The influence of non-Gaussian surface roughness on elastic contacts loaded in both normal and tangential directions has been investigated. A numerical solution method based on the multilevel scheme and incorporating the theorem of Ciavarella/Jaeger has been implemented, which allows fast calculation of partial slip loading conditions, including the energy dissipation for a fully reversed tangential loading cycle. The effect of varying roughness rms, skewness, kurtosis, and correlation lengths on contact areas, stiffness values, and energy dissipation is presented, and the significance of these parameters and of the loading method are discussed. It was found that the energy dissipation can be greatly increased by greater surface roughness. Maps showing how the energy dissipation is distributed within the contact are presented, which provide some explanation for this observation and the scatter that may occur for surfaces of nominally similar roughness. The suitability of these parameters for predicting the contact behavior of rough surfaces is also considered.
Issue Section:
Contact Mechanics
References
1.
Greenwood
, J. A.
, and Williamson
, J. B. P.
, 1966, “Contact of Nominally Flat Surfaces
,” Proc. R. Soc. London, Ser. A
, 295
(1442
), pp. 300
–319
.2.
Bush
, A. W.
, Gibson
, R. D.
, and Thomas
, T. R.
, 1975, “The Elastic Contact of a Rough Surface
,” Wear
, 35
(1
), pp. 87
–111
.3.
Chang
, W. R.
, Etsion
, I.
, and Bogy
, D. B.
, 1987, “An Elastic-Plastic Model for the Contact of Rough Surfaces
,” ASME J. Tribol.
, 109
(2
), pp. 257
–263
.4.
Ciavarella
, M.
, Demelio
, G.
, Barber
, J. R.
, and Jang
, Y. H.
, 2000, “Linear Elastic Contact of the Weierstrass Profile
,” Proc. R. Soc. London, Ser. A
, 456
(1994
), pp. 387
–405
.5.
Persson
, B. N. J.
, 2001, “Elastoplastic Contact Between Randomly Rough Surfaces
,” Phys. Rev. Lett.
, 87
(11
), p. 116101
.6.
Persson
, B. N. J.
, 2001, “Theory of Rubber Friction and Contact Mechanics
,” J. Chem. Phys.
, 115
(8
), pp. 3840
–3861
.7.
Ciavarella
, M.
, Murolo
, G.
, Demelio
, G.
, and Barber
, J. R.
, 2004, “Elastic Contact Stiffness and Contact Resistance for the Weierstrass Profile
,” J. Mech. Phys. Solids
, 52
(6
), pp. 1247
–1265
.8.
Jackson
, R. L.
, and Green
, I.
, 2011, “On the Modeling of Elastic Contact Between Rough Surfaces
,” Tribol. Trans.
, 54
(2
), pp. 300
–314
.9.
Björklund
, S.
, 1997, “A Random Model for Micro-Slip Between Nominally Flat Surfaces
,” ASME J. Tribol.
, 119
(4
), pp. 726
–732
.10.
Hagman
, L. A.
, and Olofsson
, U.
, 1998, “A Model for Micro-Slip Between Flat Surfaces Based on Deformation of Ellipsoidal Elastic Asperities – Parametric Study and Experimental Investigation
,” Tribol. Int.
, 31
(4
), pp. 209
–217
.11.
Kasarekar
, A. T.
, Bolander
, N. W.
, Sadeghi
, F.
, and Tseregounis
, S.
, 2007, “Modeling of Fretting Wear Evolution in Rough Circular Contacts in Partial Slip
,” Int. J. Mech. Sci.
, 49
(6
), pp. 690
–703
.12.
Dini
, D.
, and Hills
, D. A.
, 2009, “Frictional Energy Dissipation in a Rough Hertzian Contact
,” ASME J. Tribol.
, 131
(2
), p. 021401
.13.
Eriten
, M.
, Polycarpou
, A. A.
, and Bergman
, L. A.
, 2010, “Physics-Based Modeling for Partial Slip Behavior of Spherical Contacts
,” Int. J. Solids Struct.
, 47
(18–19
), pp. 2554
–2567
.14.
Filippi
, S.
, Akay
, A.
, and Gola
, M. M.
, 2004, “Measurement of Tangential Contact Hysteresis During Microslip
,” ASME J. Tribol.
, 126
(3
), pp. 482
–489
.15.
Kartal
, M. E.
, Mulvihill
, D. M.
, Nowell
, D.
, and Hills
, D. A.
, 2010, “Determination of the Frictional Properties of Titanium and Nickel Alloys Using the Digital Image Correlation Method
,” Exp. Mech.
, 51
(3
), pp. 359
–371
.16.
Eriten
, M.
, Polycarpou
, A. A.
, and Bergman
, L. A.
