Research Papers

Plane Contact and Partial Slip Behaviors of Elastic Layers With Randomly Rough Surfaces

[+] Author and Article Information
Fan Jin, Qiang Wan

Institute of Systems Engineering,
China Academy of Engineering Physics,
Mianyang, Sichuan 621900, China

Xu Guo

State Key Laboratory of Structural Analysis
for Industrial Equipment,
Department of Engineering Mechanics,
Dalian University of Technology,
Dalian 116023, China
e-mail: guoxu@dlut.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received May 5, 2015; final manuscript received May 23, 2015; published online June 19, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(9), 091006 (Sep 01, 2015) (7 pages) Paper No: JAM-15-1223; doi: 10.1115/1.4030742 History: Received May 05, 2015; Revised May 23, 2015; Online June 19, 2015

A plane contact and partial slip model of an elastic layer with randomly rough surface were established by combining the Greenwood–Williamson (GW) rough contact model and the Cattaneo–Mindlin partial slip model. The rough surface of the elastic layer bonded to a rigid base is modeled as an ensemble of noninteracting asperities with identical radius of curvature and Gaussian-distributed heights. By employing the Hertzian solution and the Cattaneo–Mindlin solution to each individual asperity of the rough surface, we derive the total normal force, the real contact area, and the total tangential force for the rough surface, respectively, and then examine the normal contact and partial slip behaviors of the layer. An effective Coulomb coefficient is defined to account for interfacial friction properties. Furthermore, a typical stick–slip transition for the rough surface was also captured by distinguishing the stick and slip contacting asperities according to their respective indentation depths. Our analysis results show that an increasing layer thickness may result in a larger real contact area, a lower mean contact pressure, and a higher effective Coulomb coefficient.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


