Predicting the Tensile Behaviour of Cast Alloys by a Pattern Recognition Analysis on Experimental Data
Abstract
:1. Introduction
2. Aims and Scope
- -
- Predict the mechanical properties of metals and, in particular, the tensile properties such as, yield strength, ultimate strength, ultimate strain and Young’s modulus, starting from experimental data. In addition, it would be possible to investigate the relationship between these properties and fundamental aspects of metallurgy, as in the cases of constituent elements, microstructures, process parameters or treatments.
- -
- Use information directly taken from micrographs by a conventional process of image analysis but globally converted into macro-indicators related to the content of graphite, ferrite, perlite, nodularity and vermicularity. In addition, it would be possible to discuss the interrelations existing between all these features—mechanical and metallurgical—with the scope to recognize essential and overabundant information. This investigation will involve two different families of cast alloys, a nodular cast iron (SGI) and a less common compact graphite cast iron (CGI).
- -
- Select and use these essential data inside a Machine Learning (ML) approach, based on pattern recognition, with the scope to perform an ‘intelligent analysis’ of experimental measures. In this task, some of the most common methods of ML will be applied, specifically the Random Forest (RF), the Artificial Neural Network (NN) and the k-nearest neighbours (kNN). These classifiers will be implemented by the use of conventional codes and accessible platforms, comparing them in terms of functionality and accuracy in prediction, especially in association with the consistency and quality of the dataset used for training but also considering the overall variability of the phenomena under investigation.
- -
- Introduce essential concerns regarding the real applicability of these techniques for scopes related to the material design, product/process quality control and so on, including practical suggestions on the way to simplify the procedure towards an industrially-oriented application.
3. Materials and Methods
3.1. Experimental Data
3.1.1. Casting
- 1)
- Spheroidal Graphite Iron (SGI), a material also called nodular or ductile iron with respect to its high ductility, offered by the spheroidal shape of graphite;
- 2)
- Compacted Graphite Iron (CGI), a material with intermediate properties between grey and nodular iron, thanks to a more compact form of graphite that is becoming quite popular, particularly in the automotive sector [48].
3.1.2. Metallurgical and Mechanical Properties
- -
- Quantity of Graphite
- -
- Quantity of Ferrite
- -
- Quantity of Perlite
- -
- Grade of Nodularity
- -
- Grade of Vermicularity
- -
- Ultimate Tensile Strength [UTS],
- -
- Yield Strength [YS],
- -
- Ultimate Strain [ε],
- -
- Young’s modulus [E].
3.2. Machine Learning Algorithms
3.2.1. Random Forest (RF)
3.2.2. Neural Network (NN)
3.2.3. K-Nearest Neighbours (kNN)
3.3. Correlations
- 0 < rxy < 0.3 there is a weak correlation;
- 0.3 < rxy < 0.7 there is a moderate correlation;
- rxy > 0.7 there is a strong correlation.
- -
- experimental measures by way of estimating the influence between different properties;
- -
- experimental and predicted values by way of estimating the accuracy of the ML methods.
4. Results
4.1. Experimental Measures
4.2. Spheroidal Graphite Cast Iron
4.3. Compacted Graphite Cast Iron
5. Discussion
5.1. Prediction Model Validation
5.2. Data Preliminary Analysis
- -
- the SGI is more affected than the CGI with respect to changes in the metallurgical properties;
- -
- the content of graphite is not so relevant for the definition of mechanical properties, especially in the case of SGI, while it has a light negative effect on CGI;
- -
- the contents of ferrite and perlite, more than others, directly influence the material strength, especially in the case of SGI;
- -
- the ductility is directly related to ferrite and perlite content but not to graphite in the case of SGI, while the graphite shows a light negative effect on CGI;
- -
- the Young’s modulus, evaluated as standard, is practically uncorrelated, except for a slight dependency to the nodularity and to the vermicularity, more relevant in the case of CGI.
