References
- Hughes D, Hansen N. Graded nanostructures produced by sliding and exhibiting universal behavior. Phys Rev Lett. 2001;87(13):135503.
- Suresh S. Graded materials for resistance to contact deformation and damage. Science. 2001;292(5526):2447–2451.
- Wu X, Jiang P, Chen L, et al. Extraordinary strain hardening by gradient structure. Proc Natl Acad Sci U S A. 2014;111(20):7197–7201.
- Ma E, Zhu T. Towards strength–ductility synergy through the design of heterogeneous nanostructures in metals. Mater Today. 2017;20(6):323–331.
- Cheng Z, Zhou H, Lu Q, et al. Extra strengthening and work hardening in gradient nanotwinned metals. Science. 2018;362:6414.
- Wang YF, Wang MS, Fang XT, et al. Extra strengthening in a coarse/ultrafine grained laminate: role of gradient interfaces. Int J Plast. 2019;123:196–207.
- Wu X, Jiang P, Chen L, et al. Synergetic strengthening by gradient structure. Mater Res Lett. 2014;2(4):185–191.
- Yang M, Pan Y, Yuan F, et al. Back stress strengthening and strain hardening in gradient structure. Mater Res Lett. 2016;4(3):145–151.
- Huang H, Wang Z, Lu J, et al. Fatigue behaviors of AISI 316L stainless steel with a gradient nanostructured surface layer. Acta Mater. 2015;87:150–160.
- Hasan MN, Liu YF, An XH, et al. Simultaneously enhancing strength and ductility of a high-entropy alloy via gradient hierarchical microstructures. Int J Plast. 2019;123:178–195.
- Chen G, Qiao JW, Jiao ZM, et al. Strength-ductility synergy of Al0.1CoCrFeNi high-entropy alloys with gradient hierarchical structures. Scr Mater. 2019;167:95–100.
- Fu Z, MacDonald BE, Li Z, et al. Engineering heterostructured grains to enhance strength in a single-phase high-entropy alloy with maintained ductility. Mater Res Lett. 2018;6(11):634–640.
- Wu H, Fan G. An overview of tailoring strain delocalization for strength-ductility synergy. Prog Mater Sci. 2020;113:100675.
- Lee HH, Yoon JI, Park HK, et al. Unique microstructure and simultaneous enhancements of strength and ductility in gradient-microstructured Cu sheet produced by single-roll angular-rolling. Acta Mater. 2019;166:638–649.
- Lu X, Zhang X, Shi M, et al. Dislocation mechanism based size-dependent crystal plasticity modeling and simulation of gradient nano-grained copper. Int J Plast. 2019;113:52–73.
- Zhu Y, Ameyama K, Anderson PM, et al. Heterostructured materials: superior properties from hetero-zone interaction. Mater Res Lett. 2021;9(1):1–31.
- Fang T, Li W, Tao N, et al. Revealing extraordinary intrinsic tensile plasticity in gradient nano-grained copper. Science. 2011;331(6024):1587–1590.
- Wu X, Zhu Y. Heterogeneous materials: a new class of materials with unprecedented mechanical properties. Mater Res Lett. 2017;5(8):527–532.
- Cheng Z, Bu L, Zhang Y, et al. Unraveling the origin of extra strengthening in gradient nanotwinned metals. Proc Natl Acad Sci U S A. 2022;119:3.
- Ungár T, Ott S, Sanders P, et al. Dislocations, grain size and planar faults in nanostructured copper determined by high resolution X-ray diffraction and a new procedure of peak profile analysis. Acta Mater. 1998;46(10):3693–3699.
- Williamson G, Smallman R. Dislocation densities in some annealed and cold-worked metals from measurements on the X-ray Debye-Scherrer spectrum. Philos Mag. 1956;1(1):34–46.
- He B, Hu B, Yen H, et al. High dislocation density–induced large ductility in deformed and partitioned steels. Science. 2017;357(6355):1029–1032.
- Wang M, Xu XY, Wang HY, et al. Evolution of dislocation and twin densities in a Mg alloy at quasi-static and high strain rates. Acta Mater. 2020;201:102–113.
- Pantleon W. Resolving the geometrically necessary dislocation content by conventional electron backscattering diffraction. Scr Mater. 2008;58(11):994–997.