, 2011, “Development of a Lap Joint Fretting Apparatus
,” Exp. Mech.
, 51
(8
), pp. 1405
–1419
.17.
Jang
, J. H.
, and Barber
, J. R.
, 2011, “Effect of Phase on the Frictional Dissipation in Systems Subjected to Harmonically Varying Loads
,” Eur. J. Mech. A/Solid
, 30
(3
), pp. 269
–274
.18.
Eriten
, M.
, Polycarpou
, A. A.
, and Bergman
, L. A.
, 2011, “Physics-Based Modeling for Fretting Behavior of Nominally Flat Rough Surfaces
,” Int. J. Solids Struct.
, 48
(10
), pp. 1436
–1450
.19.
Sanliturk
, K. Y.
, Ewins
, D. J.
, and Stanbridge
, A. B.
, 2001, “Underplatform Dampers for Turbine Blades: Theoretical Modeling, Analysis, and Comparison With Experimental Data
,” ASME J. Eng. Gas Turb. Power
, 123
(4
), pp. 919
–929
.20.
Petrov
, E. P.
, and Ewins
, D. J.
, 2004, “State-of-the-Art Dynamic Analysis for Non-Linear Gas Turbine Structures
,” Proc. Inst. Mech. Eng. Part G: J. Aerosp. Eng.
, 218
(3
), pp. 199
–211
.21.
Ciavarella
, M.
, Greenwood
, J. A.
, and Paggi
, M.
, 2008, “Inclusion of ‘Interaction’ in the Greenwood and Williamson Contact Theory
,” Wear
, 265
(5–6
), pp. 729
–734
.22.
Webster
, M. N.
, and Sayles
, R. S.
, 1986, “A Numerical Model for the Elastic Frictionless Contact of Real Rough Surfaces
,” ASME J. Tribol.
, 108
(3
), pp. 314
–20
.23.
Majumdar
, A.
, and Bhushan
, B.
, 1990, “Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces
,” ASME J. Tribol.
, 112
(2
), pp. 205
–16
.24.
Chen
, W. W.
, and Wang
, Q. J.
, 2009, “A Numerical Static Friction Model for Spherical Contacts of Rough Surfaces, Influence of Load, Material, and Roughness
,” ASME J. Tribol.
, 131
(2
), p. 021402
.25.
Popescu
, G.
, Morales-Espejel
, G. E.
, Wemekamp
, B.
, and Gabelli
, A.
, 2006, “An Engineering Model for Three-Dimensional Elastic-Plastic Rolling Contact Analyses
,” Tribol. Trans.
, 49
(3
), pp. 387
–399
.26.
Chang
, W. R.
, Etsion
, I.
, and Bogy
, D. B.
, 1988, “Static Friction Coefficient Model for Metallic Rough Surfaces
,” ASME J. Tribol.
, 110
(1
), pp. 57
–63
.27.
Ogilvy
, J. A.
, 1992, “Numerical Simulation of Elastic-Plastic Contact Between Anisotropic Rough Surfaces
,” J. Phys. D: Appl. Phys.
, 25
(12
), pp. 1798
–1809
.28.
Jacq
, C.
, Nelias
, D.
, Lormand
, G.
, and Girodin
, G.
, 2002, “Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code
,” ASME J. Tribol.
, 124
(4
), pp. 653
–667
.29.
Cohen
, D.
, Kligerman
, Y.
, and Etsion
, I.
, 2008, “A Model for Contact and Static Friction of Nominally Flat Rough Surfaces Under Full Stick Contact Condition
,” ASME J. Tribol.
, 130
(3
), p. 031401
.30.
Cohen
, D.
, Kligerman
, Y.
, and Etsion
, I.
, 2009, “The Effect of Surface Roughness on Static Friction and Junction Growth of an Elastic-Plastic Spherical Contact
,” ASME J. Tribol.
, 131
(2
), p. 021404
.31.
Li
, L.
, Etsion
, I.
, and Talke
, F. E.
, 2010, “Contact Area and Static Friction of Rough Surfaces With High Plasticity Index
,” ASME J. Tribol.
, 132
(3
), p. 031401
.32.
Lee
, C.
, Eriten
, M.
, and Polycarpou
, A. A.
, 2010, “Application of Elastic–Plastic Static Friction Models to Rough Surfaces With Asymmetric Asperity Distribution
,” ASME J. Tribol.
, 132
(2
), p. 031602
.33.
Chen
, W. W.
, Liu
, S.
, and Wang
, Q. J.
, 2008, “Fast Fourier Transform Based Numerical Methods for Elasto-Plastic Contacts of Nominally Flat Surfaces
,” ASME J. Appl. Mech.
, 75
(1
), p. 011022
.34.
Fulleringer
, B.