5.3. Expert Algorithms
5.4. Mean Values and Variability
5.5. Mean Values and Error Estimation
5.6. Correlations
5.7. Results Summary
- -
- ML methods confirm their general validity in predicting the mechanical properties of metals;
- -
- this seems true, even in the presence of a quite limited dataset to be used for training;
- -
- information can be directly taken from micrographs by a conventional process of image analysis and macro-indicators without the need to go through deeper metallurgical investigations;
- -
- in particular, the NN method seems the most appropriate of those considered;
- -
- the kNN method, although it has good accuracy, also shows a tendency to systematic errors;
- -
- the accuracy in prediction is different for each specific property under investigation, achieving the best results for UTS and YS but also offering acceptable indications in the other cases;
- -
- the average values of experiments and predictions (measured by μ) often coincide in practice;
- -
- the deviation with respect to the average values (measured by σ) shows a variability in prediction in line with the intrinsic variability as revealed by the experimental measurements;
- -
- the Pearson correlation (rxy) can be conveniently adopted for a quick evaluation of data but also for the validation of predictions.
6. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
Appendix A
SGI | Spheroidal cast iron |
CGI | Compact graphite cast iron |
GR | Graphite |
FE | Ferrite |
PE | Perlite |
NO | Grade of Nodularity |
VE | Grade of Vermicularity |
HB | Brinell hardness |
AI | Artificial Intelligence |
ANN | Artificial Neural Network |
ML | Machine Learning |
RF | Random Forest method |
NN | Neural Network method |
kNN | k-Nearest Neighbours method |
μ | Mean Value |
σ | Standard Deviation |
σ% | Relative Standard Deviation |
rxy | Pearson Correlation Coeff. |
UTS | Ultimate Tensile Strength |
YS | Yield Strength |
ε | Ultimate Strain/Ductility |
E | Young’s/Elasticity Modulus |
Appendix B
Specimen | GR | FE | PE | NO | VE | UTS | YS | ε | E |
---|---|---|---|---|---|---|---|---|---|
% | % | % | % | % | MPa | MPa | % | GPa | |
1 | 9.1 | 47.5 | 43.4 | 53.9 | 36.8 | 500.0 | 315.3 | 10.2 | 154.5 |
2 | 12.2 | 47.1 | 40.8 | 63.6 | 27.2 | 501.0 | 302.3 | 10.3 | 164.6 |
3 | 13.6 | 42.5 | 43.9 | 75.2 | 17.0 | 508.7 | 315.7 | 8.6 | 184.9 |
4 | 8.6 | 48.6 | 42.8 | 62.6 | 30.4 | 496.8 | 301.2 | 11.6 | 184.9 |
5 | 12.1 | 48.5 | 39.5 | 67.1 | 26.2 | 494.8 | 325.4 | 8.5 | 170.5 |
