Abstract
Herein, we trained machine learning (ML) model to quickly and accurately conduct the strength prediction of refractory high entropy alloys (RHEAs) matrix. Gradient Boosting (GB) regression model shows an outstanding performance against other ML models. In addition, the heat of fusion and atomic size difference is shown to be paramount to the strength of the high entropy alloys (HEAs) matrix. In addition, we discussed the contribution of each feature to the solid solution strengthening (SSS) of HEAs. The excellent predictive accuracy shows that the GB model can be efficient and reliable for the design of RHEAs with desired strength.
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The data and methods reported in this paper are available from the corresponding author upon reasonable request.
References
Yeh JW, Chen SK, Lin SJ, Gan JY, Chin TS, Shun TT, Tsau CH, Chang SY. Nanostructured high-entropy alloys with multiple principal elements: novel alloy design concepts and outcomes. Adv Eng Mater. 2004;6(5):299.
Cantor B, Chang I, Knight P, Vincent A. Microstructural development in equiatomic multicomponent alloys. Mater Sci Eng A. 2004;375:213.
Yeh JW. Physical metallurgy of high-entropy alloys. Jom. 2015;67(10):2254.
George EP, Raabe D, Ritchie RO. High-entropy alloys. Nat Rev Mater. 2019;4(8):515.
Senkov ON, Wilks GB, Miracle DB, Chuang CP, Liaw PK. Refractory high-entropy alloys. Intermetallics. 2010;18:1758.
Senkov ON, Miracle DB, Chaput KJ, Couzinie JP. Development and exploration of refractory high entropy alloys—review. J Mater Res. 2018;33:3092.
Li W, Xie D, Li D, Zhang Y, Gao Y, Liaw PK. Mechanical behavior of high-entropy alloys. Prog Mater Sci. 2021;118: 100777.
Kumar NAPK, Li C, Leonard KJ, Bei H, Zinkle SJ. Microstructural stability and mechanical behavior of FeNiMnCr high entropy alloy under ion irradiation. Acta Mater. 2016;113:230.
Shi Y, Yang B, Liaw P. Corrosion-resistant high-entropy alloys: a Review. Metals. 2017;7(2):43.
Li M, Gazquez J, Borisevich A, Mishra R, Flores KM. Evaluation of microstructure and mechanical property variations in AlxCoCrFeNi high entropy alloys produced by a high-throughput laser deposition method. Intermetallics. 2018;95:110.
Li M, Flores KM. Laser processing as a high-throughput method to investigate microstructure-processing-property relationships in multiprincipal element alloys. J Alloys Compd. 2020;825: 154025.
Xing Q, Ma J, Zhang Y. Phase thermal stability and mechanical properties analyses of (Cr, Fe, V)-(Ta, W) multiple-based elemental system using a compositional gradient film. Int J Miner Metall Mater. 2020;27(10):1379.
Labusch R. A statistical theory of solid solution hardening. Phys Status Solidi B. 1970;41(2):659.
Fleischer RL. Substitutional solution hardening. Acta Metall. 1963;11(3):203.
Yao HW, Qiao JW, Hawk JA, Zhou HF, Chen MW, Gao MC. Mechanical properties of refractory high-entropy alloys: experiments and modeling. J Alloys Compd. 2017;696:1139.
Varvenne C, Leyson GPM, Ghazisaeidi M, Curtin WA. Solute strengthening in random alloys. Acta Mater. 2017;124:660.
LaRosa CR, Shih M, Varvenne C, Ghazisaeidi M. Solid solution strengthening theories of high-entropy alloys. Mater Charact. 2019;151:310.
Toda-Caraballo I, Rivera-Díaz-del-Castillo PEJ. Modelling solid solution hardening in high entropy alloys. Acta Mater. 2015;85:14.
Moreen HA, Taggart R, Polonis DH. A model for the prediction of lattice parameters of solid solutions. Metall Mater Trans. 1971;2(1):265.
Varvenne C, Luque A, Curtin WA. Theory of strengthening in fcc high entropy alloys. Acta Mater. 2016;118:164.
Yin B, Curtin WA. First-principles-based prediction of yield strength in the RhIrPdPtNiCu high-entropy alloy. npj Comput Mater. 2019;5:14.
