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A.Y. Badmos and H.K.D.H. Bhadeshia,

Phase Transformations Group,

Department of Materials Science and Metallurgy,

University of Cambridge,

Cambridge, U.K.

To predict the yield strength, ultimate tensile strength and elongation of the mechanically alloyed oxide dispersion strengthened (MA-ODS) ferritic stainless steels as a non-linear function of the important processing and service variables.

Language: | FORTRAN |

Product form: | Source code |

DOUBLE PRECISION AW(14),YSRES(26),UTSRES(26),ELRES(26) DOUBLE PRECISION AVER,SIGYS,SIGUTS,SIGEL INTEGER ID DOUBLE PRECISION X(12),AMIN(13),AMAX(13),AW(14) DOUBLE PRECISION W1Y1(14,12),W2Y1(14),THETA1Y1(14) DOUBLE PRECISION W1Y2(10,12),W2Y2(10),THETA1Y2(10) DOUBLE PRECISION W1Y3(11,12),W2Y3(11),THETA1Y3(11) DOUBLE PRECISION W1Y4(16,12),W2Y4(16),THETA1Y4(16) DOUBLE PRECISION W1Y5(6,12),W2Y5(6),THETA1Y5(6) DOUBLE PRECISION SIGMA,RES(26) DOUBLE PRECISION W1U1(16,12),W2U1(16),THETA1U1(16) DOUBLE PRECISION W1U2(15,12),W2U2(15),THETA1U2(15) DOUBLE PRECISION W1U3(15,12),W2U3(15),THETA1U3(15) DOUBLE PRECISION X(14),AMINEL(15),AMAXEL(15),AW(14) DOUBLE PRECISION W1E1(14,14),W2E1(14),THETA1E1(14) DOUBLE PRECISION W1E2(14,14),W2E2(14),THETA1E2(14) DOUBLE PRECISION W1E3(11,14),W2E3(11),THETA1E3(11) DOUBLE PRECISION W1E4(13,14),W2E4(13),THETA1E4(13) DOUBLE PRECISION W1E5(8,14),W2E5(8),THETA1E5(8) DOUBLE PRECISION W1E6(7,14),W2E6(7),THETA1E6(7)

MAP_MA-STEELS_NEURAL uses the parameters obtained from a neural network training process to predict the yield strength, ultimate tensile strength and percent elongation of the MA-ODS ferritic steels.

Tensile properties data from published literature were analysed using a neural network technique within a Bayesian framework (Ref. 1-2). The analysis, though empirical, can after appropriate training and with the use of committee of models, produce results which are metallurgically reasonable.

The predictions are made with committees which are composed of 5 models for yield strength, 3 models for ultimate tensile strength and 6 models for elongation. These are as a function of the following variables within the stated ranges:

Parameter | Maximum | Minimum |
---|---|---|

Chromium, wt.% | 0.1300D+02 | 0.2000D+02 |

Aluminium, wt.% | 0.0000D+00 | 0.4500D+01 |

Titanium, wt.% | 0.5000D+00 | 0.3500D+01 |

Molybdenum, wt.% | 0.0000D+00 | 0.1500D+01 |

Yttria, wt.% | 0.0000D+00 | 0.5000D+00 |

Annealing temp., C | 0.2000D+02 | 0.1330D+04 |

Annealing time, sec. | 0.0000D+00 | 0.1200D+03 |

Ageing temp., C | 0.2000D+02 | 0.8000D+03 |

Ageing time, sec. | 0.0000D+00 | 0.2888D+04 |

Cold-work, % | 0.0000D+00 | 0.7000D+02 |

Test temp., C | 0.0000D+00 | 0.1250D+04 |

Strain rate, 1/s. | 0.3330D-07 | 0.3330D-01 |

In addition to the parameters above, yield strength and ultimate tensile strength are also included as variables in the predictions of elongation.

To run the program MAP_MA-STEELS_NEURAL the following files are required, and
**should not be altered**:

**Y1WT, Y2WT, Y3WT, Y4WT, Y5WT**- Contain neural network information for yield strength.
**U1WT, U2WT, U3WT**- Contain neural network information for ultimate tensile strength.
**E1WT, E2WT, E3WT, E4WT, E5WT, E6WT**- Contain neural network information for elongation.

The raw data used in the training of the neural network is contained in the file `neural-dataset'

- A.Y. Badmos and H.K.D.H. Bhadeshia, Neural Network Models for the Tensile Properties of the Mechanically Alloyed ODS Iron-Alloys, accepted for publication in Materials Science and Technology.
- A.Y. Badmos, Ph.D. Thesis, University of Cambridge, UK, 1998.

