Qiang Li

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Recently the final worn shape of elastic indenters due to fretting wear was analytically solved using the method of dimensionality reduction. In this paper we extend this model to dual-motion fretting wear and take into account that the indenter is initially pressed with constant indentation depth and moved horizontally with constant displacement. Two key parameters, the maximal indentation depth during oscillation and the stick area radius in the final state as well as the liming shape of indenter are analytically calculated. It is shown that the oscillation amplitudes and the initially indented or moved displacements have an influence on the final shaking-down shape.


Fretting Wear, Dual-motion, Tangential Force, Oscillation

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Kennedy, P., Peterson, M.B., Stallings, L., 1982, An Evaluation of Fretting at Small Slip Amplitudes. In: Materials Evaluation under Fretting Conditions, ASTM Spec. Tech. Publ., 780, pp. 30–48.

Zhang, H., Brown, L.T., Blunt, L.A., Jiang, X., Barrans, S.M., 2009, Understanding initiation and propagation of fretting wear on the femoral stem in total hip replacement, Wear, 266, pp. 566–569.

Zheng, J. F. et al., 2010, Fretting wear behaviors of a railway axle steel, Tribol. Int. 43, pp. 906–911.

Antler, M., 1985, Electrical effects of fretting connector contact materials: A review, Wear, 106, pp. 5–33.

Szolwinski, M.P., Farris, T.N., 1996, Mechanics of fretting fatigue crack formation, Wear, 198, pp. 93–107.

Fisher, N.J., Chow, A.B., Weckwerth, M.K., 1995, Experimental Fretting Wear Studies of Steam Generator Materials, J. Press. Vessel Technol., 117, pp. 312–320.

Liu, J., Shen, H.M., Yang, Y.R., 2014, Finite element implementation of a varied friction model applied to torsional fretting wear, Wear, 314, pp. 220–227.

Ciavarella, M., Demelio, G., 2001, A review of analytical aspects of fretting fatigue, with extension to damage parameters, and application to dovetail joints, Int. J. Solids Struct., 38, pp. 1791–1811.

Popov, V.L., 2014, Analytic solution for the limiting shape of profiles due to fretting wear, Sci. Rep., 4, 3749.

Dimaki, A.V., Dmitriev, A.I., Chai, Y.S., Popov V.L., 2014, Rapid simulation procedure for fretting wear on the basis of the method of dimensionality reduction, Int. J. Solids Struct., 51, pp. 4215–4220.

Li, Q., Filippov, A.E., Dimaki, A.V., Chai, Y.S., Popov, V.L., 2014, Simplified simulation of fretting wear using the method of dimensionality reduction, Phys. Mesomech., 17, pp. 236-241.

Dimaki, A.V., Dmitriev, A.I., Menga, N., Papangelo, A., Ciavarella, M., Popov, V.L., 2016, Fast High-Resolution Simulation of the Gross Slip Wear of Axially Symmetric Contacts, Tribol. Trans., 59, pp. 189-194.

Mao, X.Y., Liu, W., Ni, Y.Z., Popov, V.L., 2015, Limiting shape of profile due to dual-mode fretting wear in a contact with an elastomer, J. Mech. Eng. Sci., 203-210, pp. 1989-1996.

Dimaki, A.V., Popov, V.L., 2015, A model of fretting wear in the contact of an axisymmetric indenter and a visco-elastic half-space, AIP Conf. Proc., 1683, 020040.

Dmitriev, A.I., Voll, L.B., Psakhie, S.G., Popov, V.L., 2016, Universal limiting shape of worn profile under multiple-mode fretting conditions: theory and experimental evidence, Sci. Rep., 6, 23231.

Reye, T., 1860, Zur Theorie der Zapfenreibung, Der Civil., 4, pp. 235–255.

Popov, V.L., 2010, Contact mechanics and friction, Springer, Berlin.

Popov, V.L., 2013, Method of reduction of dimensionality in contact and friction mechanics: A linkage between micro and macro scales, Friction, 1, pp. 41–62.

Popov, V.L., Heß, M., 2015, Method of dimensionality reduction in contact mechanics and friction, Springer, Berlin.

Heß, M., 2011, Über die Abbildung ausgewählter dreidimensionaler Kontakte auf Systeme mit niedrigerer räumlicher Dimension, Cuvillier-Verlag, Göttingen.

Heß, M., 2012, On the reduction method of dimensionality: The exact mapping of axisymmetric contact problems with and without adhesion, Phys. Mesomech., 15, pp. 264–269.



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