Thiel F, Geissler D, Nielsch K, Kauffmann A, Seils S, Heilmaier M, Utt D, Albe K, Motylenko M, Rafaja D, Freudenberger J. Origins of strength and plasticity in the precious metal based high-entropy alloy AuCuNiPdPt. Acta Mater. 2020;185:400.
Li L, Fang Q, Li J, Liu B, Liu Y, Liaw PK. Lattice-distortion dependent yield strength in high entropy alloys. Mater Sci Eng A. 2020;784: 139323.
Zhang L, Xiang Y, Han J, Srolovitz DJ. The effect of randomness on the strength of high-entropy alloys. Acta Mater. 2019;166:424.
Wen C, Zhang Y, Wang C, Xue D, Bai Y, Antonov S, Dai L, Lookman T, Su Y. Machine learning assisted design of high entropy alloys with desired property. Acta Mater. 2019;170:109.
Zou C, Li J, Wang WY, Zhang Y, Lin D, Yuan R, Wang X, Tang B, Wang J, Gao X, Kou H, Hui X, Zeng X, Qian M, Song H, Liu Z-K, Xu D. Integrating data mining and machine learning to discover high-strength ductile titanium alloys. Acta Mater. 2021;202:211.
Wu Q, Wang Z, Hu X, Zheng T, Yang Z, He F, Li J, Wang J. Uncovering the eutectics design by machine learning in the Al–Co–Cr–Fe–Ni high entropy system. Acta Mater. 2020;182:278.
Li Y, Liu Y, Luo S, Wang Z, Wang K, Huang Z, Zhao H, Jiang L. Neural network model for correlating microstructural features and hardness properties of nickel-based superalloys. J Mater Res Technol. 2020;9(6):14467.
Rickman JM, Chan HM, Harmer MP, Smeltzer JA, Marvel CJ, Roy A, Balasubramanian G. Materials informatics for the screening of multi-principal elements and high-entropy alloys. Nat Commun. 2019;10(1):2618.
Islam N, Huang W, Zhuang HL. Machine learning for phase selection in multi-principal element alloys. Comput Mater Sci. 2018;150:230.
Huang W, Martin P, Zhuang HL. Machine-learning phase prediction of high-entropy alloys. Acta Mater. 2019;169:225.
Qin Z, Wang Z, Wang Y, Zhang L, Li W, Liu J, Wang Z, Li Z, Pan J, Zhao L, Liu F, Tan L, Wang J, Han H, Jiang L, Liu Y. Phase prediction of Ni-base superalloys via high-throughput experiments and machine learning. Mater Res Lett. 2020;9(1):32.
Kaufmann K, Vecchio KS. Searching for high entropy alloys: a machine learning approach. Acta Mater. 2020;198:178.
Yan Y, Lu D, Wang K. Accelerated discovery of single-phase refractory high entropy alloys assisted by machine learning. Comput Mater Sci. 2021;199: 110723.
Wu S, Kondo Y, Kakimoto M, Yang B, Yamada H, Kuwajima I, Lambard G, Hongo K, Xu Y, Shiomi J, Schick C, Morikawa J, Yoshida R. Machine-learning-assisted discovery of polymers with high thermal conductivity using a molecular design algorithm. Npj Comput Mater. 2019;5(1):66.
Zhang Y, Ling C. A strategy to apply machine learning to small datasets in materials science. Npj Comput Mater. 2018;4(1):25.
Qian X, Peng S, Li X, Wei Y, Yang R. Thermal conductivity modeling using machine learning potentials: application to crystalline and amorphous silicon. Mater Today Phys. 2019;10: 100140.
Wan J, Jiang JW, Park HS. Machine learning-based design of porous graphene with low thermal conductivity. Carbon. 2020;157:262.
Tan B, Lu Y, Zhou J, Chouhan T, Wang H, Golani P, Xu M, Xu Q, Guan C, Liu Z. Machine learning-guided synthesis of advanced inorganic materials. Mater Today. 2020;41:72.
Raccuglia P, Elbert KC, Adler PD, Falk C, Wenny MB, Mollo A, Zeller M, Friedler SA, Schrier J, Norquist AJ. Machine-learning-assisted materials discovery using failed experiments. Nature. 2016;533(7601):73.
Liu S, Kappes BB, Amin-ahmadi B, Benafan O, Zhang X, Stebner AP. Physics-informed machine learning for composition–process–property design: shape memory alloy demonstration. Appl Mater Today. 2021;22: 100898.