, and Nelias
, D.
, 2010, “On the Tangential Displacement of a Surface Point Due to a Cuboid of Uniform Plastic Strain in a Half-Space
,” ASME J. Appl. Mech.
, 77
(2
), p. 021014
.35.
Tabor
, D.
, 1959, “Junction Growth in Metallic Friction: The Role of Combined Stresses and Surface Contamination
,” Proc. R. Soc. London, Ser. A
, 251
(1266
), pp. 378
–393
.36.
Etsion
, I.
, 2010, “Revisiting the Cattaneo-Mindlin Concept of Interfacial Slip in Tangentially Loaded Compliant Bodies
,” ASME J. Tribol.
, 132
(2
), p. 020801
.37.
Chilamakuri
, S.
, and Bhushan
, B.
, 1998, “Contact Analysis of Non-Gaussian Random Surfaces
,” Proc. Inst. Mech. Eng. Part J: J. Eng. Tribol.
, 212
(1
), pp. 19
–32
.38.
Kim
, T. W.
, Bhushan
, B.
, and Cho
, Y. J.
, 2006, “The Contact Behavior of Elastic/Plastic Non-Gaussian Rough Surfaces
,” Tribol. Lett.
, 22
(1
), pp. 1
–13
.39.
Zhang
, H.
, Zhong
, W.
, and Gu
, Y.
, 1998, “A Combined Parametric Quadratic Programming and Iteration Method for 3-D Elastic-Plastic Frictional Contact Problem Analysis
,” Comput. Methods Appl. Mech. Eng.
, 155
(3–4
), pp. 307
–324
.40.
Stanley
, H. M.
, and Kato
, T.
, 1997, “FFT-Based Method for Rough Surface Contact
,” ASME J. Tribol.
, 119
(3
), pp. 481
–485
.41.
Lubrecht
, A. A.
, and Ioannides
, E.
, 1991, “A Fast Solution of the Dry Contact Problem and the Associated Sub-Surface Stress Field, Using Multilevel Techniques
,” ASME J. Tribol.
, 113
(1
), pp. 128
–133
.42.
Polonsky
, I. A.
, and Keer
, L. M.
, 2000, “Fast Methods for Solving Rough Contact Problems: A Comparative Study
,” ASME J. Tribol.
, 122
(1
), pp. 36
–41
.43.
Brandt
, A.
, and Lubrecht
, A. A.
, 1990, “Multilevel Matrix Multiplication and Fast Solution of Integral Equations
,” J. Comput. Phys.
, 90
(2
), pp. 348
–370
.44.
Venner
, C. H.
, and Lubrecht
, A. A.
, 2000, Multilevel Methods in Lubrication, Tribology Series 37
, Elsevier
, Amsterdam
.45.
Jäger
, J.
, 1998, “A New Principle in Contact Mechanics
,” ASME J. Tribol.
, 120
(4
), pp. 677
–684
.46.
Ciavarella
, M.
, 1998, “Tangential Loading of General Three-Dimensional Contacts
,” ASME J. Appl. Mech.
, 65
(4
), pp. 998
–1003
.47.
Mindlin
, R. D.
, 1949, “Compliance of Elastic Bodies in Contact
,” ASME J. Appl. Mech.
, 16
(3
), pp. 259
–268
.48.
Cattaneo
, C.
, 1938, “Sul Contatto di Due Corpi Elastici: Distribuzione Locale degli Sforzi
,” Rend. Accad. Naz. Lincei
, 27
, pp. 342
–348, 434–436, 474–478
.49.
Dini
, D.
, and Nowell
, D.
, 2003, “Prediction of the Slip Zone Friction Coefficient in Flat and Rounded Contact
,” Wear
, 254
(3–4
), pp. 364
–369
.50.
Johnson
, N. L.
, 1949, “Systems of Frequency Curves Generated by Methods of Translation
,” Biometrika
, 36
(1–2
), pp. 149
–176
.51.
Kim
, T. W.
, and Bhushan
, B.
, 2006, “Generation of Composite Surfaces With Bimodal Distribution and Contact Analysis for Optimum Tribological Performance
,” ASME J. Tribol.
, 128
(4
), pp. 851
–864
.52.
Munisamy
, R. L.
, Hills
, D. A.
, and Nowell
, D.
, 1994, “Static Axisymmetric Contacts Subject to Shearing Forces
,” ASME J. Appl. Mech.
, 61
(2
), pp. 278
–283
.53.
Reina
, S.
, Paynter
, R. J. H.
, Hills
, D. A.
, and Dini
, D.
, 2010, “Determining the Coefficient of Friction Between Solids Without Sliding
,” Wear
, 269
(5–6
), pp. 339
–343
.Copyright © 2012
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