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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.
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