Quantitative Relationships Between the Strength-Plasticity and Strength-Electrical Conductivity of Metallic Materials

doi:10.11900/0412.1961.2025.00248

Acta Metall Sin

2026, Vol. 62

Issue (2): 253-262 DOI: 10.11900/0412.1961.2025.00248

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Quantitative Relationships Between the Strength-Plasticity and Strength-Electrical Conductivity of Metallic Materials

ZHANG Zhefeng(

), HOU Jiapeng, LIU Rui, LI Xiaotao, ZHANG Zhenjun, ZHANG Peng

Shenyang National Laboratory for Materials Science, Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110016, China

Cite this article:

ZHANG Zhefeng, HOU Jiapeng, LIU Rui, LI Xiaotao, ZHANG Zhenjun, ZHANG Peng. Quantitative Relationships Between the Strength-Plasticity and Strength-Electrical Conductivity of Metallic Materials. Acta Metall Sin, 2026, 62(2): 253-262.

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Abstract

A general mutual constraint exists between the strength-plasticity and the strength-electrical conductivity of metallic materials. This study proposes an independent space model of dislocation motion to show that the trade-off relation between the strength and plasticity of metallic materials is controlled by the independent spatial size of dislocation motion. Furthermore, the model is used to show that the metal type, alloy composition, deformation temperature, and strain rate are the key factors regulating the spatial size, whereas the microstructure or grain size distribution has a limited influence on it. This finding explains why it is difficult to simultaneously improve strength and plasticity through microstructure or grain size optimization when the metal type, composition, and deformation parameters are fixed. Further, based on the grain size dependence of dislocation piling-up in single-phase alloys, a quantitative trade-off model between tensile strength and uniform elongation is established and experimentally verified in a variety of metal alloy systems. Three high-strength and high-electrical conductivity principles for metal wires are proposed by analyzing the differentiated effects of grain boundaries, orientation, and nanoprecipitation relative dislocation piling-up and electron scattering: elongated grains, strong texture orientation, and nanoprecipitate regulation. Based on the three principles, a quantitative model describing the relationship between strength and electrical conductivity is constructed, and the underlying mechanisms of typical phenomena, such as the synergistic improvement and mutual constraint of strength and electrical conductivity in different metal wires, are systematically explained. Finally, high-performance conductors based on three principles, with performance that breaks through the existing strength-electrical conductivity constraint, are developed. Establishing quantitative models describing the relationships between strength and plasticity, as well as between the strength and electrical conductivity of metallic materials, can efficiently guide material selection, composition design, and microstructure process control, ensuring the service safety of components.

Key words: metallic material strength plasticity electrical conductivity dislocation grain boundary precipitate

Received: 25 August 2025

ZTFLH:

TG113

Fund: National Natural Science Foundation of China(52321001);National Natural Science Foundation of China(52130002);National Natural Science Foundation of China(52322105);National Natural Science Foundation of China(52571160);National Natural Science Foundation of China(52401122);Strategic Priority Research Program of the Chinese Academy of Sciences(XDB1420000)

Corresponding Authors: ZHANG Zhefeng, professor, Tel: (024)23971043, E-mail: zhfzhang@imr.ac.cn

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	ZHANG Zhefeng
	HOU Jiapeng
	LIU Rui
	LI Xiaotao
	ZHANG Zhenjun
	ZHANG Peng

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https://www.ams.org.cn/EN/10.11900/0412.1961.2025.00248 OR https://www.ams.org.cn/EN/Y2026/V62/I2/253

Fig.1 Independent dislocation space and the physical mechanism^[19](a) strength and plasticity related critical dislocation distances (l^* and h^*)
(b) l^*-h^* relation of near saturated screw dislo-cations in Al (Inset in the lower left corner shows annihilation state of dislocations, while inset in the upper right corner shows stable state of disloca-tions. l—pipe-up distance, h—glide plane distance, b—Burgers vector modulus)
(c) dislocation annihilation activation energy (ΔE_act) changing with the dislocation space (A) in Al (ΔE_act→0 when A = A^* (A^* = l^* × h^*). ΔE $a c t 0$ —constant annihilation activation energy, ΔE $a c t *$ —critical annihilation activation energy)

Fig.2 Independent dislocation space and basic strength-plasticity relationship^[19](a) principle of strength and plasticity constraints and synchronous improvement
(b, c) practical cases of synchronous improvement in strength and plasticity by decreasing the stacking fault energy (SFE) (b) and increasing the degree of short-range order (SRO) (c)

