.4973 125 0.9990D+00 2.4975
None.
finite differences, enrichment, bainite ageing
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
MAP Website administration / map@msm.cam.ac.uk