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  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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To estimate the Charpy toughness of steel welds (manual metal arc or submerged arc), as a function of strength, microstructure, chemical composition and temperature over a limited range of inputs as stated in [1].

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Product form:Source code

DOUBLE PRECISION X(100), W1(10,100), W2(10),THETA1(100), H(10),
& AMIN(15),AMAX(15)

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MAP_NEURAL_WELD_TOUGHNESS is an interactive program which uses the results of a neural network training process to permit the estimation of the Charpy impact toughness for manual metal arc and submerged arc weld metal samples. This is as a function of the following variables, within the stated ranges:-

Process, submerged arc (0.5) or manual metal arc (-0.5)

Parameter Minimum Maximum
Yield strength /MPa 0.3470D+03 0.6450D+03
Carbon /wt% 0.2900D-01 0.1300D+00
Silicon/wt% 0.2800D+00 0.1140D+01
Manganese/wt% 0.7700D+00 0.2250D+01
Phosphorus/wt% 0.8000D-02 0.2800D-01
Sulphur/wt% 0.2000D-02 0.1700D-01
Aluminium/wt% 0.1000D-02 0.4000D-01
Nitrogen/ppmw 0.2600D+02 0.1190D+03
Oxygen/ppmw 0.2340D+03 0.8210D+03
Primary microstructure/% 0.0000D+00 0.9100D+02
Allotriomorphic ferrite/% 0.1600D+02 0.6200D+02
Acicular ferrite/% 0.1100D+02 0.8100D+02
Temperature / K 0.2130D+03 0.2930D+03
Charpy toughness / J 4.00 215.0

The program uses the file "WEIGHTS" to obtain the neural network training information.

The data that were used originally to train the neural network are also available under the section entitled Materials Data (Weld Toughness Data).

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  1. H. K. D. H. Bhadeshia, D. J. C. MacKay and L.-E. Svensson, Materials Science and Technology, 11, 1995, 1046-1051.

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Input parameters

X - real array of dimension 100
X contains the normalized values of the input variables.

W1 - real array of dimension (10,100)
W1 contains weights read in from file "WEIGHTS".

W2 - real array of dimension 10
W2 contains weights read in from file "WEIGHTS".

THETA1 - real array of dimension 100
THETA1 contains biases read in from file "WEIGHTS".

H - real array of dimension 10
H contains a part of the transfer function.

AMIN - real array of dimension 15
AMIN contains the minimum value of the variable in the experimental dataset used to develop the model.

AMAX - real array of dimension 15
AMAX contains the maximum value of the variable in the experimental dataset used to develop the model.

Output parameters

The program gives the Charpy toughness value in Joules. Output is to STDOUT.

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Error Indicators


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The full calculation of the error bars as presented in [1] is not reproduced in this program. An average error of ± 40 J may be assumed reasonable but will not be reliable in all cases.

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Further Comments


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1. Program text

       Complete program.

2. Program data

           PROCESS (-0.5 for MMA, 0.5 for Submerged Arc)?
           Yield Strength at 20 Centigrade, MPa  (347-645)?
           Carbon, wt.% (0.029-0.130)?
           Silicon, wt.% (0.28-1.14)?
           Manganese, wt.% (0.77-2.50) ?
           Phosphorus, wt.% (0.008-0.028)?
           Sulphur, wt.% (0.002-0.017)?
           Aluminium, wt.% (0.001-0.040)?
           Nitrogen, ppmw (26-119)?
           Oxygen, ppmw (234-821)?
           Primary Microstructure % (0-91)?
           Allotriomorphic Ferrite % (16-62)?
           Acicular Ferrite %(11-81)?
           Temperature, Centigrade (-60 to 20) ?

3. Program results

                          ** WELD CHARPY TOUGHNESS **           

                    Darwin College, Cambridge & ESAB AB (Sweden)
                           Bhadeshia, Svensson & MacKay      

           Process        0.5                Yield Strength       450.  MPa 
           Carbon       0.100  wt.%          Silicon            0.400  wt.%
           Manganese    0.900  wt.%          Phosphorus         0.008  wt.%
           Sulphur      0.005  wt.%          Aluminium          0.010  wt.%
           Nitrogen       50.  ppmw          Oxygen              300.  ppmw
           Primary        20.  %             Allotriomorphic      54.  %   
           Acicular       40.  %             Temperature          20.  C   

           Charpy Toughness, Joules =     121.

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Auxiliary Routines


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neural network, weld toughness

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Download source code

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MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

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