6 | 11.2 | 42.8 | 46.0 | 68.8 | 23.7 | 508.8 | 314.8 | 8.0 | 185.7 |
7 | 8.3 | 43.6 | 48.1 | 50.9 | 40.9 | 501.4 | 309.2 | 9.8 | 153.0 |
8 | 12.6 | 43.6 | 43.8 | 79.0 | 15.2 | 500.5 | 309.4 | 8.8 | 178.2 |
9 | 6.3 | 52.8 | 40.9 | 56.4 | 34.4 | 510.2 | 302.1 | 8.0 | 155.0 |
10 | 8.6 | 43.7 | 47.8 | 65.7 | 24.3 | 549.9 | 344.7 | 11.7 | 168.9 |
11 | 12.1 | 44.8 | 43.1 | 75.5 | 17.1 | 561.5 | 347.5 | 13.4 | 178.2 |
12 | 8.1 | 49.0 | 42.9 | 75.7 | 17.3 | 545.4 | 329.1 | 12.8 | 165.4 |
13 | 9.2 | 40.8 | 50.0 | 66.9 | 23.6 | 554.4 | 352.4 | 10.4 | 155.3 |
14 | 7.1 | 44.6 | 48.3 | 68.6 | 22.3 | 544.8 | 346.4 | 10.9 | 176.7 |
15 | 9.4 | 47.3 | 43.4 | 75.1 | 17.1 | 557.4 | 348.7 | 12.2 | 174.7 |
16 | 13.2 | 34.2 | 52.7 | 86.1 | 9.4 | 570.4 | 354.8 | 11.4 | 141.7 |
17 | 11.3 | 30.5 | 58.2 | 85.7 | 9.4 | 586.4 | 366.5 | 7.5 | 186.0 |
18 | 13.7 | 39.2 | 47.1 | 84.4 | 10.8 | 564.4 | 354.9 | 9.8 | 167.0 |
19 | 9.1 | 32.1 | 58.8 | 78.2 | 16.3 | 582.9 | 370.9 | 8.0 | 173.7 |
20 | 10.2 | 30.8 | 59.1 | 80.8 | 14.1 | 572.5 | 353.0 | 8.5 | 149.2 |
21 | 7.6 | 33.5 | 58.8 | 84.6 | 10.2 | 581.9 | 364.4 | 12.7 | 200.6 |
22 | 9.3 | 24.6 | 66.1 | 89.6 | 5.9 | 651.7 | 376.8 | 9.9 | 160.4 |
23 | 7.0 | 22.7 | 70.3 | 81.6 | 11.9 | 668.7 | 397.5 | 9.0 | 183.3 |
24 | 6.5 | 24.8 | 68.7 | 74.2 | 17.7 | 666.6 | 381.2 | 8.8 | 166.4 |
25 | 10.2 | 55.7 | 34.1 | 77.7 | 16.6 | 514.2 | 319.0 | 15.2 | 164.6 |
26 | 7.0 | 51.6 | 41.4 | 72.5 | 19.7 | 515.7 | 335.7 | 8.1 | 159.6 |
27 | 7.1 | 45.2 | 47.7 | 61.9 | 27.6 | 523.9 | 332.0 | 10.7 | 185.9 |
Mean (μ) | 9.7 | 41.2 | 49.2 | 72.7 | 20.1 | 549.4 | 339.7 | 10.2 | 170.0 |
St. Dev. (σ) | 2.3 | 9.0 | 9.4 | 10.2 | 8.8 | 50.6 | 26.7 | 1.9 | 13.9 |
R. St. Dev. (σ%) | 24% | 22% | 19% | 14% | 44% | 9% | 8% | 19% | 8% |
Specimen | GR | FE | PE | NO | VE | UTS | YS | ε | E |
---|---|---|---|---|---|---|---|---|---|
% | % | % | % | % | MPa | MPa | % | GPa | |
1 | 21.0 | 60.2 | 18.8 | 16.1 | 81.2 | 318.8 | 253.1 | 3.3 | 136.1 |
2 | 17.3 | 62.3 | 20.4 | 12.1 | 85.1 | 350.1 | 274.3 | 2.2 | 182.5 |
3 | 13.9 | 62.9 | 23.2 | 15.4 | 82.2 | 307.5 | 237.8 | 3.3 | 146.3 |
4 | 14.5 | 61.6 | 23.9 | 9.4 | 88.5 | 314.1 | 252.4 | 2.2 | 137.1 |
5 | 14.5 | 62.6 | 22.9 | 23.4 | 74.3 | 316.2 | 259.1 | 2.5 | 142.1 |
6 | 13.2 | 64.8 | 22.0 | 13.0 | 84.4 | 308.4 | 252.3 | 2.4 | 140.8 |
7 | 15.7 | 64.3 | 20.0 | 17.5 | 79.7 | 321.7 | 258.5 | 3.4 | 151.4 |
8 | 12.6 | 61.9 | 25.6 | 11.7 | 86.4 | 315.0 | 249.7 | 2.7 | 152.9 |
9 | 16.7 | 53.5 | 29.8 | 9.0 | 88.9 | 312.4 | 249.5 | 3.6 | 156.3 |
