Phase-field-informed machine learning on creep behavior of Ni-based single-crystal superalloys

Abstract

Creep strain characterizes the degree of creep damage and the creep life of superalloys. The creep process is accompanied by element redistribution and microstructure evolution; understanding the multi-characteristic relationships of creep morphology and strain/stress is essentially important for the design and prediction of superalloys. Accurate prediction of creep strain necessitates comprehensive feature data. In this work, a phase-field (PF)-informed machine learning (ML) is developed to investigate the creep strain of Ni-12.2Al-6Co-2.5Ta (at.%) superalloy. The creep damage crystal plasticity PF model is employed to simulate the creep morphology, composition and strain evolution. A ML-based quantitative prediction model for creep strain is established to assess the impact of composition and microstructure on creep behavior. Moreover, to enhance the accuracy and generalization of the ML model, statistical features are added using two-point analysis and principal component analysis (PCA) methods for characterizing the two-phase morphology. Additionally, the Shapley Additive Explanations algorithm is used to explain the intrinsic relationships of γ’ rafting, γ’ volume fraction, and creep strain. The phase classification model has an accuracy rate of over 99.2%; the mean square error of the quantitative creep strain prediction model is reduced from 0.304 to 0.235 by using two-point analysis and PCA dimensionality reduction. This study demonstrates the effectiveness of integrating PF information-driven ML in developing image recognition and creep performance prediction models for superalloys.

Keywords

Machine learning / phase-field / creep strain / microstructure / Ni-based superalloys

References

[1] Tan L,Shi D,Lyu S.Effect of microstructure rafting on deformation behaviour and crack mechanism during high-temperature low-cycle fatigue of a Ni-based single crystal superalloy.Int J Fatigue2025;190:108619

[2] Pollock TM.Alloy design for aircraft engines.Nat Mater2016;15:809-15

[3] Ge M,Wang X.Effects of Ta on the high temperature creep behavior and deformation mechanism of a Ni-based single crystal superalloy.Mater Sci Eng A2024;916:147335

[4] Ru Y,Pei Y.Improved 1200 °C stress rupture property of single crystal superalloys by γ’-forming elements addition.Scr Mater2018;147:21-6

[5] Xia W,Yue L.Microstructural evolution and creep mechanisms in Ni-based single crystal superalloys: a review.J Alloys Compd2020;819:152954

[6] Zhang P,Niu Q.Correlation microstructural evolution with creep-rupture properties of a novel directionally solidified Ni-based superalloy M4706.J Mater Sci2022;57:17812-27

[7] Murakumo T,Koizumi Y.Creep behaviour of Ni-base single-crystal superalloys with various γ’ volume fraction.Acta Mater2004;52:3737-44

[8] Liu Y,Wang Z.Machine learning in materials genome initiative: a review.J Mater Sci Technol2020;57:113-22

[9] Liu P,Antonov S.Machine learning assisted design of γ’-strengthened Co-base superalloys with multi-performance optimization.npj Comput Mater2020;6:334

[10] Zhao Y.Understanding and design of metallic alloys guided by phase-field simulations.npj Comput Mater2023;9:1038

[11] Oommen V,Goswami S,Karniadakis GE.Learning two-phase microstructure evolution using neural operators and autoencoder architectures.npj Comput Mater2022;8:876

[12] Yang K,Zhang Y.Self-supervised learning and prediction of microstructure evolution with convolutional recurrent neural networks.Patterns2021;2:100243 PMCID:PMC8134942

[13] Zhu Y,Wei Q.Linear-superelastic Ti-Nb nanocomposite alloys with ultralow modulus via high-throughput phase-field design and machine learning.npj Comput Mater2021;7:674

[14] Van Lich L,Hong Hue DT.The design of compositionally modulated lead-free ferroelectrics with large electromechanical response via high-throughput phase-field simulations and machine learning.Mater Res Bull2023;167:112433

[15] Shen ZH,Jiang JY.Phase-field modeling and machine learning of electric-thermal-mechanical breakdown of polymer-based dielectrics.Nat Commun2019;10:1843 PMCID:PMC6478924

[16] Li W,Liu C.Optimizing piezoelectric nanocomposites by high-throughput phase-field simulation and machine learning.Adv Sci2022;9:e2105550 PMCID:PMC9069389