- Lebensohn R, Tomé C. A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: application to zirconium alloys. Acta Metall Mater. 1993;41(9):2611–2624.
- Beyerlein IJ, Tomé CN. A dislocation-based constitutive law for pure Zr including temperature effects. Int J Plast. 2008;24(5):867–895.
- Oliver D. Proposed new criteria of ductility from a new law connecting the percentage elongation with size of test-piece. Proc Inst Mech Eng. 1928;115(1):827–864.
- Mathew M, Mannan S, Rodriguez P. Influence of gage dimensions on elongation values for type 316 stainless steel. J Test Eval. 1985;13(3):191–195.
- Hatakeyama K, Sugawara A, Tojyo T, et al. Factors affecting bend formability of tempered copper alloy sheets. Mater Trans. 2002;43(11):2908–2912.
- Kupke A, Barnett M, Luckey G, et al. Determination of the bendability of ductile materials. IOP Conf Ser Mater Sci Eng. 2018;418:0012077.
- Gong Y, Wu Y, Hua M, et al. Influence of processing factors on the sheared-edge formability of vanadium bearing dual-phase steels produced using continuous galvanizing line simulations. J Mater Sci. 2020;55(13):5639–5654.
- Li D, Fan G, Huang X, et al. Enhanced strength in pure Ti via design of alternating coarse- and fine-grain layers. Acta Mater. 2021;206:116627.
- 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(47):14501–14505.
- Huang CX, Wang YF, Ma XL, et al. Interface affected zone for optimal strength and ductility in heterogeneous laminate. Mater Today. 2018;21(7):713–719.
- Ojima M, Inoue J, Nambu S, et al. Stress partitioning behavior of multilayered steels during tensile deformation measured by in situ neutron diffraction. Scr Mater. 2012;66(3-4):139–142.
- Huang M, Xu C, Fan G, et al. Role of layered structure in ductility improvement of layered Ti-Al metal composite. Acta Mater. 2018;153:235–249.
- Ma XL, Huang CX, Xu WZ, et al. Strain hardening and ductility in a coarse-grain/nanostructure laminate material. Scr Mater. 2015;103:57–60.
- Wang Y, Wei Y, Zhao Z, et al. Activating dispersed strain bands in tensioned nanostructure layer for high ductility: the effects of microstructure inhomogeneity. Int J Plast. 2022;149:103159.
- Wang Y, Huang C, Li Y, et al. Dense dispersed shear bands in gradient-structured Ni. Int J Plast. 2020;124:186–198.
- Cao R, Yu Q, Pan J, et al. On the exceptional damage-tolerance of gradient metallic materials. Mater Today. 2020;32:94–107.
- Hong SI, Laird C. Mechanisms of slip mode modification in F.C.C. solid solutions. Acta Metall Mater. 1990;38(8):1581–1594.
- Pierce DT, Jiménez JA, Bentley J, et al. The influence of stacking fault energy on the microstructural and strain-hardening evolution of Fe–Mn–Al–Si steels during tensile deformation. Acta Mater. 2015;100:178–190.
- Neeraj T, Mills M. Short-range order (SRO) and its effect on the primary creep behavior of a Ti–6wt.%Al alloy. Mater Sci Eng A. 2001;319-321:415–419.
- Csontos AA, Starke EA. The effect of inhomogeneous plastic deformation on the ductility and fracture behavior of age hardenable aluminum alloys. Int J Plast. 2005;21(6):1097–1118.
- Wang Z. Cyclic deformation response of planar-slip materials and a new criterion for the wavy-to-planar-slip transition. Philos Mag. 2004;84(3-5):351–379.
- Gutierrez-Urrutia I, Raabe D. Dislocation and twin substructure evolution during strain hardening of an Fe–22wt.% Mn–0.6wt.% C TWIP steel observed by electron channeling contrast imaging. Acta Mater. 2011;59(16):6449–6462.
- Li P, Li SX, Wang ZG, et al. Unified factor controlling the dislocation evolution of fatigued face-centered cubic crystals. Acta Mater. 2017;129:98–111.
- Bayley C, Brekelmans W, Geers M. A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity. Int J Solids Struct. 2006;43(24):7268–7286.
- Li J, Weng GJ, Chen S, et al. On strain hardening mechanism in gradient nanostructures. Int J Plast. 2017;88:89–107.