11 | 11.4 | 64.9 | 23.7 | 15.1 | 82.7 | 338.3 | 273.0 | 4.4 | 175.6 |
12 | 9.2 | 67.6 | 23.3 | 21.6 | 74.6 | 338.8 | 257.3 | 4.2 | 146.4 |
14 | 11.2 | 65.8 | 22.9 | 17.9 | 80.0 | 336.8 | 274.0 | 4.6 | 132.1 |
15 | 10.3 | 63.0 | 26.8 | 16.7 | 81.4 | 339.2 | 270.9 | 4.2 | 145.7 |
16 | 14.6 | 56.6 | 28.9 | 19.5 | 78.5 | 345.8 | 263.9 | 3.4 | 145.8 |
17 | 10.1 | 62.9 | 27.0 | 16.7 | 81.7 | 346.4 | 278.4 | 3.7 | 159.2 |
18 | 11.1 | 63.5 | 25.5 | 16.2 | 81.8 | 354.6 | 288.3 | 3.1 | 165.6 |
19 | 9.8 | 59.9 | 30.3 | 17.8 | 80.5 | 345.0 | 274.9 | 3.4 | 152.6 |
20 | 12.8 | 58.3 | 28.9 | 24.0 | 74.0 | 345.7 | 284.1 | 3.2 | 129.8 |
22 | 12.9 | 52.9 | 34.2 | 18.5 | 79.5 | 370.7 | 281.0 | 3.9 | 144.3 |
23 | 12.6 | 53.4 | 34.0 | 16.3 | 81.9 | 374.0 | 295.8 | 3.4 | 137.9 |
24 | 9.7 | 55.2 | 35.2 | 13.3 | 85.4 | 380.8 | 296.7 | 3.9 | 167.9 |
Mean (μ) | 13.0 | 61.2 | 25.8 | 16.6 | 81.2 | 337.2 | 267.9 | 3.4 | 149.9 |
St. Dev. (σ) | 3.0 | 4.3 | 4.7 | 4.0 | 4.2 | 21.8 | 16.3 | 0.7 | 14.0 |
R. St. Dev. (σ%) | 23% | 7% | 18% | 24% | 5% | 6% | 6% | 21% | 9% |
Appendix C
UTS | YS | ε | E | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
MPa | RF | NN | kNN | MPa | RF | NN | kNN | % | RF | NN | kNN | GPa | RF | NN | kNN |
495 | 510 | 509 | 497 | 325 | 348 | 316 | 301 | 8.5 | 8.0 | 8.0 | 8.0 | 171 | 185 | 186 | 160 |
497 | 510 | 510 | 495 | 301 | 349 | 302 | 302 | 11.6 | 10.7 | 10.2 | 8.0 | 185 | 165 | 153 | 155 |
500 | 501 | 501 | 497 | 315 | 302 | 309 | 301 | 10.2 | 8.0 | 8.0 | 8.0 | 155 | 185 | 153 | 153 |
501 | 510 | 509 | 497 | 302 | 301 | 315 | 301 | 10.3 | 8.0 | 8.0 | 8.0 | 165 | 185 | 185 | 169 |
501 | 562 | 564 | 509 | 309 | 316 | 355 | 316 | 8.8 | 9.0 | 9.0 | 7.5 | 178 | 149 | 142 | 165 |
501 | 500 | 500 | 497 | 309 | 332 | 315 | 301 | 9.8 | 11.4 | 8.6 | 8.6 | 153 | 169 | 155 | 155 |
509 | 557 | 501 | 501 | 316 | 309 | 355 | 309 | 8.6 | 8.8 | 8.5 | 8.8 | 185 | 178 | 178 | 178 |
509 | 554 | 501 | 495 | 315 | 345 | 325 | 302 | 8.0 | 10.2 | 10.7 | 9.8 | 186 | 178 | 165 | 155 |
510 | 500 | 500 | 497 | 302 | 336 | 309 | 301 | 8.0 | 10.9 | 9.8 | 8.5 | 155 | 165 | 155 | 153 |
514 | 510 | 509 | 501 | 319 | 336 | 316 | 309 | 15.2 | 8.1 | 12.8 | 8.1 | 165 | 178 | 178 | 178 |
516 | 545 | 524 | 495 | 336 | 329 | 302 | 319 | 8.1 | 12.8 | 15.2 | 8.5 | 160 | 177 | 165 | 165 |
524 | 501 | 510 | 497 | 332 | 345 | 315 | 301 | 10.7 | 10.9 | 10.2 | 10.3 | 186 | 185 | 155 | 155 |
545 | 562 | 516 | 501 | 329 | 349 | 349 | 309 | 12.8 | 13.4 | 15.2 | 8.1 | 165 | 178 | 175 | 178 |
