Comptes Rendus
Effects of multi-scale roughness and frictional heating on solid body contact deformation
Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 149-162.

Solid body contact is restricted to a discrete number of randomly distributed microscopic areas resulting from the deformation of interacting surface protrusions (asperities). The deformation mode of these asperity contacts can be elastic, elastic–plastic, or fully plastic, depending on the local surface interference, asperity radius of curvature, coefficient of friction, and mechanical properties of the solid surfaces. Traditionally, the surface topography has been described by statistical models which rely on unrealistic simplifications of the shape, height, and size of the asperities. Such assumptions were avoided in contemporary contact mechanics analyses, which use fractal geometry to accomplish a surface topography description over a wide range of length scales. The main objective of this article is to provide an assessment of the role of multi-scale topography (roughness) and frictional heating in contact deformation of elastic–plastic solid bodies. Contact relationships, derived at the asperity level, which include the mechanical properties of surface layer and substrate medium, layer thickness, local surface interference, and equivalent asperity radius of curvature, are presented for different modes of deformation. These asperity-level relationships and a fractal model of the surface topography are incorporated into a numerical integration scheme to analyze multi-scale thermomechanical contact deformation over the entire real contact area of homogeneous and layered media possessing realistic surface topographies.

Le contact entre corps solides n'a lieu que sur un nombre fini de zones microscopiques réparties aléatoirement, qui résultent de la déformation d'aspérités en interaction. Le mode de déformation de ces aspérités en contact peut être élastique, partiellement élastique et partiellement plastique, ou complètement plastique, suivant l'interférence locale des surfaces, le rayon de courbure des aspérités, le coefficient de frottement et les propriétés mécaniques des surfaces. Traditionnellement, la topographie des surfaces a été décrite à l'aide de modèles statistiques qui reposent sur des simplifications irréalistes de la forme, la hauteur et la taille des aspérités. Les analyses mécaniques actuelles du contact évitent de telles hypothèses en utilisant la géométrie fractale pour décrire la topographie des surfaces sur une large gamme d'échelles. Le but essentiel de cet article est d'examiner le rôle de la topographie multi-échelles (rugosité) et de l'échauffement par frottement dans la déformation de contact de corps solides élasto-plastiques. Des relations de contact obtenues à l'échelle des aspérités, qui font intervenir les propriétés mécaniques de la zone de surface et du substrat sous-jacent, l'épaisseur de la couche, l'interférence des surfaces et le rayon de courbure équivalent des aspérités, sont présentées pour différents modes de déformation. Ces relations d'origine microscopique, jointes à un modèle fractal de la topographie des surfaces, sont incorporées dans un schéma d'intégration numérique, afin d'analyser la déformation thermomécanique de contact de la totalité de la zone de contact de milieux homogènes et laminés possédant des topographies de surface réalistes.

Published online:
DOI: 10.1016/j.crme.2007.11.005
Keywords: Friction, Asperities, Fractal surfaces, Frictional heating, Homogeneous and layered media, Multi-scale contact deformation, Thermomechanical surface tractions
Mot clés : Friction, Aspérités, Surfaces fractales, Échauffement par frottement, Milieux homogènes et laminés, Déformation de contact multi-échelle, Tractions surfaciques thermomécaniques

Kyriakos Komvopoulos 1

1 Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
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Kyriakos Komvopoulos. Effects of multi-scale roughness and frictional heating on solid body contact deformation. Comptes Rendus. Mécanique, Volume 336 (2008) no. 1-2, pp. 149-162. doi : 10.1016/j.crme.2007.11.005.

[1] H. Hertz Über die berührung fester elastischer körper, J. Reine Angewandte Mathematik, Volume 92 (1882), pp. 156-171

[2] Y.-O. Tu A numerical solution for an axially symmetric contact problem, J. Appl. Mech., Volume 34 (1967), pp. 283-286

[3] M. Hannah Contact stress and deformation in a thin elastic layer, Quart. J. Mech. Appl. Math., Volume 4 (1951), pp. 94-105

[4] D.M. Burmister The general theory of stresses and displacements in layered systems, J. Appl. Phys., Volume 16 (1945), pp. 89-94

[5] V.M. Aleksandrov; V.A. Babeshko; V.A. Kucherov Contact problems for an elastic layer of slight thickness, J. Appl. Math. Mech. (PMM), Volume 30 (1966), pp. 124-142