[17] Tso W,Seidman DN.Active learning sensitivity analysis of γ’(L1₂) precipitate morphology of ternary co-based superalloys.Materialia2023;28:101760

[18] Xu D,Huo X,Yang M.Advances in data-assisted high-throughput computations for material design.Mater Genome Eng Adv2023;1:e11

[19] Karniadakis GE,Lu L,Wang S.Physics-informed machine learning.Nat Rev Phys2021;3:422-40

[20] Chen L.From classical thermodynamics to phase-field method.Prog Mater Sci2022;124:100868

[21] Qin Q,Long H,Li Y.Prediction of creep properties of Co–10Al–9W superalloys with machine learning.J Mater Sci2024;59:4571-85

[22] Zhao Y.Integrated unified phase-field modeling (UPFM).Mater Genome Eng Adv2024;2:e44

[23] Shan Y,Song J,Li Y.Precipitation kinetics and creep properties of multicomponent Ni-based superalloys.J Mater Sci2024;59:20715-34

[24] Chen J,Yang M.Temperature dependence of kinetics pathway of γ’ precipitation in Co-Al-W superalloys: a phase-field study.J Alloys Compd2022;922:166319

[25] Zhou N,Mills M.Large-scale three-dimensional phase field simulation of γ’-rafting and creep deformation.Philos Mag2010;90:405-36

[26] Wang D,Shi S,Yan Z.Phase-field simulation of γ’ precipitates rafting and creep property of Co-base superalloys.Mater Design2020;196:109077

[27] Utada S,Cormier J.Ultra-high temperature creep of Ni-based SX superalloys at 1250 °C.Metals2021;11:1610

[28] Liu Y,Wang Z.Predicting creep rupture life of Ni-based single crystal superalloys using divide-and-conquer approach based machine learning.Acta Mater2020;195:454-67

[29] Li X,Li X.High-temperature creep behavior and damage mechanism of an advanced powder metallurgy Ni-based superalloy.Adv Eng Mater2024;26:2400230

[30] Omprakash CM,Kamaraj M.Creep behaviour of directionally solidified nickel-base superalloy CM 247: a three-dimensional representation of creep curves.Trans Indian Inst Met2021;74:1787-97

[31] Ronneberger O,Brox T.U-Net: convolutional networks for biomedical image segmentation. In Medical image computing and computer-assisted intervention - MICCAI 2015. Cham: Springer International Publishing; 2015. pp. 234-41.

[32] Qin Z,Wang Z.High-throughput characterization methods for Ni-based superalloys and phase prediction via deep learning.J Mater Res Technol2022;21:1984-97

[33] Zhou Z,Tajbakhsh N.UNet++: a nested U-Net architecture for medical image segmentation.Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Supportpp 3-11

[34] He K,Ren S.Deep residual learning for image recognition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, USA. Jun 27-30, 2016. IEEE, 2016; pp, 770-8.

[35] Zhang N,Liu P.Machine learning-based quantitative analysis of metal ductile fracture surface.Materialia2023;32:101904

[36] Wang Y,Su C.Field kinetic model and computer simulation of precipitation of L1₂ ordered intermetallics from f.c.c. solid solution.Acta Mater1998;46:2983-3001

[37] Kline DM.Revisiting squared-error and cross-entropy functions for training neural network classifiers.Neural Comput Appl2005;14:310-8

[38] Zhu L,Chen Q.Prediction of ultimate tensile strength of Al-Si alloys based on multimodal fusion learning.Mater Genome Eng Adv2024;2:e26

[39] Fu C,Li L,Feng Q.Evaluation of service conditions of high pressure turbine blades made of DS Ni-base superalloy by artificial neural networks.Mater Today Commun2020;22:100838

[40] Underwood EE.The mathematical foundations of quantitative stereology. In: stereology and quantitative metallography. ASTM International, 1972; pp. 3-38.

