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Program MAP_STEEL_FINN

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of subroutine's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary subroutines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

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Purpose

Uses a finite difference method for the solution of the problem of X enrichment during the ageing of bainitic steels.

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Specification

Complete program.

Language:FORTRAN
Product form:Source code

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Description

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.

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References

  1. H.K.D.H. Bhadeshia, Materials Science and Technology, 5, (1989), 131-137.

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Parameters

Input parameters

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.

Output parameters

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.

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Error Indicators

None.

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Accuracy

No information supplied.

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Further Comments

None.

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Example

1. Program text

       Complete program

2. Program data

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

3. Program results

 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

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Auxiliary Routines

None.

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Keywords

finite differences, enrichment, bainite ageing

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Download

Download source code

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