Bhandari U, Rafi MR, Zhang C, Yang S. Yield strength prediction of high-entropy alloys using machine learning. Mater Today Commun. 2021;26: 101871.
Zhang L, Qian K, Huang J, Liu M, Shibuta Y. Molecular dynamics simulation and machine learning of mechanical response in non-equiatomic FeCrNiCoMn high-entropy alloy. J Mater Res Technol. 2021;13:2043.
Li J, Zhang Y, Cao X, Zeng Q, Zhuang Y, Qian X, Chen H. Accelerated discovery of high-strength aluminum alloys by machine learning. Commun Mater. 2020;1(1):73.
Wen C, Wang C, Zhang Y, Antonov S, Xue D, Lookman T, Su Y. Modeling solid solution strengthening in high entropy alloys using machine learning. Acta Mater. 2021;212: 116917.
Rice JR. Dislocation nucleation from a crack tip: An analysis based on the Peierls concept. J Mech Phys Solids. 1992;40(2):239.
Theodore Gray. Periodic Table, https://periodictable.com/About/index.html, Accessed: 20 Jul 2022
Takeuchi A, Inoue A. Classification of bulk metallic glasses by atomic size difference, heat of mixing and period of constituent elements and its application to characterization of the main alloying element. Mater Trans. 2005;46(12):2817.
Zhang Y, Wen C, Wang C, Antonov S, Xue D, Bai Y, Su Y. Phase prediction in high entropy alloys with a rational selection of materials descriptors and machine learning models. Acta Mater. 2020;185:528.
Huang X, Jin C, Zhang C, Zhang H, Fu H. Machine learning assisted modelling and design of solid solution hardened high entropy alloys. Mater Des. 2021;211: 110177.
Natekin A, Knoll A. Gradient boosting machines, a tutorial. Front Neurorobot. 2013;7:21.
Friedman JH. Greedy function approximation: a gradient boosting machine. Ann Stat. 2001;29(5):1189.
Senkov ON, Wilks GB, Scott JM, Miracle DB. Mechanical properties of Nb25Mo25Ta25W25 and V20Nb20Mo20Ta20W20 refractory high entropy alloys. Intermetallics. 2011;19(5):698.
Li Z, Fu L, Zheng H, Yu R, Lv L, Sun Y, Dong X, Shan A. Effect of annealing temperature on microstructure and mechanical properties of a severe cold-rolled FeCoCrNiMn high-entropy alloy. Metall Mater Trans A. 2019;50(7):3223.
Lee C, Chou Y, Kim G, Gao MC, An K, Brechtl J, Zhang C, Chen W, Poplawsky JD, Song G, Ren Y, Chou YC, Liaw PK. Lattice-distortion-enhanced yield strength in a refractory high-entropy alloy. Adv Mater. 2020;32(49):2004029.
An Z, Mao S, Liu Y, Wang L, Zhou H, Gan B, Zhang Z, Han X. A novel HfNbTaTiV high-entropy alloy of superior mechanical properties designed on the principle of maximum lattice distortion. J Mater Res Technol. 2021;79:109.
Wang Z, Fang Q, Li J, Liu B, Liu Y. Effect of lattice distortion on solid solution strengthening of BCC high-entropy alloys. J Mater Res Technol. 2018;34(2):349.
Wang M, Ma ZL, Xu ZQ, Cheng XW. Effects of vanadium concentration on mechanical properties of V NbMoTa refractory high-entropy alloys. Mater Sci Eng A. 2021;808: 140848.
Dong YG, Chen S, Jia NN, Zhang QH, Wang L, Xue YF, Jin K. Microstructures and mechanical properties of Ta–Nb–Zr–Ti–Al refractory high entropy alloys with varying Ta/Ti ratios. Tungsten. 2021;3(4):406.
Natarajan S, Gopalan V, Rajan RAA, Jen CP. Effect of rare earth metals (Y, La) and refractory metals (Mo, Ta, Re) to improve the mechanical properties of W-Ni-Fe alloy-a review. Materials. 2021;14(7):1600.
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This work is supported by the Faculty Startup Fund in the New York State College of Ceramics at Alfred University.
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Yan, YG., Wang, K. The intrinsic strength prediction by machine learning for refractory high entropy alloys. Tungsten 5, 531–538 (2023). https://doi.org/10.1007/s42864-022-00169-y
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DOI: https://doi.org/10.1007/s42864-022-00169-y