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The program, which is NOT available from this site, was produced by
Mark Gibbs and David MacKay,
Cavendish Laboratory,
University of Cambridge,
Madingley Road,
Cambridge, CB3 0HE, U.K.
The data files for use with the program were produced by
F. Tancret and H.K.D.H. Bhadeshia,
Dept. of Material Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.
Added to MAP: August 1999.
An application of the Tpros program for calculating the yield stress of nickel-based superalloys.
The Tpros program is self-contained, but must be downloaded from its own web-site. [Link to Tpros program]
| Language: | C |
| Product form: | Source code and executable files for UNIX/Linux machines. |
The problem we are interested in is that of predicting the yield stress of nickel-based superalloys. This prediction is made as a function of temperature and the elemental composition. The modelling procedure is a purely empirical one; the model is trained on a set of experimental data for which the "outputs" (yield strengths) are known, and creates a kind of non-linear, multi-parameter "regression" of the outputs versus the inputs. This "regression" has already been produced and the model is delivered ready to perform predictions for nickel-based alloys of any desired composition (within certain specified limits). A perusal of the paper by Tancret et al. [1] is strongly recommended before proceeding further. It provides details about the database, the model and its use.
MAP provides a set of data files which can be used with the Tpros program for calculating the yield strength of nickel-based superalloys. The Tpros program itself is not included with this distribution, as we do not maintain it. (We cannot, therefore, be responsible for any failures due to backward compatibility with later versions of Tpros.) The nipros.tar file, which can be downloaded from here, contains the following files:
| h | - | Hyperparameters file. |
| inputs.norm | - | Normalised inputs file (composition and test temperature of alloys in the database). |
| min-max | - | Minimum and maximum values for the wt.% of each element and the temperature (°C) used in the original database. (i.e. the minimum and maximum values of each column in the original database before normalisation.) |
| nipros.man | - | A manual giving further details about running and using the Tpros program for calculating the yield strength. |
| output.norm | - | Normalised yield stress values. |
| paper.rtf | - | A file containing the paper in reference 1 in rtf format. |
| TspecNi | - | Tpros specification file for predictions. |
| unnorm.f | - | A FORTRAN program for un-normalising the output data files. |
These files must be placed in the same directory as the Tpros executable program and should not be changed. The file inputs.norm contains 192 lines of normalised data, specifying a range of different alloy compositions and test temperatures. The file output.norm contains the experimentally determined values for the yield strength for each entry in the inputs.norm file. These files were fed into the Gaussian Process model, which produced as output the file h, containing the parameters of the non-linear, multi-parameter fit to the data. The Tpros program uses this for predicting values of the yield strength for other alloy compositions and test temperatures. The file nipros.man contains a manual which provides a detailed set of instructions for downloading and running the Tpros program for calculating the yield strength. A summary of the information in this manual is given here.
The compositions and test temperatures of the alloys for which the yield strengths are to be calculated, need to be placed in an input file. Each line of data corresponds to a different alloy composition or test temperature. (There is no restriction on the number of lines of data in the input file.)
For each alloy, 16 data items must be specified:
| Column number | Variable |
| 1 | normalised Ni wt.% |
| 2 | normalised Cr wt.% |
| 3 | normalised Co wt.% |
| 4 | normalised Mo wt.% |
| 5 | normalised W wt.% |
| 6 | normalised Ta wt.% |
| 7 | normalised Nb wt.% |
| 8 | normalised Al wt.% |
| 9 | normalised Ti wt.% |
| 10 | normalised Fe wt.% |
| 11 | normalised Mn wt.% |
| 12 | normalised Si wt.% |
| 13 | normalised C wt.% |
| 14 | normalised B wt.% |
| 15 | normalised Zr wt.% |
| 16 | normalised test temperature (°C) |
The actual composition (in wt.%) must be normalised using the equation:
normalised value = (value - Min)/(Max - Min) - 0.5
where the values for Min and Max are defined as follows:| Column number | Variable | Min | Max |
| 1 | Ni (wt.%) | 38 | 76 |
| 2 | Cr (wt.%) | 12 | 30 |
| 3 | Co (wt.%) | 0 | 20 |
| 4 | Mo (wt.%) | 0 | 10 |
| 5 | W (wt.%) | 0 | 6 |
| 6 | Ta (wt.%) | 0 | 1.5 |
| 7 | Nb (wt.%) | 0 | 6.5 |
| 8 | Al (wt.%) | 0 | 4.9 |
| 9 | Ti (wt.%) | 0 | 5 |
| 10 | Fe (wt.%) | 0 | 40 |
| 11 | Mn (wt.%) | 0 | 0.5 |
| 12 | Si (wt.%) | 0 | 0.5 |
| 13 | C (wt.%) | 0.03 | 0.35 |
| 14 | B (wt.%) | 0 | 0.16 |
| 15 | Zr (wt.%) | 0 | 0.2 |
| 16 | Test temperature (°C) | 21 | 1093 |
The predicted values for the yield strength produced by the Tpros program are written to a file called pred.res.norm. This output file contains 1 line of 5 data items for each line of input data:
| column 1 | - | the normalised predicted yield strength. |
| column 2 | - | a value for the error (equal to sigma), which includes both the experimental noise of the database and an estimation of the uncertainty in the prediction. |
| column 3 | - | the predicted output minus sigma. |
| column 4 | - | the predicted output plus sigma. |
| column 5 | - | an estimation of the noise level in the database; it is the same for all cases. |
The normalised values for the yield strength in columns 1, 3 and 4, must be un-normalised using the equation:
The values in column 2 can be un-normalised using the equation:
The values of Min and Max for the yield strength are 28 MPa and 1310 MPa, respectively. The FORTRAN program, unnorm.f, can be used to translate the output files to produce the actual values of the yield strength.