[6] Y.C. Pao; T.-S. Wu; Y.P. Chiu Bounds on the maximum contact stress of an indented elastic layer, J. Appl. Mech., Volume 38 (1971), pp. 608-614

[7] P.K. Gupta; J.A. Walowit Contact stresses between an elastic cylinder and a layered elastic solid, J. Lubr. Technol., Volume 96 (1974), pp. 250-257

[8] G. Dumas; C.N. Baronet Elastoplastic indentation of a half-space by an infinitely long rigid circular cylinder, Int. J. Mech. Sci., Volume 18 (1971), pp. 519-530

[9] G.B. Sinclair; P.S. Follansbee; K.L. Johnson Quasi-static normal indentation of an elasto-plastic half-space by a rigid sphere—II. Results, Int. J. Solids Struct., Volume 21 (1985), pp. 865-888

[10] E.R. Kral; K. Komvopoulos; D.B. Bogy Elastic–plastic finite element analysis of repeated indentation of a half-space by a rigid sphere, J. Appl. Mech., Volume 60 (1993), pp. 829-841

[11] K. Komvopoulos Finite element analysis of a layered elastic solid in normal contact with a rigid surface, J. Tribol., Volume 110 (1988), pp. 477-485

[12] K. Komvopoulos Elastic–plastic finite element analysis of indented layered media, J. Tribol., Volume 111 (1989), pp. 430-439

[13] A.K. Bhattacharya; W.D. Nix Analysis of elastic and plastic deformation associated with indentation testing of thin films on substrates, Int. J. Solids Struct., Volume 24 (1988), pp. 1287-1298

[14] E.R. Kral; K. Komvopoulos Three-dimensional finite element analysis of surface deformation and stresses in an elastic–plastic layered medium subjected to indentation and sliding contact loading, J. Appl. Mech., Volume 63 (1996), pp. 365-375

[15] J. Dundurs; K.C. Tsai; L.M. Keer Contact between elastic bodies with wavy surfaces, J. Elast., Volume 3 (1973), pp. 109-115

[16] M.N. Webster; R.S. Sayles A numerical model for the elastic frictionless contact of real rough surfaces, J. Tribol., Volume 108 (1986), pp. 314-320

[17] J. Seabra; D. Berthe Influence of surface waviness and roughness on the normal pressure distribution in the Hertzian contact, J. Tribol., Volume 109 (1987), pp. 462-470

[18] D. Berthe; Ph. Vergne An elastic approach to rough contact with asperity interactions, Wear, Volume 117 (1987), pp. 211-222

[19] K. Komvopoulos; D.-H. Choi Elastic finite element analysis of multi-asperity contacts, J. Tribol., Volume 114 (1992), pp. 823-831

[20] D. Nowell; D.A. Hills Hertzian contact of ground surfaces, J. Tribol., Volume 111 (1989), pp. 175-179

[21] E. Ioannides; J.C. Kuijpers Elastic stresses below asperities in lubricated contacts, J. Tribol., Volume 108 (1986), pp. 394-402

[22] A.W. Bush; R.D. Gibson; T.R. Thomas The elastic contact of a rough surface, Wear, Volume 35 (1975), pp. 87-111

[23] A.W. Bush; R.D. Gibson; G.P. Keogh Strongly anisotropic rough surfaces, J. Lubr. Technol., Volume 101 (1979), pp. 15-20

[24] J.I. McCool Predicting microfracture in ceramics via a microcontact model, J. Tribol., Volume 108 (1986), pp. 380-386

[25] B.B. Mandelbrot How long is the coast of Britain? Statistical self-similarity and fractional dimension, Science, Volume 156 (1967), pp. 636-638

[26] B.B. Mandelbrot Stochastic models for the Earth's relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands, Proc. Natl. Acad. Sci., Volume 72 (1975), pp. 3825-3828

[27] B.B. Mandelbrot The Fractal Geometry of Nature, Freeman, New York, 1983 (pp. 1–83 and 116–118)

[28] A. Majumdar; B. Bhushan Fractal model of elastic–plastic contact between rough surfaces, J. Tribol., Volume 113 (1991), pp. 1-11

[29] P. Sahoo; S.K. Roy Chowdhury A fractal analysis of adhesion at the contact between rough solids, Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol., Volume 210 (1996), pp. 269-279

[30] W. Yan; K. Komvopoulos Contact analysis of elastic–plastic fractal surfaces, J. Appl. Phys., Volume 84 (1998), pp. 3617-3624

