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Acta Mechanica

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21-03-2023 | Original Paper

A modified Greenwood–Williamson contact model with asperity interactions

Authors: Cheng-Ya Li, Gang-Feng Wang

Published in: Acta Mechanica | Issue 7/2023

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Abstract

Accurate relation between load and area is of great interest in tribology, especially for large contact fraction, in which the asperity interactions play an import role. The constant mean contact radius obtained in the original Greenwood–Williamson model is adopted in this work; Then, the asperity interactions are dealt with by arranging the random distributed contact spots to hexagon distribution. Finite element simulation is employed to consider only a representative unit with symmetrical boundary conditions, and the corresponding load-area relation is determined up to almost complete contact. For a given contact fraction, interactions induce larger load compared to the GW model without asperity interactions. Furthermore, by comparing with the analytical result given by an incremental contact for small contact fraction, the obtained load-area relation is extended to a general formulation, which shows good agreement with direct finite element simulations. The obtained relations are more general and applicable for a large range of contact fraction. This model provides an efficient method to predict the overall contact response of rough surfaces and reduces the computational burden greatly.

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Müser, M.H., Dapp, W.B., Bugnicourt, R., Sainsot, P., Lesaffre, N., Lubrecht, T.A., Persson, B.N.J., Harris, K., Bennett, A., Schulze, K., Rohde, S., et al.: Meeting the contact-mechanics challenge. Tribol. Lett. 65(4), 118 (2017). https://doi.org/10.1007/s11249-017-0900-2CrossRef

Greenwood, J.A., Williamson, J.B.P.: Contact of nominally flat surfaces. Proc. Roy. Soc. Lond. A 295, 300–319 (1966). https://doi.org/10.1098/rspa.1966.0242CrossRef

Bush, A.W., Gibson, R.D., Thomas, T.R.: The elastic contact of a rough surface. Wear 35, 87–111 (1975). https://doi.org/10.1016/0093-6413(76)90006-9CrossRef

Chang, W.R., Etsion, I., Bogy, D.B.: An elastic-plastic model for the contact of rough surfaces. ASME J. Tribol. 101, 257–263 (1987). https://doi.org/10.1115/1.3261348CrossRef

Yuan, W.K., Long, J.M., Ding, Y., Wang, G.F.: Statistical contact model of rough surfaces: the role of surface tension. Int. J. Solids Struct. 138(1), 217–223 (2018). https://doi.org/10.1016/j.ijsolstr.2018.01.014CrossRef

Persson, B.N.J.: Theory of rubber friction and contact mechanics. J. Chem. Phys. 115(8), 3840–3861 (2001). https://doi.org/10.1063/1.1388626CrossRef

Carbone, G., Bottiglione, F.: Asperity contact theories: Do they predict linearity between contact area and load? J. Mech. Phys. Solids 56(8), 2555–2572 (2008). https://doi.org/10.1016/j.jmps.2008.03.011CrossRefMATH

Wang, G.F., Liang, X.M., Yan, D.: An incremental equivalent circular contact model for rough surfaces. ASME J. Tribol. 143(8), 081503 (2021). https://doi.org/10.1115/1.4050602CrossRef

Liang, X.M., Ding, Y., Duo, Y., Yuan, W.K., Wang, G.F.: Elastic-perfectly plastic contact of rough surfaces: an incremental equivalent circular model. ASME J. Tribol. 144(5), 051501 (2022). https://doi.org/10.1115/1.4051979CrossRef

10.

Zhai, C.P., Hanaor, D., Gan, Y.X.: Contact stiffness of multiscale surfaces by truncation analysis. Int. J. Mech. Sci. 131–132, 305–316 (2017). https://doi.org/10.1016/j.ijmecsci.2017.07.018CrossRef

11.

Pullen, J., Williamson, J.B.P.: On the plastic contact of rough surfaces. Proc. Roy. Soc. A 327, 159–173 (1972). https://doi.org/10.1098/rspa.1972.0038CrossRef

12.

Zhao, Y.W., Chang, L.: A model of asperity interactions in elastic-plastic contact of rough surfaces. ASME J. Tribol. 123, 857–864 (2001). https://doi.org/10.1115/1.1338482CrossRef

13.

Nowell, D., Hills, D.A.: Hertzian contact of ground surfaces. ASME J. Tribol. 111, 175–179 (1989). https://doi.org/10.1115/1.3261869CrossRef

14.