545 | 509 | 516 | 509 | 346 | 332 | 332 | 315 | 10.9 | 10.7 | 10.7 | 8.0 | 177 | 178 | 186 | 155 |
550 | 509 | 497 | 497 | 345 | 352 | 301 | 301 | 11.7 | 10.4 | 10.7 | 8.0 | 169 | 186 | 153 | 155 |
554 | 545 | 510 | 501 | 352 | 345 | 336 | 302 | 10.4 | 8.0 | 8.0 | 8.0 | 155 | 177 | 185 | 165 |
557 | 509 | 514 | 501 | 349 | 329 | 336 | 309 | 12.2 | 8.0 | 8.0 | 8.1 | 175 | 178 | 165 | 160 |
562 | 501 | 509 | 501 | 348 | 329 | 316 | 309 | 13.4 | 8.0 | 8.0 | 8.0 | 178 | 185 | 165 | 160 |
564 | 573 | 570 | 501 | 355 | 355 | 348 | 309 | 9.8 | 10.2 | 8.0 | 8.0 | 167 | 201 | 178 | 178 |
570 | 582 | 564 | 564 | 355 | 367 | 367 | 353 | 11.4 | 7.5 | 8.5 | 7.5 | 142 | 167 | 167 | 149 |
573 | 583 | 652 | 570 | 353 | 381 | 377 | 355 | 8.5 | 8.0 | 9.9 | 7.5 | 149 | 174 | 183 | 142 |
582 | 564 | 669 | 570 | 364 | 371 | 377 | 353 | 12.7 | 7.5 | 9.9 | 7.5 | 201 | 174 | 183 | 142 |
583 | 573 | 652 | 570 | 371 | 353 | 398 | 353 | 8.0 | 8.5 | 9.0 | 7.5 | 174 | 201 | 183 | 142 |
586 | 573 | 652 | 570 | 367 | 364 | 355 | 353 | 7.5 | 8.0 | 8.8 | 8.0 | 186 | 201 | 160 | 142 |
652 | 586 | 573 | 570 | 377 | 355 | 398 | 353 | 9.9 | 7.5 | 7.5 | 7.5 | 160 | 149 | 183 | 142 |
667 | 510 | 669 | 573 | 381 | 336 | 398 | 353 | 8.8 | 13.4 | 11.4 | 8.6 | 166 | 160 | 183 | 149 |
669 | 545 | 667 | 573 | 398 | 353 | 381 | 353 | 9.0 | 8.8 | 9.9 | 7.5 | 183 | 166 | 166 | 149 |
UTS | YS | ε | E | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
MPa | RF | NN | kNN | MPa | RF | NN | kNN | % | RF | NN | kNN | GPa | RF | NN | kNN |
308 | 316 | 350 | 308 | 238 | 288 | 252 | 252 | 3.3 | 3.4 | 2.2 | 2.4 | 146 | 146 | 141 | 132 |
308 | 355 | 314 | 308 | 252 | 238 | 274 | 238 | 2.4 | 3.3 | 2.2 | 2.2 | 141 | 176 | 183 | 146 |
312 | 371 | 315 | 312 | 250 | 252 | 281 | 250 | 3.6 | 3.3 | 3.9 | 3.9 | 156 | 138 | 137 | 137 |
314 | 312 | 312 | 314 | 252 | 250 | 250 | 238 | 2.2 | 3.6 | 3.6 | 2.2 | 137 | 153 | 183 | 141 |
315 | 308 | 314 | 315 | 250 | 252 | 252 | 238 | 2.7 | 2.2 | 2.2 | 2.2 | 153 | 168 | 137 | 137 |
316 | 322 | 346 | 316 | 259 | 284 | 284 | 257 | 2.5 | 3.4 | 3.4 | 3.4 | 142 | 146 | 151 | 130 |
319 | 350 | 322 | 319 | 253 | 259 | 274 | 238 | 3.3 | 3.4 | 2.2 | 2.2 | 136 | 151 | 183 | 141 |
322 | 319 | 319 | 322 | 259 | 252 | 259 | 238 | 3.4 | 3.4 | 3.2 | 3.2 | 151 | 141 | 136 | 132 |
337 | 355 | 339 | 337 | 274 | 257 | 257 | 238 | 4.6 | 4.2 | 4.2 | 3.1 | 132 | 176 | 146 | 146 |
338 | 339 | 337 | 338 | 273 | 288 | 250 | 252 | 4.4 | 4.2 | 4.6 | 2.4 | 176 | 166 | 132 | 132 |
