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Research Papers: Contact Mechanics

Modeling Tangential Contact of Rough Surfaces With Elastic- and Plastic-Deformed Asperities

[+] Author and Article Information
Dong Wang

Institute of Systems Engineering,
China Academy of Engineering Physics,
Mianyang, Sichuan 621999, China
e-mail: king_east@sina.cn

Chao Xu

School of Astronautics,
Northwestern Polytechnical University,
Xi'an, Shaanxi 710072, China
e-mail: chao_xu@nwpu.edu.cn

Qiang Wan

Institute of Systems Engineering,
China Academy of Engineering Physics,
Mianyang, Sichuan 621999, China
e-mail: wanzhenyu@126.com

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received August 22, 2016; final manuscript received December 17, 2016; published online May 26, 2017. Editor: Michael Khonsari.

J. Tribol 139(5), 051401 (May 26, 2017) (8 pages) Paper No: TRIB-16-1275; doi: 10.1115/1.4035776 History: Received August 22, 2016; Revised December 17, 2016

A new tangential contact model between a rough surface and a smooth rigid flat is proposed in this paper. The model considers the contribution of both elastically deformed asperities and plastically deformed asperities to the total tangential load of rough surface. The method combining the Mindlin partial slip solution with the Hertz solution is used to model the contact formulation of elastically deformed asperities, and for the plastically deformed asperities, the solution combining the fully plastic theory of normal contact with the bilinear relation between the tangential load and deformation developed by Fujimoto is implemented. The total tangential contact load is obtained by Greenwood and Williamson statistical analysis procedure. The proposed model is first compared to the model considering only elastically deformed asperities, and the effect of mean separation and plasticity index on the relationship between the tangential load and deformation is also investigated. It is shown that the present model can be used to describe the stick–slip behavior of the rough surface, and it is a more realistic-based model for the tangential rough contact. A comparison with published experimental results is also made. The proposed model agrees very well with the experimental results when the normal load is small, and shows an error when the normal load is large.

