REFERENCES
1. Li, L.; Zhang, Z.; Zhang, P.; Zhang, Z. A review on the fatigue cracking of twin boundaries: crystallographic orientation and stacking fault energy. Prog. Mater. Sci. 2023, 131, 101011.
2. Pineau, A.; Amine Benzerga, A.; Pardoen, T. Failure of metals III: fracture and fatigue of nanostructured metallic materials. Acta. Mater. 2016, 107, 508-44.
3. Liu, R.; Tian, Y. Z.; Zhang, Z. J.; Zhang, P.; An, X. H.; Zhang, Z. F. Exploring the fatigue strength improvement of Cu-Al alloys. Acta. Mater. 2018, 144, 613-26.
4. Koyama, M.; Zhang, Z.; Wang, M. M.; et al. Bone-like crack resistance in hierarchical metastable nanolaminate steels. Science 2017, 355, 1055-7.
5. Qu, Z.; Zhang, Z.; Liu, R.; et al. High fatigue resistance in a titanium alloy via near-void-free 3D printing. Nature 2024, 626, 999-1004.
6. Zhao, Q.; Li, X.; Hu, J.; Jiang, Y.; Yang, K.; Wang, Q. Ultra-high cycle fatigue and ultra-slow crack growth behavior of additively manufactured AlSi7Mg alloy. Int. J. Struct. Integr. 2024, 15, 382-407.
7. Liu, R.; Zhang, P.; Zhang, Z. J.; Wang, B.; Zhang, Z. F. A practical model for efficient anti-fatigue design and selection of metallic materials: I. Model building and fatigue strength prediction. J. Mater. Sci. Technol. 2021, 70, 233-49.
8. Stinville, J. C.; Charpagne, M. A.; Cervellon, A.; et al. On the origins of fatigue strength in crystalline metallic materials. Science 2022, 377, 1065-71.
9. Yang, S.; Meng, D.; Díaz, A.; Yang, H.; Su, X.; de Jesus, A. M. P. Probabilistic modeling of uncertainties in reliability analysis of mid-and high-strength steel pipelines under hydrogen-induced damage. Int. J. Struct. Integr. 2025, 16, 39-59.
10. Pineau, A.; Mcdowell, D. L.; Busso, E. P.; Antolovich, S. D. Failure of metals II: fatigue. Acta. Mater. 2016, 107, 484-507.
11. Renk, O.; Hohenwarter, A.; Gammer, C.; Eckert, J.; Pippan, R. Achieving 1 GPa fatigue strength in nanocrystalline 316L steel through recovery annealing. Scr. Mater. 2022, 217, 114773.
13. Wang, B.; Zhang, P.; Duan, Q. Q.; et al. Synchronously improved fatigue strength and fatigue crack growth resistance in twinning-induced plasticity steels. Mater. Sci. Eng. A. 2018, 711, 533-42.
14. Lu, L.; Pan, Q.; Hattar, K.; Boyce, B. L. Fatigue and fracture of nanostructured metals and alloys. MRS. Bull. 2021, 46, 258-64.
15. Wang, X. Q.; Han, W. Z. Oxygen-gradient titanium with high strength, strain hardening and toughness. Acta. Mater. 2023, 246, 118674.
16. Dan, X.; Ren, C.; Song, Z.; et al. Exceptional strength and ductility in heterogeneous multi-gradient TiAl alloys through additive manufacturing. Acta. Mater. 2024, 281, 120395.
17. Wu, D.; Hao, M.; Zhang, T.; et al. Heterostructures enhance simultaneously strength and ductility of a commercial titanium alloy. Acta. Mater. 2023, 257, 119182.
18. Li, X.; Lu, L.; Li, J.; Zhang, X.; Gao, H. Mechanical properties and deformation mechanisms of gradient nanostructured metals and alloys. Nat. Rev. Mater. 2020, 5, 706-23.
19. Cheng, Z.; Zhou, H.; Lu, Q.; Gao, H.; Lu, L. Extra strengthening and work hardening in gradient nanotwinned metals. Science 2018, 362, eaau1925.
20. Ren, C. X.; Wang, Q.; Hou, J. P.; Zhang, Z. J.; Zhang, Z. F.; Langdon, T. G. The nature of the maximum microhardness and thickness of the gradient layer in surface-strengthened Cu-Al alloys. Acta. Mater. 2021, 215, 117073.