[31] K. Komvopoulos; W. Yan Three-dimensional elastic–plastic fractal analysis of surface adhesion in microelectromechanical systems, J. Tribol., Volume 120 (1998), pp. 808-813

[32] K. Komvopoulos; N. Ye Three-dimensional contact analysis of elastic–plastic layered media with fractal surface topographies, J. Tribol., Volume 123 (2001), pp. 632-640

[33] S. Wang; K. Komvopoulos A fractal theory of the interfacial temperature distribution in the slow sliding regime: Part I—Elastic contact and heat transfer analysis, J. Tribol., Volume 116 (1994), pp. 812-823

[34] S. Wang; K. Komvopoulos A fractal theory of the interfacial temperature distribution in the slow sliding regime: Part II—Multiple domains, elastoplastic contacts and applications, J. Tribol., Volume 116 (1994), pp. 824-832

[35] K. Komvopoulos; N. Ye Elastic–plastic finite element analysis for the head-disk interface with fractal topography description, J. Tribol., Volume 124 (2002), pp. 775-784

[36] Z.-Q. Gong; K. Komvopoulos Thermomechanical analysis of semi-infinite solid in sliding contact with a fractal surface, J. Tribol., Volume 127 (2005), pp. 331-342

[37] R.S. Sayles; T.R. Thomas Surface topography as a nonstationary random process, Nature, Volume 271 (1978), pp. 431-434

[38] A. Majumdar; C.L. Tien Fractal characterization and simulation of rough surfaces, Wear, Volume 136 (1990), pp. 313-327

[39] M.V. Berry; Z.V. Lewis On the Weierstrass–Mandelbrot fractal function, Proc. Roy. Soc. London, Ser. A, Volume 370 (1980), pp. 459-484

[40] K. Komvopoulos; W. Yan A fractal analysis of stiction in microelectromechanical systems, J. Tribol., Volume 119 (1997), pp. 391-400

[41] M. Ausloos; D.H. Berman A multivariate Weierstrass–Mandelbrot function, Proc. Roy. Soc. London, Ser. A, Volume 400 (1985), pp. 331-350

[42] K. Komvopoulos Surface engineering and microtribology for microelectromechanical systems, Wear, Volume 200 (1996), pp. 305-327

[43] D. Tabor The hardness of solids, Rev. Phys. Technol., Volume 1 (1970), pp. 145-179

[44] R.B. King Elastic analysis of some punch problems for a layered medium, Int. J. Solids Struct., Volume 23 (1987), pp. 1657-1664

[45] K. Komvopoulos; Z.-Q. Gong Stress analysis of a layered elastic solid in contact with a rough surface exhibiting fractal behavior, Int. J. Solids Struct., Volume 44 (2007), pp. 2109-2129

[46] H. Blok Theoretical study of temperature rise at surfaces of actual contact under oiliness lubricating conditions, Proc. General Discussion on Lubrication and Lubricants, vol. 2, Inst. Mech. Eng. (London), 1937, pp. 222-235

[47] J.C. Jaeger Moving sources of heat and the temperature at sliding contacts, Proc. R. Soc. NSW, Volume 76 (1942), pp. 203-224

[48] F.D. Ju; J.H. Huang Heat checking in the contact zone of a bearing seal (A two-dimensional model of a single moving asperity), Wear, Volume 79 (1982), pp. 107-118

[49] J.H. Huang; F.D. Ju Thermomechanical cracking due to moving frictional loads, Wear, Volume 102 (1985), pp. 81-104

[50] N. Ye; K. Komvopoulos Three-dimensional finite element analysis of elastic–plastic layered media under thermomechanical surface loading, J. Tribol., Volume 125 (2003), pp. 52-59

[51] Z.-Q. Gong; K. Komvopoulos Mechanical and thermomechanical elastic–plastic contact analysis of layered media with patterned surfaces, J. Tribol., Volume 126 (2004), pp. 9-17

[52] H. Uetz; J. Föhl Wear as an energy transformation process, Wear, Volume 49 (1978), pp. 253-264

[53] K.L. Johnson Contact Mechanics, Cambridge University Press, Cambridge, UK, 1985

[54] J.R. Barber Thermoelastic displacements and stresses due to a heat source moving over the surface of a half plane, J. Appl. Mech., Volume 51 (1984), pp. 636-640

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