Bhushan, B., 1999, Principles and Applications of Tribology, Wiley, New York.
Wood, R. J., 2007, “Tribo-Corrosion of Coatings: A Review,” J. Phys. D: Appl. Phys., 40(18), pp. 5502–5521. [CrossRef]
Holmberg, K., and Mattews, A., 2001, “Tribological Properties of Metallic and Ceramic Coatings,” Modern Tribology Handbook, B.Bhushan, ed., CRC Press, New York, Chap. 23. [CrossRef]
Ching, H. A., Choudhury, D., Nine, M. J., and Osman, N. A. A., 2014, “Effects of Surface Coating on Reducing Friction and Wear of Orthopaedic Implants,” Sci. Technol. Adv. Mater., 15(1), p. 014402. [CrossRef]
Meijers, P., 1968, “The Contact Problem of a Rigid Cylinder on an Elastic Layer,” Appl. Sci. Res., 18(1), pp. 353–383. [CrossRef]
Aleksandrov, V. M., 1969, “Asymptotic Solution of the Contact Problem for a Thin Layer,” PMM, 33(1), pp. 49–63. [CrossRef]
Alblas, J. B., and Kuipers, M., 1970, “On the Two-Dimensional Problem of a Cylindrical Stamp Pressed Into a Thin Elastic Layer,” Acta Mech., 9(3–4), pp. 292–311. [CrossRef]
Greenwood, J. A., and Barber, J. R., 2012, “Indentation of an Elastic Layer by a Rigid Cylinder,” Int. J. Solids Struct., 49(21), pp. 2962–2977. [CrossRef]
Komvopoulos, K., and Gong, Z. Q., 2007, “Stress Analysis of a Layered Elastic Solid in Contact With a Rough Surface Exhibiting Fractal Behavior,” Int. J. Solids Struct., 44(78), pp. 2109–2129. [CrossRef]
Persson, B. N. J., 2006, “Contact Mechanics for Randomly Rough Surfaces,” Surf. Sci. Rep., 61(4), pp. 201–227. [CrossRef]
Greenwood, J. A., and Williamson, J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. R. Soc. London A, 295(1442), pp. 300–319. [CrossRef]
Greenwood, J. A., Putignano, C., and Ciavarella, M., 2011, “A Greenwood & Williamson Theory for Line Contact,” Wear, 270(3), pp. 332–334. [CrossRef]
Ciavarella, M., Dibello, S., and Demelio, G., 2008, “Conductance of Rough Random Profiles,” Int. J. Solids Struct., 45(3–4), pp. 879–893. [CrossRef]
Zhao, Y., and Chang, L., 2002, “A Micro-Contact and Wear Model for Chemical–Mechanical Polishing of Silicon Wafers,” Wear, 252(3–4), pp. 220–226. [CrossRef]
Morrow, C., Lovell, M. R., and Ning, X., 2003, “A JKR-DMT Transition Solution for Adhesive Rough Surface Contact,” J. Phys. D: Appl. Phys., 36(5), pp. 534–540. [CrossRef]
Zhang, W., Jin, F., Guo, X., and Zhang, S., 2014, “Adhesive Contact on Randomly Rough Surfaces Based on the Double-Hertz Model,” ASME J. Appl. Mech., 81(5), p. 051008. [CrossRef]
Jones, R. E., 2007, “A Greenwood-Williamson Model of Small-Scale Friction,” ASME J. Appl. Mech., 74(1), pp. 31–40. [CrossRef]
Cattaneo, C., 1938, “Sul contatto di due corpi elastici: Distribuzione locale degli sforzi,” R. C. Accad. Naz. Lincei, 27, pp. 474–478.
Mindlin, R. D., 1949, “Compliance of Elastic Bodies in Contact,” ASME J. Appl. Mech., 16, pp. 259–268.
Etsion, I., 2008, “Discussion: ‘A Greenwood-Williamson Model of Small-Scale Friction’,” ASME J. Appl. Mech., 75(4), p. 045501. [CrossRef]
Corwin, A. D., Street, M. D., Carpick, R. W., Ashurst, W. R., and de Boer, M. P., 2004, “Pre-Sliding Tangential Deflection Can Govern Friction in MEMS Devices,” ASME Paper No. TRIB2004-64360. [CrossRef]
Peng, W., and Bhushan, B., 2001, “Three-Dimensional Contact Analysis of Layered Elastic/Plastic Solids With Rough Surfaces,” Wear, 249(9), pp. 741–760. [CrossRef]
Peng, W., and Bhushan, B., 2002, “Sliding Contact Analysis of Layered Elastic/Plastic Solids With Rough Surfaces,” ASME J. Tribol., 124(1), pp. 46–61. [CrossRef]
Nowell, D., and Hills, D. A., 1998, “Contact Problems Incorporating Elastic Layers,” Int. J. Solids Struct., 24(1), pp. 105–115. [CrossRef]
Wang, Z. J., Wang, W. Z., Wang, H., Zhu, D., and Hu, Y. Z., 2010, “Partial Slip Contact Analysis on Three-Dimensional Elastic Layered Half-Space,” ASME J. Tribol., 132(2), p. 021403. [CrossRef]
Chen, P., and Chen, S., 2013, “Partial Slip Contact Between a Rigid Punch With an Arbitrary Tip-Shape and an Elastic Graded Solid With a Finite Thickness,” Mech. Mater., 59(1), pp. 24–35. [CrossRef]
Chen, P., Chen, S., and Peng, Z., 2012, “Thermo-Contact Mechanics of a Rigid Cylindrical Punch Sliding on a Finite Graded Layer,” Acta Mech., 223(12), pp. 2647–2665. [CrossRef]
Chen, P., and Chen, S., 2013, “Thermo-Mechanical Contact Behavior of a Finite Graded Layer Under a Sliding Punch With Heat Generation,” Int. J. Solids Struct., 50(7–8), pp. 1108–1119. [CrossRef]
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
Kesari, H., Doll, J., Pruitt, B., Wei, C., and Lew, A., 2010, “The Role of Surface Roughness During Adhesive Elastic Contact,” Philos. Mag. Lett., 90(12), pp. 891–902. [CrossRef] [PubMed]


Grahic Jump Location
Fig. 1

An elastic layer bonded to a rigid substrate in contact with a rigid cylinder. A normal compressive line force P is first applied followed by a subsequent tangential line force Q with no slip.

Grahic Jump Location
Fig. 2

Comparison between the exact a-δ relations (dots) and the corresponding fitted curves (lines) for (a) ν=0.3 and (b) ν=0.5, respectively

Grahic Jump Location
Fig. 3

Plane contact between a rigid smooth surface and an elastic layer with a randomly rough surface in (a) a real case and (b) a simplified model

Grahic Jump Location
Fig. 4

The dimensionless normal force P/NE*σ versus the dimensionless real contact area A/NRσ for (a) ν=0.3 and (b) ν=0.5, respectively

Grahic Jump Location
Fig. 5

The dimensionless mean real contact pressure versus the dimensionless layer thickness for (a) ν=0.3 and (b) ν=0.5, respectively

Grahic Jump Location
Fig. 6

Variation of the tangential forces contributed by the stick and slip asperities as a function of the tangential displacement for (a) ν=0.3 and (b) ν=0.5, respectively. Here, τcr*=0.01, d*=1, h*=100, and M=2.

Grahic Jump Location
Fig. 7

The effective Coulomb coefficient versus the dimensionless layer thickness for (a) ν = 0.3 and (b) ν = 0.5, respectively



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In