**AW**- real array of dimension 14- AW contains the input data from the file ALLINPUT, which includes the variables known to be important in influencing the mechanical properties of the alloys.
**X**- real array of dimensions 12 (yield & UTS) and 14 (elongation)- Contains normalized input variables.
**W1Y1**- real array of dimension (14,12)- W1Y1 contains weights read in from the file Y1WT, which are coefficients for the first member of the committee model used in the prediction of yield strength.
**W2Y1**- real array of dimension 14- W2Y1 contains weights read in from the file Y1WT, which are coefficients for the first member of the committee model used in the prediction of yield strength.
**THETA1Y1**- real array of dimension 14- THETA1Y1 contains the biases associated with W1Y1, and is read in from the file Y1WT.
**THETA2Y1**- real- THETA2Y1 is the bias associated with W2Y1, and is read in from the file Y1WT.
**W1Y2**- real array of dimension (10,12)- W1Y2 contains weights read in from the file Y2WT, which are coefficients for the second member of the committee model used in the prediction of yield strength.
**W2Y2**- real array of dimension 10- W2Y2 contains weights read in from the file Y2WT, which are coefficients for the second member of the committee model used in the prediction of yield strength.
**THETA1Y2**- real array of dimension 10- THETA1Y2 contains the biases associated with W1Y2, and is read in from the file Y2WT.
**THETA2Y2**- real- THETA2Y2 is the bias associated with W2Y2, and is read in from the file Y2WT.
**W1Y3**- real array of dimension (11,12)- W1Y3 contains weights read in from the file Y3WT, which are coefficients for the third member of the committee model used in the prediction of yield strength.
**W2Y3**- real array of dimension 11- W2Y3 contains weights read in from the file Y3WT, which are coefficients for the third member of the committee model used in the prediction of yield strength.
**THETA1Y3**- real array of dimension 11- THETA1Y3 contains the biases associated with W1Y3, and is read in from the file Y3WT.
**THETA2Y3**- real- THETA2Y4 is the bias associated with W2Y4, and is read in from the filE Y4WT.
**W1Y4**- real array of dimension (16,12)- W1Y4 contains weights read in from the file Y4WT, which are coefficients for the fourth member of the committee model used in the prediction of yield strength.
**W2Y4**- real array of dimension 16- W2Y4 contains weights read in from the file Y4WT, which are coefficients for the fourth member of the committee model used in the prediction of yield strength.
**THETA1Y4**- real array of dimension 16- THETA1Y4 contains the biases associated with W1Y6, and is read in from the file Y4WT.
**THETA2Y4**- real- THETA2Y4 is the bias associated with W2Y4, and is read in from the file Y4WT.
**W1Y5**- real array of dimension (6,12)- W1Y5 contains weights read in from the file Y5WT, which are coefficients for the fifth member of the committee model used in the prediction of yield strength.
**W2Y5**- real array of dimension 6- W2Y5 contains weights read in from the file Y5WT, which are coefficients for the fifth member of the committee model used in the prediction of yield strength.
**THETA1Y5**- real array of dimension 6- THETA1Y5 contains the biases associated with W1Y5, and is read in from the file Y5WT.
**THETA2Y5**- real- THETA2Y5 is the bias associated with W2Y5, and is read in from the file Y5WT.
**W1U1**- real array of dimension (16,12)- W1U1 contains weights read in from the file U1WT, which are coefficients for the first member of the committee model used in the prediction of ultimate tensile strength.
**W2U1**- real array of dimension 16- W2U1 contains weights read in from the file U1WT, which are coefficients for the first member of the committee model used in the prediction of ultimate tensile strength.
**THETA1U1**- real array of dimension 16- THETA1U1 contains the biases associated with W1U1, and is read in from the file U1WT.
**THETA2U1**- real- THETA2U1 is the bias associated with W2U1, and is read in from the file U1WT.
**W1U2**- real array of dimension (15,12)- W1U1 contains weights read in from the file U2WT, which are coefficients for the second member of the committee model used in the prediction of ultimate tensile strength.
**W2U2**- real array of dimension 15- W2U2 contains weights read in from the file U2WT, which are coefficients for the second member of the committee model used in the prediction of ultimate tensile strength.
**THETA1U2**- real array of dimension 15- THETA1U2 contains the biases associated with W1U2, and is read in from the file U2WT.
**THETA2U2**- real- THETA2U2 is the bias associated with W2U2, and is read in from the file U2WT.
**W1U3**- real array of dimension (15,12)- W1U3 contains weights read in from the file U3WT, which are coefficients for the third member of the committee model used in the prediction of the ultimate tensile strength.
**W2U3**- real array of dimension 15- W2U3 contains weights read in from the file U3WT, which are coefficients for the third member of the committee model used in the prediction of the ultimate tensile strength.
**THETA1U1**- real array of dimension 15- THETA1U3 contains the biases associated with W1U3, and is read in from the file U3WT.
**THETA2U3**- real- THETA2U3 is the bias associated with W2U3, and is read in from the file U3WT.
**W1E1**- real array of dimension (14,14)- W1E1 contains weights read in from the file E1WT, which are coefficients for the first member of the committee model used in the prediction of elongation.
**W2E1**- real array of dimension 14- W2E1 contains weights read in from the file E1WT, which are coefficients for the first member of the committee model used in the prediction of elongation.
**THETA1E1**- real array of dimension 14- THETA1E1 contains the biases associated with W1E1, and is read in from the file E1WT.
**THETA2E1**- real- THETA2E1 is the bias associated with W2E1, and is read in from the file E1WT.
**W1E2**- real array of dimension (14,14)- W1E2 contains weights read in from the file E2WT, which are coefficients for the second member of the committee model used in the prediction of elongation.
**W2E2**- real array of dimension 14- W2E1 contains weights read in from the file E2WT, which are coefficients for the second member of the committee model used in the prediction of elongation.
**THETA1E2**- real array of dimension 14- THETA1E2 contains the biases associated with W1E2, and is read in from the file E2WT.
**THETA2E2**- real- THETA2E2 is the bias associated with W2E2, and is read in from the file E2WT.
**W1E3**- real array of dimension (11,14)- W1E3 contains weights read in from the file E3WT, which are coefficients for the third member of the committee model used in the prediction of elongation.
**W2E3**- real array of dimension 11- W2E3 contains weights read in from the file E3WT, which are coefficients for the third member of the committee model used in the prediction of elongation.
**THETA1E3**- real array of dimension 11- THETA1E3 contains the biases associated with W1E3, and is read in from the file E3WT.
**THETA2E3**- real- THETA2E3 is the bias associated with W2E3, and is read in from the file E3WT.
**W1E4**- real array of dimension (13,14)- W1E4 contains weights read in from the file E4WT, which are coefficients for the fourth member of the committee model used in the prediction of elongation.
**W2E4**- real array of dimension 13- W2E4 contains weights read in from the file E4WT, which are coefficients for the fourth member of the committee model used in the prediction of elongation.
**THETA1E4**- real array of dimension 13- THETA1E4 contains the biases associated with W1E4, and is read in from the file E4WT.
**THETA2E4**- real- THETA2E4 is the bias associated with W2E4, and is read in from the file E4WT.
**W1E5**- real array of dimension (8,14)- W1E5 contains weights read in from the file E5WT, which are coefficients for the fifth member of the committee model used in the prediction of elongation.
**W2E5**- real array of dimension 8- W2E5 contains weights read in from the file E5WT, which are coefficients for the fifth member of the committee model used in the prediction of elongation.
**THETA1E5**- real array of dimension 8- THETA1E5 contains the biases associated with W1E5, and is read in from the file E5WT.
**THETA2E5**- real- THETA2E5 is the bias associated with W2E5, and is read in from the file E5WT.
**W1E6**- real array of dimension (7,14)- W1E6 contains weights read in from the file E6WT, which are coefficients for the sixth member of the committee model used in the prediction of elongation.
**W2E6**- real array of dimension 7- W2E6 contains weights read in from the file E6WT, which are coefficients for the sixth member of the committee model used in the prediction of elongation.
**THETA1E6**- real array of dimension 7- THETA1E6 contains the biases associated with W1E6, and is read in from the file E6WT.
**THETA2E6**- real- THETA2E6 is the bias associated with W2E6, and is read in from the file E6WT.
**AMIN**- real array of dimension 12- AMIN contains the minimum value of the variables in the experimental dataset used to develop the models for the yield strength and the ultimate tensile strength.
**AMAX**- real array of dimension 12- AMAX contains the maximum value of the variables in the experimental dataset used to develop the models for the yield strength and the ultimate tensile strength.
**AMINEL**- real array of dimension 14- AMIN contains the minimum value of the variables in the experimental dataset used to develop the model for the elongation.
**AMAXEL**- real array of dimension 14- AMAX contains the maximum value of the variables in the experimental dataset used to develop the model for the elongation.