Fig.3 Strength-ductility trade-off model^[20]
(a) under external loading, dislocations pile up at the grain boundaries. When the piling-up of dislocations triggers grain-boundary cracking, failure occurs to determine the critical applied stress (D—grain size, τ_c—critical applied stress, H_c—critical height of neighbor slip plane)
(b) accounting for the plastic deformation contributed by dislocation gliding at the critical failure state to calculate the uniform elongation (l'—shear distance of slip plane)
(c) summary of the trade-off model: strength and ductility follow an inverse proportionality. Tuning grain size provides different strength-ductility balances but makes simultaneous improvement. The model indicates three routes to achieve strength-ductility synergy: (1) increasing the intrinsic gliding resistance to dislocations, (2) strengthening interfaces, and
(3) promoting slip uniformity (σ₀—intrinsic resistance to dislocation slip, E_c—critical strain energy density for interfacial cracking, ε₀—elastic strain of about 0.5%)
(d) comparisons between the trade-off model and the experimental data (UTS—ultimate tensile strength, UE—uniform elongation)

Fig.4 Schematics of three principles including fine-long grains, hard texture (L—length of elongated grain, t—width of grain) (a) and nano-scale precipitates (b) for designing metallic conductors with high strength and high electrical conductivity; and quantitative models for strength and electrical conductivity (EC) relating to elongated grain parameters^[22] (YS—yield strength) (c) and precipitate radius (r—radius of precipitate, r_c—critical radius of precipitate) (d)

