Abstract
A contact problem is considered for an elastic axisymmetric indenter, the shape of which is described by a power-law function, and an elastic half-space in the conditions of capillary adhesion, i.e., in the presence of a liquid meniscus pulling onto the surfaces outside the contact region. The contacting bodies are subjected to normal and tangential loads under the conditions of partial slip, the two-term Coulomb friction law being assumed in the slip region. Under the assumption of similar materials of the indenter and half-space, the analytic relations are obtained for the tangential stress distribution in the contact region, tangential load and displacement, as well as the equation for the determination of the stick region radius. The contact characteristics are analyzed depending on the indenter shape, surface tension of the liquid, and capillary pressure in the meniscus.
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REFERENCES
Y. Sun, C. Song, Z. Liu, et al., “Effect of relative humidity on the tribological/conductive properties of Cu/Cu rolling contact pairs,” Wear 436, 203023 (2019).
R. Maboudian, W. R. Ashurst, and C. Carraro, “Tribological challenges in micromechanical systems,” Tribol. Lett. 12, 95–100 (2002).
M. Klaassen, E. G. de Vries, and M. A. Masen, “The static friction response of non-glabrous skin as a function of surface energy and environmental conditions,” Biotribology 11, 124–131 (2017).
C. Cattaneo, “Sul contatto di due corpi elastici: distribuzione locale degli sforzi,” Atti Accad. Naz. Lincei, Cl. Sci. Fis., Mat. Nat., Rend. 27, 342–348 (1938).
R. D. Mindlin, “Compliance of elastic bodies in contact,” ASME Trans. J. Appl. Mech. 16, 259–268 (1949).
J. Jäger, “Axi-symmetric bodies of equal material in contact under torsion or shift,” Arch. Appl. Mech. 65, 478–487 (1995).
M. Ciavarella, “Tangential loading of general three-dimensional contacts,” ASME Trans. J. Appl. Mech. 65 (4), 998–1003 (1998).
I. Argatov and G. Mishuris, “Tangential contact of elastically similar bodies,” in Indentation Testing of Biological Materials (Springer, Cham, 2018), pp. 129–146.
I. G. Goryacheva, N. I. Malanchuk, and P. M. Martynyak, “Contact interaction of bodies with periodic relief during partial slip,” J. Appl. Math. Mech. 76 (5), 621–630 (2012).
A. N. Lyubicheva and I. Y. Tsukanov, “The influence of 2D periodic surface texture on the partial slip problem for elastic bodies,” Eur. J. Mech. A 91, 104405 (2022).
O. T. Sari, G. G. Adams, and S. Muftu, “Nano-scale effects in the sliding and rolling of a cylinder on a substrate,” ASME Trans. J. Appl. Mech. 72 (5), 633–640 (2005).
G. G. Adams, “Stick, partial slip and sliding in the plane strain micro contact of two elastic bodies,” R. Soc. Open Sci. 1, 140363 (2014).
J. Yan and G. Huang, “A double-hertz model for adhesive contact between cylinders under inclined forces,” Proc. R. Soc. A 475, 20180589 (2019).
A. R. Savkoor, Dry Adhesive Friction of Elastomers: a Study of the Fundamental Mechanical Aspects (Univ. Technol., Delft, 1987).
V. L. Popov and A. V. Dimaki, “Friction in an adhesive tangential contact in the Coulomb-Dugdale approximation,” J. Adhesion 93 (14), 1131–1145 (2017).
M. Bazrafshan, M. B. Rooij, and D. J. Schipper, “On the role of adhesion and roughness in stick-slip transition at the contact of two bodies: a numerical study,” Tribol. Int. 121, 381–388 (2018).
I. G. Goryacheva and Y. Y. Makhovskaya, “Capillary adhesion in the contact between elastic solids,” J. Appl. Math. Mech. 63 (1), 117–122 (1999).
K. Johnson, Contact Mechanics (Univ. Press, Cambridge, 1985).
V. I. Dovnorovich and V. F. Yashin, Some Three-Dimensional Problems of the Theory of Elasticity (Belorussian Institute of Railway Engineering, Gomel, 1961) [in Russian].
L. A. Galin, Contact Problems. The Legacy of L. A. Galin, Ed. by G. M. L. Gladwell (Nauka, Moscow, 1980; Springer, 2008).
B. V. Derjaguin, N. V. Churaev, and V. M. Muller, Surface Forces (Nauka, Moscow, 1985; Consultants Bureau, New York, 1987).
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The study was supported by the Russian Foundation for Basic Research, grant no. 21-58-52006.
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Translated by M. Chubarova
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Makhovskaya, Y.Y. Capillary Adhesion of Elastic Bodies under the Conditions of Partial Slip. Mech. Solids 57, 1689–1700 (2022). https://doi.org/10.3103/S0025654422070123
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DOI: https://doi.org/10.3103/S0025654422070123