Machine Learning-Based Comprehensive Prediction Model for L12 Phase-Strengthened Fe-Co-Ni-Based High-Entropy Alloys

doi:10.1007/s40195-024-01774-1

Abstract

Abstract:

L1₂ phase-strengthened Fe-Co-Ni-based high-entropy alloys (HEAs) have attracted considerable attention due to their excellent mechanical properties. Improving the properties of HEAs through conventional experimental methods is costly. Therefore, a new method is needed to predict the properties of alloys quickly and accurately. In this study, a comprehensive prediction model for L1₂ phase-strengthened Fe-Co-Ni-based HEAs was developed. The existence of the L1₂ phase in the HEAs was first predicted. A link was then established between the microstructure (L1₂ phase volume fraction) and properties (hardness) of HEAs, and comprehensive prediction was performed. Finally, two mutually exclusive properties (strength and plasticity) of HEAs were coupled and co-optimized. The Shapley additive explained algorithm was also used to interpret the contribution of each model feature to the comprehensive properties of HEAs. The vast compositional and process search space of HEAs was progressively screened in three stages by applying different prediction models. Finally, four HEAs were screened from hundreds of thousands of possible candidate groups, and the prediction results were verified by experiments. In this work, L1₂ phase-strengthened Fe-Co-Ni-based HEAs with high strength and plasticity were successfully designed. The new method presented herein has a great cost advantage over traditional experimental methods. It is also expected to be applied in the design of HEAs with various excellent properties or to explore the potential factors affecting the microstructure/properties of alloys.

Key words: High-entropy alloy, Machine learning, L1₂ phase, Comprehensive prediction, Shapley additive explanation (SHAP)

Xin Li, Chenglei Wang, Laichang Zhang, Shengfeng Zhou, Jian Huang, Mengyao Gao, Chong Liu, Mei Huang, Yatao Zhu, Hu Chen, Jingya Zhang, Zhujiang Tan. Machine Learning-Based Comprehensive Prediction Model for L1₂ Phase-Strengthened Fe-Co-Ni-Based High-Entropy Alloys[J]. Acta Metallurgica Sinica (English Letters), 2024, 37(11): 1858-1874.

Figures/Tables 18

Fig. 1 Schematic diagram of a comprehensive prediction system for L12 phase-strengthened Fe-Co-Ni-based HEAs

Table 1 Features and their numbers of data

Number	Feature	Number	Feature
1	Fe content (at.%)	10	Homogenization temperature (k)
2	Co content (at.%)	11	Homogenization time (h)
3	Ni content (at.%)	12	Cold rolling (%)
4	Al content (at.%)	13	First aging temperature (k)
5	Ti content (at.%)	14	First aging time (h)
6	Cr content (at.%)	15	Second aging temperature (k)
7	Cu content (at.%)	16	Second aging time (h)
8	Mn content (at.%)	17	Water cooling
9	Nb content (at.%)	18	Air cooling
		19	Furnace cooling

Fig. 2 Performance and SHAP significance plots of L12 phase existence prediction models: a, c, e ROC curves of different predictive models, b, d, f ROC curves of different prediction models after screening out some useless features, g importance of features of predictive models

Fig. 3 Heat map of Pearson's correlation coefficient set between different features of EWM-based database for comprehensive prediction of L12 phase volume fraction and hardness of HEAs

Fig. 4 Predictive effectiveness of an combined prediction model for L12 phase volume fraction and hardness on test and training datasets: a-d test dataset, e-h training dataset, i distribution of SHAP values for different input features of the combined L12 phase volume fraction and hardness prediction model

Fig. 5 R2 and RMSE values of EWM-based integrated prediction model for L12 phase volume fraction and hardness of HEAs on training and test datasets: a comparison of R2 values, b comparison of RMSE values

Fig. 6 Scatterplot of SHAP values of some features of the integrated prediction model of L12 phase volume fraction and hardness for HEAs

Fig. 7 Heat map of Pearson’s correlation coefficient set between different features of the EWM-based database for comprehensive strength and plasticity prediction of HEAs

Fig. 8 Performance of the combined strength and plasticity prediction model for HEAs on test and training datasets: a-d test dataset, e-h: training data set, i distribution of SHAP values for different input features of the combined strength and plasticity prediction model

Fig. 9 R2 and RMSE values of the combined strength and plasticity prediction model for HEAs on the training and test datasets: a comparison of R2 values, b comparison of RMSE values

Fig. 10 Search space for a comprehensive prediction system for L12 phase-strengthened Fe-Co-Ni-based HEAs