21. Liu, Z.; Zhao, D.; Wang, P.; et al. Additive manufacturing of metals: microstructure evolution and multistage control. J. Mater. Sci. Technol. 2022, 100, 224-36.
22. Wu, X.; Yang, M.; Yuan, F.; et al. Heterogeneous lamella structure unites ultrafine-grain strength with coarse-grain ductility. Proc. Natl. Acad. Sci. U. S. A. 2015, 112, 14501-5.
23. Lee, H. H.; Yoon, J. I.; Park, H. K.; Kim, H. S. Unique microstructure and simultaneous enhancements of strength and ductility in gradient-microstructured Cu sheet produced by single-roll angular-rolling. Acta. Mater. 2019, 166, 638-49.
24. Zhang, Y.; Cheng, Z.; Lu, L.; Zhu, T. Strain gradient plasticity in gradient structured metals. J. Mech. Phys. Solids. 2020, 140, 103946.
25. Zhang, Y.; He, C.; Yu, Q.; et al. Nacre-like surface nanolaminates enhance fatigue resistance of pure titanium. Nat. Commun. 2024, 15, 6917.
26. Jiang, X. P.; Wang, X. Y.; Li, J. X.; et al. Enhancement of fatigue and corrosion properties of pure Ti by sandblasting. Mater. Sci. Eng. A. 2006, 429, 30-5.
27. Wang, Q.; Sun, Q.; Xiao, L.; Sun, J. Effect of surface nanocrystallization on fatigue behavior of pure titanium. J. Mater. Eng. Perform. 2015, 25, 241-9.
28. Li, X.; Sun, B. H.; Guan, B.; et al. Elucidating the effect of gradient structure on strengthening mechanisms and fatigue behavior of pure titanium. Int. J. Fatigue. 2021, 146, 106142.
29. Kim, W. J.; Hyun, C. Y.; Kim, H. K. Fatigue strength of ultrafine-grained pure Ti after severe plastic deformation. Scr. Mater. 2006, 54, 1745-50.
30. Fintová, S.; Kunz, L.; Chlup, Z.; et al. Grain refinement effect on fatigue life of two grades of commercially pure titanium. Int. J. Fatigue. 2023, 176, 107883.
31. Lu, K.; Chauhan, A.; Knöpfle, F.; Aktaa, J. Effective and back stresses evolution upon cycling a high-entropy alloy. Mater. Res. Lett. 2022, 10, 369-76.
32. Zhu, Y.; Wu, X. Perspective on hetero-deformation induced (HDI) hardening and back stress. Mater. Res. Lett. 2019, 7, 393-8.
33. Fang, X. T.; He, G. Z.; Zheng, C.; et al. Effect of heterostructure and hetero-deformation induced hardening on the strength and ductility of brass. Acta. Mater. 2020, 186, 644-55.
34. Wang, C.; Ding, L.; Shi, S.; et al. Origin mechanism of heterostructure nanograins with gradient grain size suppressing strain localization. Mater. Sci. Eng. A. 2023, 885, 145584.
35. Li, L. L.; Zhang, Z. J.; Zhang, P.; Wang, Z. G.; Zhang, Z. F. Controllable fatigue cracking mechanisms of copper bicrystals with a coherent twin boundary. Nat. Commun. 2014, 5, 3536.
36. Zhang, Z.; Wang, Z. Comparison of fatigue cracking possibility along large-and low-angle grain boundaries. Mater. Sci. Eng. A. 2020, 284, 285-91.
37. Hamada, A. S.; Karjalainen, L. P.; Surya, P. K. C. V.; Misra, R. D. K. Fatigue behavior of ultrafine-grained and coarse-grained Cr-Ni austenitic stainless steels. Mater. Sci. Eng. A. 2011, 528, 3890-6.
38. Schouwenaars, R.; Seefeldt, M.; Van Houtte, P. The stress field of an array of parallel dislocation pile-ups: implications for grain boundary hardening and excess dislocation distributions. Acta. Mater. 2010, 58, 4344-53.
39. Stricker, M.; Weygand, D.; Gumbsch, P. Irreversibility of dislocation motion under cyclic loading due to strain gradients. Scr. Mater. 2017, 129, 69-73.
40. Qu, Z.; Zhang, Z. J.; Zhu, Y. K.; et al. Coupling effects of microstructure and defects on the fatigue properties of laser powder bed fusion Ti-6Al-4V. Addit. Manuf. 2023, 61, 103355.
