Analysis of the discrete contact characteristics based on the Greenwood‒Williamson model and the localization principle

Anastasiya A. YAKOVENKO; Irina G. GORYACHEVA

doi:10.1007/s40544-023-0849-0

Friction 2024, 12(5): 1042-1056 https://doi.org/10.1007/s40544-023-0849-0

Research Article |

Open Access | Issue | Published: 02 February 2024

Analysis of the discrete contact characteristics based on the Greenwood‒Williamson model and the localization principle

Show Author's Information Hide Author's Information Anastasiya A. YAKOVENKO(

), Irina G. GORYACHEVA

Ishlinsky Institute for Problems in Mechanics RAS, Moscow 119526, Russia

Keywords:

surface roughness, elasticity, Greenwood–Williamson model, localization principle, asperity interaction

Cite this article:

YAKOVENKO AA, GORYACHEVA IG. Analysis of the discrete contact characteristics based on the Greenwood‒Williamson model and the localization principle. Friction, 2024, 12(5): 1042-1056. https://doi.org/10.1007/s40544-023-0849-0

Download citation

EndNote(RIS)

BibTeX

147

Views

Downloads

Citations

Crossref

WoS

Scopus

CSCD

Abstract Full text About this article

Abstract

The contact of a rigid body with nominally flat rough surface and an elastic half-space is considered. To solve the contact problem, the Greenwood‒Williamson statistical model and the localization principle are used. The developed contact model allows us to investigate the surface approach and the real contact area with taking into account the asperities interaction. It is shown that the mutual influence of asperities changes not only contact characteristics at the macroscale, but also the contact pressure distribution at the microscale. As follows from the results, the inclusion in the contact model of the effect of the mutual influence of asperities is especially significant for studying the real contact area, as well as the contact characteristics at high applied loads. The results calculated according to the proposed approach are in a good agreement with the experimentally observed effects, i.e., the real contact area saturation and the additional compliance exhaustion.

Full text

Abstract

Full text

Outline

About this article

Analysis of the discrete contact characteristics based on the Greenwood‒Williamson model and the localization principle

Show Author's information Hide Author's Information Anastasiya A. YAKOVENKO(

), Irina G. GORYACHEVA

Ishlinsky Institute for Problems in Mechanics RAS, Moscow 119526, Russia

Abstract

Keywords: surface roughness, elasticity, Greenwood–Williamson model, localization principle, asperity interaction

References(43)

[1]

Goryacheva I G. Mechanics of discrete contact. Tribol Int 39(5): 381–386 (2006)

DOI Google Scholar

[2]

Goryacheva I G, Yakovenko A A. Indentation of a rigid cylinder with a rough flat base into a thin viscoelastic layer. J Appl Mech Tech Phys 62(5): 723–735 (2021)

DOI Google Scholar

[3]

Majumdar A, Tien C L. Fractal characterization and simulation of rough surfaces. Wear 136(2): 313–327 (1990)

DOI Google Scholar

[4]

Majumdar A, Bhushan B. Fractal model of elastic-plastic contact between rough surfaces. J Tribol 113(1): 1–11 (1991)

DOI Google Scholar

[5]

Greenwood J A, Williamson J B P. Contact of nominally flat surfaces. Proc R Soc A Math Phys Eng Sci 295(1442): 300–319 (1966)

DOI Google Scholar

[6]

Hertz H. Über die Berührung fester elastischer Körper. J für die Reine und Angew Math 1882(92): 156–171 (1882)

DOI Google Scholar

[7]

Bush A W, Gibson R D, Thomas T R. The elastic contact of a rough surface. Wear 35(1): 87–111 (1975)

DOI Google Scholar

[8]

Yu N, Polycarpou A A. Contact of rough surfaces with asymmetric distribution of asperity heights. J Tribol 124(2): 367–376 (2002)

DOI Google Scholar

[9]

Greenwood J A. A note on Nayak’s third paper. Wear 262(1–2): 225–227 (2007)

DOI Google Scholar

[10]

Chang W R, Etsion I, Bogy D B. An elastic-plastic model for the contact of rough surfaces. J Tribol 109(2): 257–263 (1987)

DOI Google Scholar

[11]

Guo X, Ma B, Zhu Y. A magnification-based multi-asperity (MBMA) model of rough contact without adhesion. J Mech Phys Solids 133: 103724 (2019)

DOI Google Scholar

[12]

Pasaribu H R, Schipper D J. Application of a deterministic contact model to analyze the contact of a rough surface against a flat layered surface. J Tribol 127(2): 451–455 (2005)

DOI Google Scholar

[13]

Ciavarella M, Greenwood J A, Paggi M. Inclusion of “interaction” in the Greenwood and Williamson contact theory. Wear 265(5–6): 729–734 (2008)

DOI Google Scholar

[14]

Zhao Y, Chang L. A model of asperity interactions in elastic-plastic contact of rough surfaces. J Tribol 123(4): 857–864 (2001)

DOI Google Scholar

[15]

Iida K, Ono K. Design consideration of contact/near-contact sliders based on a rough surface contact model. J Tribol 125(3): 562–570 (2003)

DOI Google Scholar

[16]

Ciavarella M, Delfine V, Demelio G. A “re-vitalized” Greenwood and Williamson model of elastic contact between fractal surfaces. J Mech Phys Solids 54(12): 2569–2591 (2006)

DOI Google Scholar

[17]

Chandrasekar S, Eriten M, Polycarpou A A. An improved model of asperity interaction in normal contact of rough surfaces. J Appl Mech 80(1): 011025 (2013)