339 | 346 | 337 | 339 | 271 | 278 | 238 | 273 | 4.2 | 2.5 | 4.6 | 2.5 | 146 | 159 | 159 | 132 |
339 | 337 | 308 | 339 | 257 | 271 | 259 | 259 | 4.2 | 3.7 | 3.4 | 3.1 | 146 | 166 | 132 | 132 |
345 | 346 | 346 | 345 | 275 | 278 | 281 | 271 | 3.4 | 3.4 | 3.3 | 3.3 | 153 | 146 | 144 | 138 |
346 | 316 | 346 | 346 | 264 | 281 | 296 | 271 | 3.4 | 4.2 | 3.9 | 3.1 | 146 | 146 | 130 | 130 |
346 | 339 | 339 | 346 | 278 | 271 | 271 | 271 | 3.7 | 3.4 | 3.4 | 3.1 | 159 | 166 | 132 | 132 |
346 | 316 | 316 | 346 | 284 | 259 | 259 | 257 | 3.2 | 3.4 | 3.4 | 3.4 | 130 | 142 | 142 | 142 |
350 | 308 | 319 | 350 | 274 | 252 | 253 | 238 | 2.2 | 3.3 | 3.3 | 3.3 | 183 | 151 | 137 | 136 |
355 | 338 | 339 | 355 | 288 | 273 | 275 | 238 | 3.1 | 4.2 | 4.2 | 3.3 | 166 | 146 | 132 | 132 |
371 | 381 | 374 | 371 | 281 | 296 | 296 | 264 | 3.9 | 3.4 | 3.4 | 3.4 | 144 | 138 | 138 | 130 |
374 | 381 | 371 | 374 | 296 | 281 | 281 | 250 | 3.4 | 3.9 | 3.9 | 3.4 | 138 | 153 | 144 | 144 |
381 | 374 | 312 | 381 | 297 | 274 | 296 | 250 | 3.9 | 3.7 | 3.4 | 3.4 | 168 | 153 | 144 | 138 |
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Number of trees | 15 |
Fixed seed for random generator | 32 |
Do not split subset smaller than | 5 |
Learning speed | 0.6 |
Inertial coefficient | 0.5 |
Test mass tolerance | 0.02 |
Tolerance of the learning set | 0.03 |
Number of layers | 5 |
Metric | Chebyshev |
Number of Neighbours | 2 |
Weight | Uniform |
SGI | Graphite | Ferrite | Perlite | Nodularity | Vermicularity |
Graphite | 1.00 | 0.04 | −0.29 | 0.34 | −0.30 |
Ferrite | 0.04 | 1.00 | −0.79 | 0.13 | −0.19 |
Perlite | −0.29 | −0.79 | 1.00 | 0.03 | 0.05 |
Nodularity | 0.34 | 0.13 | 0.03 | 1.00 | −0.99 |
Vermicularity | −0.30 | −0.19 | 0.05 | −0.99 | 1.00 |
CGI | Graphite | Ferrite | Perlite | Nodularity | Vermicularity |
Graphite | 1.00 | −0.20 | −0.45 | −0.24 | 0.20 |
Ferrite | −0.20 | 1.00 | −0.79 | 0.13 | −0.19 |
Perlite | −0.45 | −0.79 | 1.00 | 0.03 | 0.05 |
Nodularity | −0.24 | 0.13 | 0.03 | 1.00 | −0.99 |
Vermicularity | 0.20 | −0.19 | 0.05 | −0.99 | 1.00 |
SGI | Graphite | Ferrite | Perlite | Nodularity | Vermicularity |
Ultimate Tensile Strength (UTS) | −0.25 | −0.87 | 0.90 | 0.63 | −0.65 |
Yield Strength (YS) | −0.19 | −0.83 | 0.84 | 0.67 | −0.69 |
Ultimate Strain (ε) | −0.03 | 0.34 | −0.32 | 0.05 | −0.06 |
Young’s Modulus (E) | −0.03 | −0.09 | 0.09 | 0.18 | −0.21 |
CGI | Graphite | Ferrite | Perlite | Nodularity | Vermicularity |
Ultimate Tensile Strength (UTS) | −0.44 | −0.46 | 0.69 | 0.23 | −0.17 |
Yield Strength (YS) | −0.46 | −0.35 | 0.61 | 0.25 | −0.17 |