[41] Liu P,Jiang X.Evolution analysis of γ’ precipitate coarsening in Co-based superalloys using kinetic theory and machine learning.Acta Mater2022;235:118101

[42] Murphy KP. Machine learning: a probabilistic perspective. MIT Press, 2012. https://api.semanticscholar.org/CorpusID:17793133. (accessed 2025-03-26)

[43] Kim Y,Ergün T.The instability of the Pearson correlation coefficient in the presence of coincidental outliers.Financ Res Lett2015;13:243-57

[44] Hao J.Machine learning made easy: a review of Scikit-learn Package in python programming language.J Educ Behav Stat2019;44:348-61https://www.researchgate.net/publication/331257851_Machine_Learning_Made_Easy_A_Review_of_Scikit-learn_Package_in_Python_Programming_Language. (accessed 2025-03-26)

[45] Tibshirani R.Regression shrinkage and selection via the lasso.J R Stat Soc B1996;58:267-88

[46] Loh W.Classification and regression trees.WIREs Data Min Knowl2011;1:14-23

[47] Vijayakumar V,Shirinpour S.Quantifying and characterizing tonic thermal pain across subjects from EEG data using random forest models.IEEE Trans Biomed Eng2017;64:2988-96 PMCID:PMC5718188

[48] Ibraheem R,dos Reis G.Path signature-based life prognostics of Li-ion battery using pulse test data.Appl Energy2025;378:124820

[49] Zhang T.Informatics is fueling new materials discovery.J Mater Inf2021;1:6

[50] Cecen A,Kalidindi SR.Versatile algorithms for the computation of 2-point spatial correlations in quantifying material structure.Integr Mater Manuf Innov2016;5:1-15

[51] Wold S,Geladi P.Principal component analysis.Chemom Intell Lab Syst1987;2:37-52

[52] Xu J,Liu X,Feng Q.Quantitative models of high temperature creep microstructure-property correlation of a nickel-based single crystal superalloy with physical and statistical features.J Mater Res Technol2022;19:2301-13

[53] Sengodan G. Prediction of two-phase composite microstructure properties through deep learning of reduced dimensional structure-response data.Compos Part B Eng2021;225:109282

[54] Brough DB,Kalidindi SR.Materials knowledge systems in python - a data science framework for accelerated development of hierarchical materials.Integr Mater Manuf Innov2017;6:36-53 PMCID:PMC5497515

[55] Zhang Y,Li L.Thermal stability prediction of copolymerized polyimides via an interpretable transfer learning model.J Mater Inf2024;4:8

[56] Yu L,Cao W.Prediction of temperature-dependent yield strength of refractory high entropy alloy based on stacking integrated framework.J Mater Inf2024;4:28

[57] Nabarro FRN.Rafting in superalloys.Metall Mater Trans A1996;27:513-30

[58] Touratier F,Poquillon D.Rafting microstructure during creep of the MC2 nickel-based superalloy at very high temperature.Mater Sci Eng A2009;510-511:244-9

[59] Lu S,Lu F,Feng Q.Creep performance in a CoNi-based single crystal superalloy with super-high γ’ volume fraction at 760 °C and equivalent high stress.J Mater Res Technol2024;29:4870-80

[60] Ju Y,Qin Q,Shan Y.Creep property and rafting kinetics of Co-based monocrystal superalloys with antiphase boundaries of γ’ phase.Mater Sci Eng A2023;880:145283

[61] Antonov S,Utada S.Evaluation and comparison of damage accumulation mechanisms during non-isothermal creep of cast Ni-based superalloys. In: Tin S, Hardy M, Clews J, Cormier J, Feng Q, Marcin J, O’brien C, Suzuki A, editors. Superalloys 2020. Cham: Springer International Publishing; 2020. pp. 228-39.

[62] Wang X,Jin T.Effects of temperature and stress on microstructural evolution during creep deformation of Ru-free and Ru-containing single crystal superalloys.Adv Eng Mater2015;17:1034-44

[63] Coakley J,Frost M.Lattice strain evolution and load partitioning during creep of a Ni-based superalloy single crystal with rafted γ’ microstructure.Acta Mater2017;135:77-87

[64] Liu P,Liu X.Study on the mechanism of γ’ phase rafting in a 4th generation nickel-based single crystal superalloy during thermal exposure at high temperatures.J Alloys Compd2024;980:173594

[65] Barrett PR.A unified constitutive model in simulating creep strains in addition to fatigue responses of Haynes 230.Int J Solids Struct2020;185-6:394-409

[66] Xu K,Liu J.Creep behavior and a deformation mechanism based creep rate model under high temperature and low stress condition for single crystal superalloy DD5.Mater Sci Eng A2020;786:139414

[67] Mohles V,Steinbach I,Bürger D.Microstructure based model for creep of single crystal superalloys in the high temperature and low stress creep regime.Mater Sci Eng A2024;909:146780