All output is to `STDOUT` and to a datafile, nominally called `OUT`.

None.

The full calculation of the error bars as presented in [1-2] is not reproduced in this program. An average error of ± 20% of 95% error limits is assumed reasonable, though not in all cases.

None.

Complete program.

20.0D0 Cr 4.50D0 Al 0.50D0 Ti 0.00D0 Mo 0.50D0 Y 1300.0D0 Annealing temperature 60.0D0 Annealing time 20.0D0 Ageing temperature 0.0D0 Ageing time 0.0D0 Cold-work 20.0D0 Test temperature 8.33D-5 Strain rate

********************************************************************************* ** Properties of Mechanically Alloyed Iron ** Cambridge University Badmos and Bhadeshia Identification Number 20 Program Version 5.2 Chromium 20.000 wt.% Aluminium 4.500 wt.% Titanium 0.500 wt.% Molybdenum 0.000 wt.% Yttria 0.500 wt.% Recrystallisation Temperature 1300. C Recrystallisation Time 60. min Ageing Temperature 20. C Ageing Time 0. min Cold Work 0. % Test Temperature 20. C Strain rate 0.00008 1/s Individual model Yield Strength (MPa): 543. 619. 627. 566. 610. Individual model Ultimate Strength (MPa): 647. 646. 683. Individual model elongations (%): 10. 7. 8. 8. 6. 7. Mean Yield Strength = 593. +- 8.MPa Mean Ultimate Strength = 658. +- 7.MPa Mean Elongation = 8. +- 13.% The error bars (95% confidence) do not include the uncertainty in fitting the data to the function, simply the unexplained noise in the data. *********************************************************************************

None.

neural network, MA-ODS iron-alloys, yield strength, ultimate tensile strength, elongation

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