[1]	Anderson P M, Hirth J P, Lothe J. Theory of Dislocations [M]. 3rd Ed., Cambridge: Cambridge University Press, 2017: 58
[2]	Meyers M, Chawla K, translated by Zhang Z F, Lu L. Mechanical Behavior of Materials [M]. Beijing: Higher Education Press, 2017: 255
	Meyers M, Chawla K著, 张哲峰, 卢磊译. 材料力学行为 [M]. 北京: 高等教育出版社, 2017: 255
[3]	Jiang S H, Wang H, Wu Y, et al. Ultrastrong steel via minimal lattice misfit and high-density nanoprecipitation [J]. Nature, 2017, 544: 460 doi: 10.1038/nature22032
[4]	An X H, Wu S D, Wang Z G, et al. Significance of stacking fault energy in bulk nanostructured materials: Insights from Cu and its binary alloys as model systems [J]. Prog. Mater. Sci., 2019, 101: 1 doi: 10.1016/j.pmatsci.2018.11.001
[5]	Zhang D Y, Qiu D, Gibson M A, et al. Additive manufacturing of ultrafine-grained high-strength titanium alloys [J]. Nature, 2019, 576: 91 doi: 10.1038/s41586-019-1783-1
[6]	Ma K K, Wen H M, Hu T, et al. Mechanical behavior and strengthening mechanisms in ultrafine grain precipitation-strengthened aluminum alloy [J]. Acta Mater., 2014, 62: 141 doi: 10.1016/j.actamat.2013.09.042
[7]	Sohrabi M J, Kalhor A, Mirzadeh H, et al. Tailoring the strengthening mechanisms of high-entropy alloys toward excellent strength-ductility synergy by metalloid silicon alloying: A review [J]. Prog. Mater. Sci., 2024, 144: 101295 doi: 10.1016/j.pmatsci.2024.101295
[8]	Wu H, Fan G H. An overview of tailoring strain delocalization for strength-ductility synergy [J]. Prog. Mater. Sci., 2020, 113: 100675 doi: 10.1016/j.pmatsci.2020.100675
[9]	Wang Y M, Chen M W, Zhou F H, et al. High tensile ductility in a nanostructured metal [J]. Nature, 2002, 419: 912 doi: 10.1038/nature01133
[10]	Lu L, Shen Y F, Chen X H, et al. Ultrahigh strength and high electrical conductivity in copper [J]. Science, 2004, 304: 422 pmid: 15031435
[11]	Wu X L, Yuan F P, Yang M X, et al. Nanodomained nickel unite nanocrystal strength with coarse-grain ductility [J]. Sci. Rep., 2015, 5: 11728 doi: 10.1038/srep11728 pmid: 26122728
[12]	Liu G, Zhang G J, Jiang F, et al. Nanostructured high-strength molybdenum alloys with unprecedented tensile ductility [J]. Nat. Mater., 2013, 12: 344 doi: 10.1038/nmat3544 pmid: 23353630
[13]	Gao J H, Jiang S H, Zhang H R, et al. Facile route to bulk ultrafine-grain steels for high strength and ductility [J]. Nature, 2021, 590: 262 doi: 10.1038/s41586-021-03246-3
[14]	He B B, Hu B, Yen H W, et al. High dislocation density-induced large ductility in deformed and partitioned steels [J]. Science, 2017, 357: 1029 doi: 10.1126/science.aan0177 pmid: 28839008
[15]	Li Z M, Pradeep K G, Deng Y, et al. Metastable high-entropy dual-phase alloys overcome the strength-ductility trade-off [J]. Nature, 2016, 534: 227 doi: 10.1038/nature17981
[16]	Pan Q S, Zhang L X, Feng R, et al. Gradient cell-structured high-entropy alloy with exceptional strength and ductility [J]. Science, 2021, 374: 984 doi: 10.1126/science.abj8114
[17]	Sakai Y, Schneider-Muntau H J. Ultra-high strength, high conductivity Cu-Ag alloy wires [J]. Acta Mater., 1997, 45: 1017 doi: 10.1016/S1359-6454(96)00248-0
[18]	Zhang H T, Fu H D, He X Q, et al. Dramatically enhanced combination of ultimate tensile strength and electric conductivity of alloys via machine learning screening [J]. Acta Mater., 2020, 200: 803 doi: 10.1016/j.actamat.2020.09.068
[19]	Liu R, Li K Q, Zhang Z J, et al. Independent dislocation space model for synchronous improvement of strength and plasticity in fcc metals [J]. J. Mater. Sci. Technol., 2025, 224: 239 doi: 10.1016/j.jmst.2024.12.002
[20]	Li X T, Liu R, Hou J P, et al. Trade-off model for strength-ductility relationship of metallic materials [J]. Acta Mater., 2025, 289: 120942 doi: 10.1016/j.actamat.2025.120942
[21]	Hou J P, Li R, Wang Q, et al. Three principles for preparing Al wire with high strength and high electrical conductivity [J]. J. Mater. Sci. Technol., 2019, 35: 742 doi: 10.1016/j.jmst.2018.11.013
[22]	Hou J P, Li X T, Wang S, et al. Quantitative model for grain boundary effects on strength-electrical conductivity relation [J]. Acta Mater., 2024, 281: 120390 doi: 10.1016/j.actamat.2024.120390
[23]	Ashby M F. Materials Selection in Mechanical Design [M]. 4th Ed., Amsterdam: Elsevier, 2011: 31
[24]	Qu S, An X H, Yang H J, et al. Microstructural evolution and mechanical properties of Cu-Al alloys subjected to equal channel angular pressing [J]. Acta Mater., 2009, 57: 1586 doi: 10.1016/j.actamat.2008.12.002
[25]	Shao C W, Zhang P, Zhu Y K, et al. Simultaneous improvement of strength and plasticity: Additional work-hardening from gradient microstructure [J]. Acta Mater., 2018, 145: 413 doi: 10.1016/j.actamat.2017.12.028
[26]	Li G D, Jiang J X, Ma H C, et al. Superior strength-ductility synergy in three-dimensional heterogeneous-nanostructured metals [J]. Acta Mater., 2023, 256: 119143 doi: 10.1016/j.actamat.2023.119143
[27]	Hirth J P, Lothe J. Theory of Dislocations [M]. 2nd Ed., New York: John Wiley & Sons, Inc., 1982: 764
[28]	Mishin Y, Mehl M J, Papaconstantopoulos D A, et al. Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations [J]. Phys. Rev., 2001, 63B: 224106