Ultimate Strain (ε) | −0.47 | 0.00 | 0.29 | 0.28 | −0.26 |
Young’s Modulus (E) | −0.11 | 0.08 | 0.00 | −0.39 | 0.38 |
SGI | Unit | Data | RF | NN | kNN |
Ultimate Tensile Strength (UTS) | MPa | 549 ± 51 (9%) | 536 ± 31 (6%) | 550 ± 64 (12%) | 520 ± 33 (6%) |
Yield Strength (YS) | MPa | 340 ± 27 (8%) | 341 ± 20 (6%) | 341 ± 31 (9%) | 320 ± 22 (7%) |
Ultimate Strain (ε) | % | 10.2 ± 1.9 (19%) | 9.4 ± 1.8 (19%) | 9.7 ± 2.0 (21%) | 8.1 ± 0.1 (8%) |
Young’s Modulus (E) | GPa | 170 ± 14 (8%) | 177 ± 13 (7%) | 170 ± 13 (8%) | 157 ± 12 (7%) |
CGI | Unit | Data | RF | NN | kNN |
Ultimate Tensile Strength (UTS) | MPa | 337 ± 22 (6%) | 340 ± 24 (7%) | 332 ± 19 (6%) | 317 ± 5 (4%) |
Yield Strength (YS) | MPa | 268 ± 16 (6%) | 268 ± 16 (6%) | 268 ± 17 (6%) | 251 ± 13 (5%) |
Ultimate Strain (ε) | % | 3.4 ± 0.7 (21%) | 3.5 ± 0.5 (14%) | 3.4 ± 0.7 (21%) | 3.0 ± 0.5 (18%) |
Young’s Modulus (E) | GPa | 150 ± 14 (9%) | 154 ± 12 (8%) | 146 ± 17 (12%) | 136 ± 20 (4%) |
Property | SGI | CGI | ||||
---|---|---|---|---|---|---|
RF | NN | kNN | RF | NN | kNN | |
Ultimate Tensile Strength (UTS) | −2.4% | 0.2% | −5.3% | 0.9% | −1.5% | −5.9% |
Yield Strength (YS) | 0.3% | 0.3% | −5.9% | 0.0% | 0.0% | −6.3% |
Ultimate Strain (ε) | −7.8% | −4.9% | −20.6% | 2.9% | −11.8% | −11.8% |
Young’s modulus (E) | 4.1% | 0.0% | −7.6% | 2.7% | −2.7% | −9.3% |
Pearson Correlation Coefficient (rxy) | SGI | CGI | ||||
---|---|---|---|---|---|---|
RF | NN | k-NN | RF | NN | kNN | |
Ultimate Tensile Strength (UTS) | 0.39 | 0.76 | 0.81 | 0.48 | 0.41 | 0.37 |
Yield Strength (YS) | 0.56 | 0.74 | 0.79 | 0.33 | 0.33 | 0.22 |
Ultimate Strain (ε) | −0.12 | 0.17 | −0.14 | 0.29 | 0.50 | 0.19 |
Young’s modulus (E) | 0.17 | −0.07 | −0.05 | −0.02 | −0.48 | −0.41 |
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Fragassa, C.; Babic, M.; Bergmann, C.P.; Minak, G. Predicting the Tensile Behaviour of Cast Alloys by a Pattern Recognition Analysis on Experimental Data. Metals 2019, 9, 557. https://doi.org/10.3390/met9050557
Fragassa C, Babic M, Bergmann CP, Minak G. Predicting the Tensile Behaviour of Cast Alloys by a Pattern Recognition Analysis on Experimental Data. Metals. 2019; 9(5):557. https://doi.org/10.3390/met9050557
Chicago/Turabian StyleFragassa, Cristiano, Matej Babic, Carlos Perez Bergmann, and Giangiacomo Minak. 2019. "Predicting the Tensile Behaviour of Cast Alloys by a Pattern Recognition Analysis on Experimental Data" Metals 9, no. 5: 557. https://doi.org/10.3390/met9050557