Ciavarella, M., Delfine, V., Demelio, G.: A re-vitalized Greenwood and Williamson model of elastic contact between fractal surfaces. J. Mech. Phys. Solids 54, 2569–2591 (2006). https://doi.org/10.1016/j.jmps.2006.05.006CrossRefMATH

15.

Ciavarella, M., Greenwood, J.A., Paggi, M.: Inclusion of interaction in the Greenwood and Williamson contact theory. Wear 265, 729–734 (2008). https://doi.org/10.1016/j.wear.2008.01.019CrossRef

16.

Afferrante, L., Carbone, G., Demelio, G.: Interacting and coalescing Hertzian asperities: a new multiasperity contact model. Wear 278–279, 28–33 (2012). https://doi.org/10.1016/j.wear.2011.12.013CrossRef

17.

Vakis, A.I.: Asperity interaction and substrate deformation in statistical summation models of contact between rough surfaces. J. Appl. Mech. 81(4), 041012 (2014). https://doi.org/10.1115/1.4025413CrossRef

18.

Song, H., Van der Giessen, E., Vakis, A.I.: Erratum: “Asperity interaction and substrate deformation in statistical summation models of contact between rough surfaces.” J. Appl. Mech. 83(8), 087001 (2016). https://doi.org/10.1115/1.4033534CrossRef

19.

Song, H., Vakis, A.I., Liu, X., Van der Giessen, E.: Statistical model of rough surface contact accounting for size-dependent plasticity and asperity interaction. J. Mech. Phys. Solids 106, 1–14 (2017). https://doi.org/10.1016/j.jmps.2017.05.014MathSciNetCrossRef

20.

Zhang, S., Song, H., Sandfeld, S., Liu, X., Wei, Y.G.: Discrete Greenwood-Williamson modeling of rough surface contact accounting for three dimensional sinusoidal asperities and asperity interaction. J. Tribol. 141(12), 121401 (2019). https://doi.org/10.1115/1.4044635CrossRef

21.

Wang, G.F., Long, J.M., Feng, X.Q.: A self-consistent model for the elastic contact of rough surfaces. Acta Mech. 226(2), 285–293 (2015). https://doi.org/10.1007/s00707-014-1177-2MathSciNetCrossRefMATH

22.

Jiang, W.G., Su, J.J., Feng, X.Q.: Effect of surface roughness on nanoindentation test of thin films. Eng. Fract. Mech. 75(17), 4965–4972 (2008). https://doi.org/10.1016/j.engfracmech.2008.06.016CrossRef

23.

Johnson, K.L., Greenwood, J.A., Higginson, J.G.: The contact of elastic regular wavy surfaces. Int. J. Mech. Sci. 27, 383–396 (1985). https://doi.org/10.1016/0020-7403(85)90029-3CrossRefMATH

24.

Li, S., Yao, Q.Z., Li, Q.Y., Feng, X.Q., Gao, H.J.: Contact stiffness of regularly patterned multi-asperity interfaces. J. Mech. Phys. Solids 111, 277–289 (2018). https://doi.org/10.1016/j.jmps.2017.10.019MathSciNetCrossRefMATH

25.

McCool, J.I.: Comparison of models for the contact of rough surfaces. Wear 107(1), 37–60 (1986). https://doi.org/10.1016/0043-1648(86)90045-1CrossRef

26.

Wang, S.H., Yuan, W.K., Liang, X.M., Wang, G.F.: A new analytical model for the flattening of Gaussian rough surfaces. Euro. J. Mech. A-Solids 94, 104578 (2022). https://doi.org/10.1016/j.euromechsol.2022.104578MathSciNetCrossRefMATH

27.

Kanafi, M.M.: Surface generator: artificial randomly rough surfaces.https://www.mathworks.com/matlabcentral/fileexchange/60817-surface-generator-artificial-randomly-rough-surfaces (2020). Accessed 30 September 2020

Title: A modified Greenwood–Williamson contact model with asperity interactions
Authors: Cheng-Ya Li
Gang-Feng Wang
Publication date: 21-03-2023
Publisher: Springer Vienna
Published in: Acta Mechanica / Issue 7/2023
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI: https://doi.org/10.1007/s00707-023-03538-x

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A modified Greenwood–Williamson contact model with asperity interactions

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