Rough surfaces are characterized by fractal geometry using a modified two-variable Weierstrass–Mandelbrot function. The developed algorithm yields three-dimensional fractal surface topographies representative of engineering rough surfaces. This surface model is incorporated into an elastic-plastic contact mechanics analysis of two approaching rough surfaces. Closed form solutions for the elastic and plastic components of the total normal force and real contact area are derived in terms of fractal parameters, material properties, and mean surface separation distance. The effects of surface topography parameters and material properties on the total deformation force are investigated by comparing results from two- and three-dimensional contact analyses and elastic and elastic-perfectly plastic material behaviors. For normal contact of elastic-perfectly plastic silica surfaces and range of surface interference examined, the interfacial force is predominantly elastic and the real contact area is approximately one percent of the apparent contact area or less, depending on the mean interfacial distance. The analysis can be easily modified to account for anisotropic fractal surfaces and different material behaviors.

1.
P. R.
Nayak
,
J. Lubr. Technol.
93
,
398
(
1971
).
Google Scholar
Crossref
Search ADS
 
2.
J. A.
Greenwood
and
J. B. P.
Williamson
,
Proc. R. Soc. London, Ser. A
295
,
300
(
1966
).
Google Scholar
 
3.
P. R.
Nayak
,
Wear
26
,
305
(
1973
).
Google Scholar
Crossref
Search ADS
 
4.
J. I.
McCool
,
Wear
107
,
37
(
1986
).
Google Scholar
Crossref
Search ADS
 
5.
R. S.
Sayles
and
T. R.
Thomas
,
Nature (London)
271
,
431
(
1978
).
Google Scholar
Crossref
Search ADS
 
6.
A.
Majumdar
and
C. L.
Tien
,
Wear
136
,
313
(
1980
).
Google Scholar
Crossref
Search ADS
 
7.
T. L.
Warren
and
D.
Krajcinovic
,
Int. J. Solids Struct.
32
,
2907
(
1995
).
Google Scholar
Crossref
Search ADS
 
8.
T. L.
Warren
,
A.
Majumdar
, and
D.
Krajcinovic
,
J. Appl. Mech.
63
,
47
(
1996
).
Google Scholar
Crossref
Search ADS
 
9.
B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, CA, 1982).
10.
M. V.
Berry
and
Z. V.
Lewis
,
Proc. R. Soc. London, Ser. A
370
,
459
(
1980
).
Google Scholar
 
11.
K.
Komvopoulos
and
W.
Yan
,
J. Tribol.
119
,
391
(
1997
).
Google Scholar
Crossref
Search ADS
 
12.
M.
Ausloos
and
D. H.
Berman
,
Proc. R. Soc. London, Ser. A
400
,
331
(
1985
).
Google Scholar
 
13.
S.
Wang
and
K.
Komvopoulos
,
J. Tribol.
116
,
812
(
1994
).
Google Scholar
Crossref
Search ADS
 
14.
J. J.
Gagnepain
and
C.
Roques-Carmes
,
Wear
109
,
119
(
1986
).
Google Scholar
Crossref
Search ADS
 
15.
W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in FORTRAN: The Art of Scientific Computing (Cambridge University Press, Cambridge, U.K., 1992), pp. 123–158 and 266–319.
16.
E. Anguiano, M. Pancorbo, and M. Aguilar, Fractals in the Natural and Applied Sciences, edited by M. M. Novak (Elsevier Science, New York, NY, 1994), pp. 37–46.
17.
S.
Wang
and
K.
Komvopoulos
,
J. Tribol.
116
,
824
(
1994
).
Google Scholar
Crossref
Search ADS
 
18.
S.
Wang
and
K.
Komvopoulos
,
J. Tribol.
117
,
203
(
1995
).
Google Scholar
Crossref
Search ADS
 
19.
J.
Pullen
and
J. B. P.
Williamson
,
Proc. R. Soc. London, Ser. A
327
,
159
(
1972
).
Google Scholar
 
20.
S. C. H.
Lin
and
I.
Pugacz-Muraszkiewicz
,
J. Appl. Phys.
43
,
119
(
1972
).
Google Scholar
Crossref
Search ADS
 
21.
G. W. McLellan and E. B. Shand, Glass Engineering Handbook (McGraw–Hill, New York, NY, 1984), pp. 2–23.
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