Abstract
The contact problem of deformed rough surfaces exists widely in complex engineering structures. How to reveal the influence mechanism of surface deformation on the contact properties is a key issue in evaluating the interface performances of the engineering structures. In this paper, a contact model is established, which is suitable for tensile and bending deformed contact surfaces. Four contact forms of asperities are proposed, and their distribution characteristics are analyzed. This model reveals the mechanism of friction generation from the perspective of the force balance of asperity. The results show the contact behaviors of the deformed contact surface are significantly different from that of the plane contact, which is mainly reflected in the change in the number of contact asperities and the real contact area. This study suggests that the real contact area of the interface can be altered by applying tensile and bending strains, thereby regulating its contact mechanics and conductive behavior.
摘要
粗糙界面的变形接触问题广泛存在于复杂的工程结构中. 如何揭示界面变形对接触特性的影响机制, 是评价工程结构界面性能 的关键问题. 本文建立了一个适用于拉伸和弯曲变形接触表面的接触模型, 提出了四种微凸体接触形式, 并分析了它们的分布特性. 该 模型从微凸体力平衡的角度揭示了摩擦产生的机制. 结果表明, 变形接触表面的接触行为与平面接触显著不同, 这主要体现在接触微 凸体数量和真实接触面积的变化上. 本研究表明, 通过施加拉伸和弯曲应变, 可以改变界面的真实接触面积, 从而调节其接触力学和导 电行为.
References
V. Phifer, M. Small, G. Bradford, J. Weiss, D. van der Laan, and L. Cooley, Investigations in the tape-to-tape contact resistance and contact composition in superconducting CORC® wires, Supercond. Sci. Technol. 35, 065003 (2022).
H. Zhao, W. R. Ta, Y. H. Zhou. The mechanical-thermal-electro contact behaviors between rough surfaces under cyclic loading. Acta. Mech. Sin. 39, 123212 (2023).
A. Yalpanian, and R. Guilbault, A fast correction for half-space theory applied to contact modeling of bodies with curved free surfaces, Tribol. Int. 147, 106292 (2020).
Y. Liu, Q. Meng, X. Yan, S. Zhao, and J. Han, Research on the solution method for thermal contact conductance between circular-arc contact surfaces based on fractal theory, Int. J. Heat Mass Transfer 145, 118740 (2019).
J. J. Gagnepain, and C. Roques-Carmes, Fractal approach to two-dimensional and three-dimensional surface roughness, Wear 109, 119 (1986).
R. Buczkowski, and M. Kleiber, Statistical models of rough surfaces for finite element 3D-contact analysis, Arch. Computat. Methods Eng. 16, 399 (2009).
P. Prokopovich, and V. Starov, Adhesion models: From single to multiple asperity contacts, Adv. Colloid Interface Sci. 168, 210 (2011).
B. A. Galanov, Models of adhesive contact between rough elastic solids, Int. J. Mech. Sci. 53, 968 (2011).
J. A. Greenwood, J. B. P. Williamson, Contact of nominally flat surface. Proc. Roy. Soc. Lond. 295, 300–319 (1966).
J. A. Greenwood, The area of contact between rough surfaces and flats, J. Lubrication Tech. 89, 81 (1967).
J. A. Greenwood, and J. H. Tripp, The elastic contact of rough spheres, J. Appl. Mech. 34, 153 (1967).
J. A. Greenwood, and J. H. Tripp, The contact of two nominally flat rough surfaces, Proc. Institution Mech. Eng. 185, 625 (1971).
X. Guo, B. Ma, and Y. Zhu, A magnification-based multi-asperity (MBMA) model of rough contact without adhesion, J. Mech. Phys. Solids 133, 103724 (2019).
H. Song, A. I. Vakis, X. Liu, and E. van der Giessen, Statistical model of rough surface contact accounting for size-dependent plasticity and asperity interaction, J. Mech. Phys. Solids 106, 1 (2017).
A. Majumdar, and B. Bhushan, Fractal model of elastic-plastic contact between rough surfaces, J. Tribol. 113, 1 (1991).
W. Yan, and K. Komvopoulos, Contact analysis of elastic-plastic fractal surfaces, J. Appl. Phys. 84, 3617 (1998).
A. Majumdar, and C. L. Tien, Fractal characterization and simulation of rough surfaces, Wear 136, 313 (1990).
B. N. J. Persson, F. Bucher, and B. Chiaia, Elastic contact between randomly rough surfaces: Comparison of theory with numerical results, Phys. Rev. B 65, 184106 (2002).