Table 2 Composition and process set of candidate HEAs to be verified after screening

Alloy	Fe (at.%)	Co (at.%)	Ni (at.%)	Cr (at.%)	Al (at.%)	Ti (at.%)	F-A-Tem (℃)	F-A-Time (h)
A1	25	31	37	-	2	5	800	8
A2	25	25	41	-	3	6	800	8
A3	23	28	37	4	4	4	800	8
A4	24	27	32	8	6	3	800	8

Fig. 11 XRD patterns of candidate HEAs (A1, A2, A3 and A4)

Fig. 12 SEM images of microstructure of candidate HEAs: a-c A1, d-f A2, g-i A3, j-l A4

Table 3 Experimental and predicted EW1 values for candidate HEAs

Alloy	L1₂ phase volume fraction (Experiment value)	Hardness (Experiment value)	EW1 (Experiment value)	EW1 (Predicted value)
A1	45%	385.5 HV	1.8273	1.9754
A2	43%	381.6 HV	1.8115	1.9865
A3	48%	393.9 HV	1.8687	1.9851
A4	47%	388.9 HV	1.8454	1.9625

Fig. 13 Tensile properties of candidate HEAs at room temperature: a tensile curves, b comparison of alloy properties, c tensile and yield strengths, d elongation

Fig. 14 Tensile fracture morphology of candidate high entropy alloys: a, b A1, c, d A2, e, f A3, g, h A4

Table 4 Experimental and predicted EW2 values for candidate HEAs

Alloy	Tensile strength (Experiment value)	Yield strength (Experiment value)	Total elongation (Experiment value)	EW2 (Experiment value)	EW2 (Predicted value)
A1	~ 1436 MPa	~ 1014 MPa	~ 32.7%	2.9695	3.1978
A2	~ 1421 MPa	~ 1021 MPa	~ 24%	2.9417	3.1965
A3	~ 1526MPa	~ 1138 MPa	~ 24.3%	2.9789	3.2368
A4	~ 1490 MPa	~ 1097 MPa	~ 32%	3.0143	3.2332

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Machine Learning-Based Comprehensive Prediction Model for L1₂ Phase-Strengthened Fe-Co-Ni-Based High-Entropy Alloys

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Alloy	Fe (at.%)	Co (at.%)	Ni (at.%)	Cr (at.%)	Al (at.%)	Ti (at.%)	F-A-Tem (℃)	F-A-Time (h)
A1	25	31	37	-	2	5	800	8
A2	25	25	41	-	3	6	800	8
A3	23	28	37	4	4	4	800	8
A4	24	27	32	8	6	3	800	8

Alloy	Fe (at.%)	Co (at.%)	Ni (at.%)	Cr (at.%)	Al (at.%)	Ti (at.%)	F-A-Tem (℃)	F-A-Time (h)
A1	25	31	37	-	2	5	800	8
A2	25	25	41	-	3	6	800	8
A3	23	28	37	4	4	4	800	8
A4	24	27	32	8	6	3	800	8

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Alloy	Fe (at.%)	Co (at.%)	Ni (at.%)	Cr (at.%)	Al (at.%)	Ti (at.%)	F-A-Tem (℃)	F-A-Time (h)
A1	25	31	37	-	2	5	800	8
A2	25	25	41	-	3	6	800	8
A3	23	28	37	4	4	4	800	8
A4	24	27	32	8	6	3	800	8

Alloy	Fe (at.%)	Co (at.%)	Ni (at.%)	Cr (at.%)	Al (at.%)	Ti (at.%)	F-A-Tem (℃)	F-A-Time (h)
A1	25	31	37	-	2	5	800	8
A2	25	25	41	-	3	6	800	8
A3	23	28	37	4	4	4	800	8
A4	24	27	32	8	6	3	800	8

Alloy	Fe (at.%)	Co (at.%)	Ni (at.%)	Cr (at.%)	Al (at.%)	Ti (at.%)	F-A-Tem (℃)	F-A-Time (h)
A1	25	31	37	-	2	5	800	8
A2	25	25	41	-	3	6	800	8
A3	23	28	37	4	4	4	800	8
A4	24	27	32	8	6	3	800	8

Alloy	Fe (at.%)	Co (at.%)	Ni (at.%)	Cr (at.%)	Al (at.%)	Ti (at.%)	F-A-Tem (℃)	F-A-Time (h)
A1	25	31	37	-	2	5	800	8
A2	25	25	41	-	3	6	800	8
A3	23	28	37	4	4	4	800	8
A4	24	27	32	8	6	3	800	8