None.
See output parameters.
None.
Complete program
For a set of alloys with the following wt.% and test temperatures (°C):
Ni Cr Co Mo W Ta Nb Al Ti Fe Mn Si C B Zr Temperature 72.69 10 8 5 0 0 0 3 1 0 0 0.2 0.10 0.01 0 21 65.58 15 11 4 0 0 0 3 1 0 0 0.3 0.11 0.01 0 21 70.79 12 10 3 0 0 0 3 1 0 0 0.1 0.10 0.01 0 750 69.77 14 10 2 0 0 0 3 1 0 0 0.1 0.12 0.01 0 750 69.70 15 10 1 0 0 0 3 1 0 0 0.2 0.09 0.01 0 750 72.35 20 0 0 1 0 0 1 5 0 0 0.4 0.23 0.02 0 900 72.71 20 0 0 1 0 0 2 4 0 0 0.2 0.25 0.02 0 900 59.48 25 8 0 1 0 0 3 3 0 0 0.3 0.20 0.02 0 650 67.44 25 0 0 1 0 0 4 2 0 0 0.3 0.23 0.03 0 650 65.51 27 0 0 1 0 0 5 1 0 0 0.2 0.26 0.03 0 650
The input file is:
0.41289 -0.61111 -0.1 0 -0.5 -0.5 -0.5 0.11224 -0.3 -0.5 -0.5 -0.1 -0.25 -0.4375 -0.5 -0.5 0.22579 -0.33333 0.05 -0.1 -0.5 -0.5 -0.5 0.11224 -0.3 -0.5 -0.5 0.1 -0.21875 -0.4375 -0.5 -0.5 0.36289 -0.5 0 -0.2 -0.5 -0.5 -0.5 0.11224 -0.3 -0.5 -0.5 -0.3 -0.25 -0.4375 -0.5 0.18004 0.33605 -0.38889 0 -0.3 -0.5 -0.5 -0.5 0.11224 -0.3 -0.5 -0.5 -0.3 -0.1875 -0.4375 -0.5 0.18004 0.33421 -0.33333 0 -0.4 -0.5 -0.5 -0.5 0.11224 -0.3 -0.5 -0.5 -0.1 -0.28125 -0.4375 -0.5 0.18004 0.40395 -0.05556 -0.5 -0.5 -0.33333 -0.5 -0.5 -0.29592 0.5 -0.5 -0.5 0.3 0.15625 -0.375 -0.5 0.31996 0.41342 -0.05556 -0.5 -0.5 -0.33333 -0.5 -0.5 -0.09184 0.3 -0.5 -0.5 -0.1 0.21875 -0.375 -0.5 0.31996 0.06526 0.22222 -0.1 -0.5 -0.33333 -0.5 -0.5 0.11224 0.1 -0.5 -0.5 0.1 0.0625 -0.375 -0.5 0.086754 0.27474 0.22222 -0.5 -0.5 -0.33333 -0.5 -0.5 0.31633 -0.1 -0.5 -0.5 0.1 0.15625 -0.3125 -0.5 0.086754 0.22395 0.33333 -0.5 -0.5 -0.33333 -0.5 -0.5 0.52041 -0.3 -0.5 -0.5 -0.1 0.25 -0.3125 -0.5 0.08675
The output file pred.res.norm, which contains the normalised values for the yield strengths, is:
0.005423 0.066927 -0.061504 0.072351 0.030084 -0.000309 0.062081 -0.062390 0.061772 0.030084 -0.128383 0.059650 -0.188032 -0.068733 0.030084 -0.147786 0.060995 -0.208781 -0.086791 0.030084 -0.146840 0.064468 -0.211307 -0.082372 0.030084 -0.203048 0.118880 -0.321929 -0.084168 0.030084 -0.257969 0.096652 -0.354621 -0.161317 0.030084 -0.002483 0.075561 -0.078044 0.073078 0.030084 -0.067076 0.092816 -0.159892 0.025740 0.030084 -0.096879 0.120929 -0.217808 0.024050 0.030084
The actual values for the yield strengths are then:
Yield strength Error Range of values for
(MPa) yield strength (MPa)
675.95 85.80 590.15 - 761.75
668.60 79.59 589.02 - 748.19
504.41 76.47 427.94 - 580.88
479.54 78.20 401.34 - 557.73
480.75 82.65 398.10 - 563.40
408.69 152.40 256.29 - 561.10
338.28 123.91 214.38 - 462.19
665.82 96.87 568.95 - 762.69
583.01 118.99 464.02 - 702.00
544.80 155.03 389.77 - 699.83
None.
nickel, superalloy, yield stress, Tpros, gaussian process, temperature, mechanical properties
Download data files from MAP
Link to Tpros program
MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.
MAP Website administration / map@msm.cam.ac.uk
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