B. N. J. Persson, Contact mechanics for randomly rough surfaces, Surf. Sci. Rep. 61, 201 (2006).
B. N. J. Persson, Theory of rubber friction and contact mechanics, J. Chem. Phys. 115, 3840 (2001).
B. N. J. Persson, Relation between interfacial separation and load: A general theory of contact mechanics, Phys. Rev. Lett. 99, 125502 (2007).
A. Emami, S. Khaleghian, and S. Taheri, Asperity-based modification on theory of contact mechanics and rubber friction for self-affine fractal surfaces, Friction 9, 1707 (2021).
Y. Wen, J. Tang, W. Zhou, L. Li, and C. Zhu, New analytical model of elastic-plastic contact for three-dimensional rough surfaces considering interaction of asperities, Friction 10, 217 (2022).
Y. H. Li, F. Shen, M. A. Güler, and L. L. Ke, A rough surface electrical contact model considering the interaction between asperities, Tribol. Int. 190, 109044 (2023).
F. Shen, Y. H. Li, and L. L. Ke, On the size distribution of truncation areas for fractal surfaces, Int. J. Mech. Sci. 237, 107789 (2023).
F. Shen, Y. H. Li, and L. L. Ke, A novel fractal contact model based on size distribution law, Int. J. Mech. Sci. 249, 108255 (2023).
J. C. Mergel, J. Scheibert, and R. A. Sauer, Contact with coupled adhesion and friction: Computational framework, applications, and new insights, J. Mech. Phys. Solids 146, 104194 (2021).
X. Yu, Y. Sun, D. Zhao, and S. Wu, A revised contact stiffness model of rough curved surfaces based on the length scale, Tribol. Int. 164, 107206 (2021).
J. L. Liou, C. M. Tsai, and J. F. Lin, A microcontact model developed for sphere- and cylinder-based fractal bodies in contact with a rigid flat surface, Wear 268, 431 (2010).
M. F. R. Zwicker, J. Spangenberg, N. Bay, P. A. F. Martins, and C. V. Nielsen, The influence of strain hardening and surface flank angles on asperity flattening under subsurface deformation at low normal pressures, Tribol. Int. 167, 107416 (2022).
D. Kono, Y. Jorobata, and H. Isobe, Holistic multi-scale model of contact stiffness considering subsurface deformation, CIRP Ann. 70, 447 (2021).
Halling J. Principles of Tribology (Macmillan, London, 1975).
K. Yamada, N. Takeda, J. Kagami, and T. Naoi, Mechanisms of elastic contact and friction between rough surfaces, Wear 48, 15 (1978).
B. Bhushan, and M. T. Dugger, Real contact area measurements on magnetic rigid disks, Wear 137, 41 (1990).
A. W. Bush, R. D. Gibson, and T. R. Thomas, The elastic contact of a rough surface, Wear 35, 87 (1975).
S. H. Wang, W. K. Yuan, X. M. Liang, and G. F. Wang, A new analytical model for the flattening of Gaussian rough surfaces, EUR. J. MECH. A-SOLID 94, 104578 (2022).
Acknowledgements
This work are supported by the Natural Science Foundation of China General Program (Grant No. 12272157), the Natural Science Foundation of China Major Program (Grant No. 12327901), the Fundamental Research Funds for the Central Universities (Grant No. lzujbky-2023-ey05), and the 111 Project (Grant No. B14044).
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Author contributions Xiaoyu Tang carried out the research and results analysis, helped organize the manuscript, and revised the final version. Wurui Ta was responsible for the conceptualization and supervision, offered methodology and funding acquisition, and wrote the initial draft, revised and edited the final version. Youhe Zhou was responsible for the conceptualization and supervision, and offered funding acquisition.
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Tang, X., Ta, W. & Zhou, Y. Contact behaviors of rough surfaces under tension and bending. Acta Mech. Sin. 41, 424067 (2025). https://doi.org/10.1007/s10409-024-24067-x
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DOI: https://doi.org/10.1007/s10409-024-24067-x