[29]	Li K Q, Zhang Z J, Li L L, et al. Effective stacking fault energy in face-centered cubic metals [J]. Acta Metall. Sin. (Engl. Lett.), 2018, 31: 873 doi: 10.1007/s40195-018-0718-4
[30]	Vegge T, Rasmussen T, Leffers T, et al. Determination of the of rate cross slip of screw dislocations [J]. Phys. Rev. Lett., 2000, 85: 3866 pmid: 11041947
[31]	Püschl W, Schoeck G. Calculation of cross-slip parameters in f.c.c. crystals [J]. Mater. Sci. Eng., 1993, A164: 286
[32]	Kocks U F, Mecking H. Physics and phenomenology of strain hardening: The FCC case [J]. Prog. Mater. Sci., 2003, 48: 171 doi: 10.1016/S0079-6425(02)00003-8
[33]	Zhang Z J, Qu Z, Xu L, et al. A general physics-based hardening law for single phase metals [J]. Acta Mater., 2022, 231: 117877 doi: 10.1016/j.actamat.2022.117877
[34]	Han D, Wang Z Y, Yan Y, et al. A good strength-ductility match in Cu-Mn alloys with high stacking fault energies: Determinant effect of short range ordering [J]. Scr. Mater., 2017, 133: 59 doi: 10.1016/j.scriptamat.2017.02.010
[35]	Otto F, Dlouhý A, Somsen C, et al. The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy [J]. Acta Mater., 2013, 61: 5743 doi: 10.1016/j.actamat.2013.06.018
[36]	Yang H K, Zhang Z J, Dong F Y, et al. Strain rate effects on tensile de-formation behaviors for Fe-22Mn-0.6C-(1.5Al) twinning-induced plasticity steel [J]. Mater. Sci. Eng., 2014, A607: 551
[37]	Wang F, Song M, Elkot M N, et al. Shearing brittle intermetallics enhances cryogenic strength and ductility of steels [J]. Science, 2024, 384: 1017 doi: 10.1126/science.ado2919 pmid: 38815014
[38]	Ma E, Liu C. Chemical inhomogeneities in high-entropy alloys help mitigate the strength-ductility trade-off [J]. Prog. Mater. Sci., 2024, 143: 101252 doi: 10.1016/j.pmatsci.2024.101252
[39]	Watanabe T, Tsurekawa S. The control of brittleness and development of desirable mechanical properties in polycrystalline systems by grain boundary engineering [J]. Acta Mater., 1999, 47: 4171 doi: 10.1016/S1359-6454(99)00275-X
[40]	Khalajhedayati A, Pan Z L, Rupert T J. Manipulating the interfacial structure of nanomaterials to achieve a unique combination of strength and ductility [J]. Nat. Commun., 2016, 7: 10802 doi: 10.1038/ncomms10802 pmid: 26887444
[41]	Zhang Z F, Li K Q, Cai T, et al. Effects of stacking fault energy on the deformation mechanisms and mechanical properties of face-centered cubic metals [J]. Acta Metall. Sin., 2023, 59: 467 doi: 10.11900/0412.1961.2022.00548
	张哲峰, 李克强, 蔡拓等. 层错能对面心立方金属形变机制与力学性能的影响 [J]. 金属学报, 2023, 59: 467 doi: 10.11900/0412.1961.2022.00548
[42]	Carlton C E, Ferreira P J. What is behind the inverse Hall-Petch effect in nanocrystalline materials? [J]. Acta Mater., 2007, 55: 3749 doi: 10.1016/j.actamat.2007.02.021
[43]	Hall E O. The deformation and ageing of mild steel: III Discussion of results [J]. Proc. Phys. Soc., 1951, 64B: 747
[44]	Miyajima Y, Komatsu S Y, Mitsuhara M, et al. Change in electrical resistivity of commercial purity aluminium severely plastic deformed [J]. Philos. Mag., 2010, 90: 4475 doi: 10.1080/14786435.2010.510453
[45]	Schmid E, Boas W. Plasticity of Crystals [M]. London: F. A. Hughes & Co. Limited, 1950: 77
[46]	Sauvage X, Bobruk E V, Murashkin M Y, et al. Optimization of electrical conductivity and strength combination by structure design at the nanoscale in Al-Mg-Si alloys [J]. Acta Mater., 2015, 98: 355 doi: 10.1016/j.actamat.2015.07.039
[47]	Bardel D, Perez M, Nelias D, et al. Coupled precipitation and yield strength modelling for non-isothermal treatments of a 6061 aluminium alloy [J]. Acta Mater., 2014, 62: 129 doi: 10.1016/j.actamat.2013.09.041
[48]	Zhang Z, Chen D. Consideration of Orowan strengthening effect in particulate-reinforced metal matrix nanocomposites: A model for predicting their yield strength [J]. Scr. Mater., 2006, 54: 1321 doi: 10.1016/j.scriptamat.2005.12.017
[49]	Seidman D N, Marquis E A, Dunand D C. Precipitation strengthening at ambient and elevated temperatures of heat-treatable Al(Sc) alloys [J]. Acta Mater., 2002, 50: 4021 doi: 10.1016/S1359-6454(02)00201-X
[50]	Booth-Morrison C, Dunand D C, Seidman D N. Coarsening resistance at 400 ^oC of precipitation-strengthened Al-Zr-Sc-Er alloys [J]. Acta Mater., 2011, 59: 7029 doi: 10.1016/j.actamat.2011.07.057
[51]	Ziman J M. Electrons and Phonons: The Theory of Transport Phenomena in Solids [M]. Oxford: Clarendon Press, 1960: 4
[52]	Myhr O R, Grong Ø, Andersen S J. Modelling of the age hardening behaviour of Al-Mg-Si alloys [J]. Acta Mater., 2001, 49: 65 doi: 10.1016/S1359-6454(00)00301-3
[53]	Perez M. Gibbs-Thomson effects in phase transformations [J]. Scr. Mater., 2005, 52: 709 doi: 10.1016/j.scriptamat.2004.12.026
[54]	Simar A, Bréchet Y, de Meester B, et al. Sequential modeling of local precipitation, strength and strain hardening in friction stir welds of an aluminum alloy 6005A-T6 [J]. Acta Mater., 2007, 55: 6133 doi: 10.1016/j.actamat.2007.07.012
[55]	Ma E, Liu C. Achieving alloys with concurrent high strength and high ductility [J]. Acta Metall. Sin., 2025, 61: 665 doi: 10.11900/0412.1961.2024.00422
	马恩, 刘畅. 如何使合金兼具高强度与高塑性 [J]. 金属学报, 2025, 61: 665

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