Real Contact Area of Fractal-Regular Surfaces and Its Implications in the Law of Friction

[+] Author and Article Information
Shao Wang

School of Mechanical and Production Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798

J. Tribol 126(1), 1-8 (Jan 13, 2004) (8 pages) doi:10.1115/1.1609493 History: Received February 04, 2003; Revised June 24, 2003; Online January 13, 2004
Copyright © 2004 by ASME
Your Session has timed out. Please sign back in to continue.


Amontons, G., 1699, “De la resistance caus’ee dans les machines,” Mémoires de l’Académie Royale A, Chez Gerard Kuyper, Amsterdam, pp. 257–282.
Bowden,  F. P., and Tabor,  D., 1939, “The Area of Contact Between Stationary and Between Moving Surfaces,” Proc. R. Soc. London, Ser. A, 169, p. 391.
Bowden, F. P., and Tabor, D., 1950, Friction and Lubrication of Solids, Oxford University Press, U.K.
Archard,  J. F., 1951, “Elastic Deformation and the Contact of Surfaces,” Nature (London), 172, pp. 918–919.
Ling,  F. F., 1989, “The Possible Role of Fractal Geometry in Tribology,” Tribol. Trans., 32, pp. 497–505.
Wang,  S., and Komvopoulos,  K., 2000, “Static Friction and Initiation of Slip at Magnetic Head-Disk Interfaces,” ASME J. Tribol., 122, pp. 246–256.
Homola,  A. M., Israelachvili,  J. N., McGuiggan,  P. M., and Gee,  M. L., 1990, “Fundamental Experimental Studies in Tribology: the Transition From “Interfacial” Friction of Undamaged Molecularly Smooth Surfaces to “Normal” Friction with Wear,” Wear, 136, pp. 65–83.
Greenwood,  J. A., and Williamson,  J. B. P., 1966, “Contact of Nominally Flat Surfaces,” Proc. R. Soc. London, Ser. A, 295, pp. 300–319.
Oden,  P. I., Majumdar,  A., Bhushan,  B., Padmanabhan,  A., and Graham,  J. J., 1992, “AFM Imaging, Roughness Analysis and Contact Mechanics of Magnetic Tape and Head Surfaces,” ASME J. Tribol., 114, pp. 666–674.
Sayles,  R. S., and Thomas,  T. R., 1979, “Measurements of the Statistical Microgeometry of Engineering Surfaces,” ASME J. Lubr. Technol., 101, pp. 409–418.
Greenwood, J. A., 1992, “Problems with Surface Roughness,” Fundamentals of Friction: Macroscopic and Microscopic Processes, Singer, I. L., and Pollock, H. M., eds., Kluwer Academic, Boston, MA, pp. 57–76.
Mandelbrot, B. B., 1983, The Fractal Geometry of Nature, Freeman, New York, NY, pp. 1–83 and 116–118.
Gagnepain,  J. J., and Roques-Carmes,  C., 1986, “Fractal Approach to Two-Dimensional and Three-Dimensional Surface Roughness,” Wear, 109, pp. 119–126.
Majumdar,  A., and Tien,  C. L., 1990, “Fractal Characterization and Simulation of Rough Surfaces,” Wear, 136, pp. 313–327.
Wang,  S., and Komvopoulos,  K., 1994, “A Fractal Theory of the Interfacial Temperature Distribution in the Slow Sliding Regime: Part I—Elastic Contact and Heat Transfer Analysis,” ASME J. Tribol., 116(4), pp. 812–823.
Majumdar,  A., and Bhushan,  B., 1991, “Fractal Model of Elastic-Plastic Contact Between Rough Surfaces,” ASME J. Tribol., 113(1), pp. 1–11.
Berry,  M. V., and Lewis,  Z. V., 1980, “On the Weierstrass-Mandelbrot Fractal Function,” Proc. R. Soc. London, Ser. A, 370, pp. 459–484.
Wang,  S., and Komvopoulos,  K., 1994, “A Fractal Theory of the Interfacial Temperature Distribution in the Slow Sliding Regime: Part II—Multiple Domains, Elastoplastic Contacts and Applications,” ASME J. Tribol., 116(4), pp. 824–832.
Wang,  S., and Komvopoulos,  K., 1995, “A Fractal Theory of the Temperature Distribution at Elastic Contacts of Fast Sliding Surfaces,” ASME J. Tribol., 117(2), pp. 203–215.
Greenwood, J. A., 1999, “What Is an Asperity?,” Tribology of Information Storage Devices (TISD’99, Abstract Book), Santa Clara, California, Dec. 6–8, Institute of Physics, p. 20.
Aramaki,  H., Cheng,  H. S., and Chung,  Y.-W., 1993, “The Contact Between Rough Surfaces with Longitudinal Texture: Part I—Average Contact Pressure and Real Contact Area,” ASME J. Tribol., 115, pp. 419–424.
Yan,  W., and Komvopoulos,  K., 1998, “Contact Analysis of Elastic-Plastic Fractal Surfaces,” J. Appl. Phys., 84, pp. 3617–3624.
Ye,  N., and Komvopoulos,  K., 2001, “Elastic-Plastic Layered Media with Fractal Surface Topographies,” ASME J. Tribol., 123(3), pp. 632–640.
Greenwood,  J. A., and Tripp,  J. H., 1967, “The Elastic Contact of Rough Spheres,” ASME J. Appl. Mech., 34, pp. 153–159.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, U.K., pp. 90–95, 171–179, 398–403, 416–422, and 427–428.
Johnson,  K. L., Greenwood,  J. A., and Higginson,  J. G., 1985, “The Contact of Elastic Regular Wavy Surfaces,” Int. J. Mech. Sci., 27(6), pp. 383–396.
Ledermann, W., and Vajda, S., eds., 1982, Handbook of Applicable Mathematics, Vol. IV: Analysis, Wiley, New York, pp. 815–816.


Grahic Jump Location
Fractal-regular surfaces constructed by superimposing the W-M function (D=1.5,G=1×10−12m,γ=1.5) on a parabolic profile for different values of the fractal domain length: (a) Lu=0.1 mm, and (b) Lu=1 mm.
Grahic Jump Location
Expansion of the apparent contact area of a macroscopic Hertzian contact and the accompanied increase in the number of fractal domains in contact for a normal load increased from (a) P to (b) P+ΔP
Grahic Jump Location
Power spectral density function for fractal-regular surfaces with different values of the fractal dimension, D, and with the same value of the initial power spectral density at the lowest frequency of the fractal structures, 1/Lu
Grahic Jump Location
Distributions of the real-to-apparent contact ratio (left half) and the plastic contact ratio (right half) for a fractal-regular surface in a nominally Hertzian contact for different values of the fractal dimension, D



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