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References

Gaul, L. , and Lenz, J. , 1997, “ Nonlinear Dynamics of Structures Assembled by Bolted Joints,” Acta Mech., 125(1–4), pp. 169–181. [CrossRef]
Segalman, D. J. , Gregory, D. L. , Starr, M. J. , Resor, B. R. , Jew, M. D. , Lauffer, J. P. , and Ames, N. M. , 2009, “ Handbook on Dynamics of Jointed Structures,” Sandia National Laboratories, Albuquerque, Mexico, Report No. SAND2009-4164.
Ahmadian, H. , Mottershead, J. E. , James, S. , Friswell, M. I. , and Reece, C. A. , 2006, “ Modelling and Updating of Large Surface-to-Surface Joints in the AWE-MACE Structure,” Mech. Syst. Signal Process., 20(4), pp. 868–880. [CrossRef]
Hertz, H. , 1881, “ On the Contact of Elastic Solids,” J. Reine Angew. Math., 92, pp. 156–171.
Greenwood, J. , and Williamson, J. , 1966, “ Contact of Nominally Flat Surfaces,” Proc. R. Soc. London Ser. A, 295(1442), pp. 300–319. [CrossRef]
Greenwood, J. , and Tripp, J. , 1970, “ The Contact of Two Nominally Flat Rough Surfaces,” Proc. Inst. Mech. Eng., 185(1), pp. 625–633. [CrossRef]
Whitehouse, D. J. , and Archard, J. , 1970, “ The Properties of Random Surfaces of Significance in Their Contact,” Proc. R. Soc. London A, 316(1524), pp. 97–121. [CrossRef]
Beheshti, A. , and Khonsari, M. , 2012, “ Asperity Micro-Contact Models as Applied to the Deformation of Rough Line Contact,” Tribol. Int., 52(3), pp. 61–74. [CrossRef]
Johnson, K. , Kendall, K. , and Roberts, A. , 1971, “ Surface Energy and the Contact of Elastic Solids,” Proc. R. Soc. London A., 324(1558), pp. 301–313. [CrossRef]
Pei, L. , Hyun, S. , Molinari, J. , and Robbins, M. O. , 2005, “ Finite Element Modeling of Elasto-Plastic Contact Between Rough Surfaces,” J. Mech. Phys. Solids, 53(11), pp. 2385–2409. [CrossRef]
Kogut, L. , and Etsion, I. , 2003, “ A Finite Element Based Elastic-Plastic Model for the Contact of Rough Surfaces,” Tribol. Trans., 46(3), pp. 383–390. [CrossRef]
Chang, W. , 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. [CrossRef]
Zhao, Y. , Maietta, D. M. , and Chang, L. , 2000, “ An Asperity Microcontact Model Incorporating the Transition From Elastic Deformation to Fully Plastic Flow,” ASME J. Tribol., 122(1), pp. 86–93. [CrossRef]
Zhao, Y. , and Chang, L. , 2001, “ A Model of Asperity Interactions in Elastic-Plastic Contact of Rough Surfaces,” ASME J. Tribol., 123(4), pp. 857–864. [CrossRef]
Kogut, L. , and Etsion, I. , 2002, “ Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat,” ASME J. Appl. Mech., 69(5), pp. 657–662. [CrossRef]
Jackson, R. L. , and Green, I. , 2005, “ A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat,” ASME J. Tribol., 127(2), pp. 343–354. [CrossRef]
Wadwalkar, S. , Jackson, R. , and Kogut, L. , 2010, “ A Study of the Elastic-Plastic Deformation of Heavily Deformed Spherical Contacts,” Proc. Inst. Mech. Eng. Part J, 224(10), pp. 1091–1102. [CrossRef]
Brizmer, V. , Kligerman, Y. , and Etsion, I. , 2006, “ The Effect of Contact Conditions and Material Properties on the Elasticity Terminus of a Spherical Contact,” Int. J. Solids Struct., 43(18), pp. 5736–5749. [CrossRef]
Megalingam, A. , and Mayuram, M. M. , 2012, “ Comparative Contact Analysis Study of Finite Element Method Based Deterministic, Simplified Multi-Asperity and Modified Statistical Contact Models,” ASME J. Tribol., 134(1), p. 014503. [CrossRef]
Keer, L. M. , Kim, S. H. , Eberhardt, A. W. , and Vithoontien, V. , 1991, “ Compliance of Coated Elastic Bodies in Contact,” Int. J. Solids Struct., 27(6), pp. 681–698. [CrossRef]
Jones, R. E. , 2007, “ A Greenwood-Williamson Model of Small-Scale Friction,” ASME J. Appl. Mech., 74(1), pp. 31–40. [CrossRef]
Mindlin, R. , 1949, “ Compliance of Elastic Bodies in Contact,” ASME J. Appl. Mech., 16(3), pp. 259–268.
Mindlin, R. , Mason, W. , Osmer, T. , and Deresiewicz, H. , 1952, “ Effects of an Oscillating Tangential Force on the Contact Surfaces of Elastic Spheres,” Pros. 1st US National Congress of Applied Mechanics, ASME, New York, pp. 203–208.
Johnson, K. L. , 1958, “ The Effect of a Tangential Contact Force on the Rolling Motion of an Elastic Sphere on a Plane,” ASME J. Appl. Mech., 80, pp. 339–346.
Johnson, K. , 1961, “ Energy Dissipation at Spherical Surfaces in Contact Transmitting Oscillating Forces,” J. Mech. Eng. Sci., 3(4), pp. 362–368. [CrossRef]
Farhang, K. , Segalman, D. , and Starr, M. , 2007, “ Approximate Constitutive Relation for Lap Joints Using a Tribo-Mechanical Approach,” ASME Paper No. DETC2007-35071.
Argatov, I. I. , and Butcher, E. A. , 2011, “ On the Iwan Models for Lap-Type Bolted Joints,” Int. J. Non-Linear Mech., 46(2), pp. 347–356. [CrossRef]
Chang, W. , Etsion, I. , and Bogy, D. , 1988, “ Static Friction Coefficient Model for Metallic Rough Surfaces,” ASME J. Tribol., 110(1), pp. 57–63. [CrossRef]
Kogut, L. , and Etsion, I. , 2004, “ A Static Friction Model for Elastic-Plastic Contacting Rough Surfaces,” ASME J. Tribol., 126(1), pp. 34–40. [CrossRef]
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. [CrossRef]
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. [CrossRef]
Ödfalk, M. , and Vingsbo, O. , 1992, “ An Elastic-Plastic Model for Fretting Contact,” Wear, 157(2), pp. 435–444. [CrossRef]
Fujimoto, T. , Kagami, J. , Kawaguchi, T. , and Hatazawa, T. , 2000, “ Micro-Displacement Characteristics Under Tangential Force,” Wear, 241(2), pp. 136–142. [CrossRef]
Zhang, X. , and Vu-Quoc, L. , 2007, “ An Accurate Elasto-Plastic Frictional Tangential Force-Displacement Model for Granular-Flow Simulations: Displacement-Driven Formulation,” J. Comput. Phys., 225(1), pp. 730–752. [CrossRef]
Vu-Quoc, L. , Lesburg, L. , and Zhang, X. , 2004, “ An Accurate Tangential Force–Displacement Model for Granular-Flow Simulations: Contacting Spheres With Plastic Deformation, Force-Driven Formulation,” J. Comput. Phys., 196(1), pp. 298–326. [CrossRef]
Chen, W. , and Deng, X. , 2005, “ Structural Damping Caused by Micro-Slip Along Frictional Interfaces,” Int. J. Mech. Sci., 47(8), pp. 1191–1211. [CrossRef]
Johnson, K. L. , 1995, Contact Mechanics, Cambridge University, Cambridge, UK.

Figures

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Fig. 1

Contact schematic of rough surface with multisummits: (a) real rough surface with a rigid smooth flat and (b) equivalent rough surface with a rigid smooth flat

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Fig. 2

Normal and tangential contact pressure distribution for elastic–plastic contact of single asperity: (a) elastically deformed asperity and (b) plastically deformed asperity

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Fig. 3

Stick–slip zone of elastically deformed asperity

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Fig. 4

Computational flowchart for contact load of rough surface

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Fig. 5

Normalized tangential deformation versus total tangential load for rough surface, when d* = 0: (a) ψ = 0.7, (b) ψ = 2.5

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Fig. 6

Gaussian distribution of asperity height and normal contact load of single asperity varying with normalized deformation

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Fig. 7

Normalized tangential deformation versus total tangential load for rough surface with different mean separation d*, when ψ = 0.7

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Fig. 8

Normalized tangential deformation versus total tangential load for rough surface with a different plasticity index ψ, when d* = 0

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Fig. 9

Comparison of proposed model and experimental test under different normal contact loads: (a) N = 234 N, f = 0.479 and (b) N = 526 N, f = 0.420

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