DOI Google Scholar

[18]

Zhao B, Zhang S, Qiu Z. Analytical asperity interaction model and numerical model of multi-asperity contact for power hardening materials. Tribol Int 92: 57–66 (2015)

DOI Google Scholar

[19]

Wen Y, Tang J, Zhou W, Li L, Zhu C. New analytical model of elastic-plastic contact for three-dimensional rough surfaces considering interaction of asperities. Friction 10(2): 217–231 (2022)

DOI Google Scholar

[20]

Waddad Y, Magnier V, Dufrénoy P, De Saxcé G. A multiscale method for frictionless contact mechanics of rough surfaces. Tribol Int 96: 109–121 (2016)

DOI Google Scholar

[21]

Vakis A I. Asperity interaction and substrate deformation in statistical summation models of contact between rough surfaces. J Appl Mech 81(4): 041012 (2014)

DOI Google Scholar

[22]

Yastrebov V A, Durand J, Proudhon H, Cailletaud G. Rough surface contact analysis by means of the Finite Element Method and of a new reduced model. Comptes Rendus Mécanique 339(7–8): 473–490 (2011)

DOI Google Scholar

[23]

Chen W W, Liu S, Wang Q J. Fast Fourier transform based numerical methods for elasto-plastic contacts of nominally flat surfaces. J Appl Mech 75(1): 011022 (2008)

DOI Google Scholar

[24]

Megalingam A, Mayuram M M. Comparative contact analysis study of finite element method based deterministic, simplified multi-asperity and modified statistical contact models. J Tribol 134(1): 014503 (2012)

DOI Google Scholar

[25]

Megalingam A, Ramji K S H. A comparison on deterministic, statistical and statistical with asperity interaction rough surface contact models. J Bio Tribo Corros 7(3): 95 (2021)

DOI Google Scholar

[26]

Goryacheva I G. The periodic contact problem for an elastic half-space. J Appl Math Mech 62(6): 959–966 (1998)

DOI Google Scholar

[27]

Johnson K L, Greenwood J A, Higginson J G. The contact of elastic regular wavy surfaces. Int J Mech Sci 27(6): 383–396 (1985)

DOI Google Scholar

[28]

Xu Y, Jackson R L, Marghitu D B. Statistical model of nearly complete elastic rough surface contact. Int J Solids Struct 51(5): 1075–1088 (2014)

DOI Google Scholar

[29]

Chu N R, Jackson R L, Wang X Z, Gangopadhyay A, Ghaednia H. Evaluating elastic-plastic wavy and spherical asperity-based statistical and multi-scale rough surface contact models with deterministic results. Materials 14(14): 3864 (2021)

DOI Google Scholar

[30]

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)

DOI Google Scholar

[31]

Goryacheva I G, Tsukanov I Y. Development of discrete contact mechanics with applications to study the frictional interaction of deformable bodies. Mech Solids 55(8): 1441–1462 (2020)

DOI Google Scholar

[32]

Yakovenko A, Goryacheva I. The discrete contact problem for a two-level system of indenters. Continuum Mech Thermodyn 35(4): 1387–1401 (2023)

DOI Google Scholar

[33]

Yakovenko A, Goryacheva I. The periodic contact problem for spherical indenters and viscoelastic half-space. Tribol Int 161: 107078 (2021)

DOI Google Scholar

[34]

Goryacheva I G, Yakovenko A A. Periodic contact problem for a two-level system of punches and a viscoelastic half-space. In: Solid Mechanics, Theory of Elasticity and Creep. Altenbach H, Mkhitaryan S M, Hakobyan V, Sahakyan A V, Eds. Cham: Springer, 2023: 115–131.

DOI

[35]

Li C Y, Wang G F. A modified Greenwood–Williamson contact model with asperity interactions. Acta Mech 234(7): 2859–2868 (2023)

DOI Google Scholar

[36]

Manners W, Greenwood J A. Some observations on Persson’s diffusion theory of elastic contact. Wear 261(5–6): 600–610 (2006)

DOI Google Scholar

[37]

Lai W T, Cheng H S. Computer simulation of elastic rough contacts. ASLE Trans 28(2): 172–180 (1985)

DOI Google Scholar

[38]

Putignano C, Afferrante L, Carbone G, Demelio G. A new efficient numerical method for contact mechanics of rough surfaces. Int J Solids Struct 49(2): 338–343 (2012)

DOI Google Scholar

[39]

McCool J I. Predicting microfracture in ceramics via a microcontact model. J Tribol 108(3): 380–385 (1986)

DOI Google Scholar

[40]

McCool J I. Relating profile instrument measurements to the functional performance of rough surfaces. J Tribol 109(2): 264–270 (1987)

DOI Google Scholar

[41]

Nayak P R. Random process model of rough surfaces. J Lubr Technol 93(3): 398–407 (1971)

DOI Google Scholar

[42]

Bartenev G M, Lavrentev V V. Friction and Wear of Polymers. Amsterdam: Elsevier, 1981.

[43]

Pullen J, Williamson J B P. On the plastic contact of rough surfaces. Proc Math Phys Eng Sci 327(1569): 159–173 (1972).

DOI Google Scholar

About this article

Publication history

Acknowledgements

Rights and permissions

Publication history

Received: 06 June 2023

Revised: 04 November 2023

Accepted: 25 November 2023

Published: 02 February 2024

Issue date: May 2024

Copyright

Acknowledgements

This study was supported the Russian Science Foundation (No. 22-49-02010).

Rights and permissions

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.