As loading forces decrease in applications such as MEMS and NEMS devices, the size of the asperity contacts which comprise the real contact area tend to decrease into the nano scale regime. This reduction in size of the contacts is only partially offset by the nominally increased smoothness of these contacting surfaces. Because the friction force depends on the real area of contact, it is important to understand how the material and topographical properties of surfaces contribute to friction forces at this nano scale. In this investigation, the single asperity nano contact model of Hurtado and Kim is incorporated into a multi-asperity model for contact and friction which includes the effect of asperity adhesion forces using the Maugis-Dugdale model. The model spans the range from nano-scale to micro-scale to macro-scale contacts. Three key dimensionless parameters have been identified which represent combinations of surface roughness measures, Burgers vector length, surface energy, and elastic properties. Results are given for the friction coefficient versus normal force, the normal and friction forces versus separation, and the pull-off force for various values of these key parameters.

1.
Tabor
,
D.
,
1981
, “
Friction-The Present State of Our Understanding
,”
ASME J. Lubr. Technol.
,
103
, pp.
169
179
.
2.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London, Ser. A
,
A295
, pp.
300
319
.
3.
Hutchinson
,
J. W.
,
2000
, “
Plasticity at the Micron Scale
,”
Int. J. Solids Struct.
,
37
, pp.
225
238
.
4.
Johnson, K. L., 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
5.
McCool
,
J. I.
,
1986
, “
Comparison of Models for the Contact of Rough Surfaces
,”
Wear
,
107
, pp.
37
60
.
6.
Greenwood
,
J. A.
, and
Tripp
,
J. H.
,
1971
, “
The Contact of Two Nominally Flat Rough Surfaces
,”
Proc. Inst. Mech. Eng.
,
185
, pp.
625
633
.
7.
Johnson
,
K. L.
,
Kendall
,
K.
, and
Roberts
,
A. D.
,
1971
, “
Surface Energy and the Contact of Elastic Solids
,”
Proc. R. Soc. London, Ser. A
,
A324
, pp.
301
313
.
8.
Derjaguin
,
B. V.
,
Muller
,
V. M.
, and
Toporov
,
Y. P.
,
1975
, “
Effect of Contact Deformations on the Adhesion of Particles
,”
J. Colloid Interface Sci.
,
53
, pp.
314
326
.
9.
Tabor
,
D.
,
1976
, “
Surface Forces and Surface Interactions
,”
J. Colloid Interface Sci.
,
58
, pp.
2
13
.
10.
Maugis
,
D.
,
1992
, “
Adhesion of Spheres: The JKR-DMT Transition Using a Dugdale Model
,”
J. Colloid Interface Sci.
,
150
, pp.
243
269
.
11.
Johnson
,
K. L.
, and
Greenwood
,
J. A.
,
1997
, “
An Adhesion Map for the Contact of Elastic Spheres
,”
J. Colloid Interface Sci.
,
192
, pp.
326
333
.
12.
Dugdale
,
D. S.
,
1960
, “
Yielding in Steel Sheets Containing Slits
,”
J. Mech. Phys. Solids
,
8
, pp.
100
104
.
13.
Chang
,
R. W.
,
Etsion
,
I.
, and
Bogy
,
D. B.
,
1987
, “
An Elastic-Plastic Model for the Contact of Rough Surfaces
,”
ASME J. Tribol.
,
109
, pp.
257
263
.
14.
Chang
,
R. W.
,
Etsion
,
I.
, and
Bogy
,
D. B.
,
1988
, “
Adhesion Model for Metallic Rough Surfaces
,”
ASME J. Tribol.
,
110
, pp.
50
56
.
15.
Chang
,
R. W.
,
Etsion
,
I.
, and
Bogy
,
D. B.
,
1988
, “
Static Friction Coefficient Model for Metallic Rough Surfaces
ASME J. Tribol.
,
110
, pp.
57
63
.
16.
Hamilton
,
G. M.
,
1983
, “
Explicit Equations for the Stresses Beneath a Sliding Spherical Contact
,”
Proc. Inst. Mech. Eng.
,
197C
, pp.
53
59
.
17.
Fuller
,
K. N. G.
, and
Tabor
,
D.
,
1975
, “
The Effect of Surface Roughness on the Adhesion of Elastic Solids
,”
Proc. R. Soc. London, Ser. A
,
345
, pp.
327
342
.
18.
Stanley
,
H. M.
,
Etsion
,
I.
, and
Bogy
,
D. B.
,
1990
, “
Adhesion of Contacting Rough Surfaces in the Presence of Sub-Boundary Lubrication
,”
ASME J. Tribol.
,
112
, pp.
98
104
.
19.
Polycarpou
,
A. A.
, and
Etsion
,
I.
,
1998
, “
Static Friction of Contacting Real Surfaces in the Presence of Sub-Boundary Lubrication
,”
ASME J. Tribol.
,
120
, pp.
296
303
.
20.
Maugis
,
D.
,
1996
, “
On the Contact and Adhesion of Rough Surfaces
,”
J. Adhes. Sci. Technol.
,
10
, pp.
161
175
.
21.
Tworzydlo
,
W. W.
,
Cecot
,
W.
,
Oden
,
J. T.
, and
Yew
,
C. H.
,
1998
, “
Computational Micro- and Macroscopic Models of Contact and Friction: Formulation, Approach and Applications
,”
Wear
,
220
, pp.
113
140
.
22.
Kapoor
,
A.
,
Williams
,
J. A.
, and
Johnson
,
K. L.
,
1994
, “
The Steady State Sliding of Rough Surfaces
,”
Wear
,
175
, pp.
81
92
.
23.
Carpick
,
R. W.
,
Agrait
,
N.
,
Ogletree
,
D. F.
, and
Salmeron
,
M.
,
1996
, “
Measurement of Interfacial Shear (Friction) With an Ultrahigh Vacuum Atomic Force Microscope
,”
J. Vac. Sci. Technol. B
,
14
, pp.
1289
1295
.
24.
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
.
25.
Hurtado
,
J. A.
, and
Kim
,
K.-S.
,
1999
, “
Scale Effects in Friction of Single Asperity Contacts: Part I; From Concurrent Slip to Single-Dislocation-Assisted Slip
,”
Proc. R. Soc. London, Ser. A
,
A455
, pp.
3363
3384
.
26.
Hurtado
,
J. A.
, and
Kim
,
K.-S.
,
1999
, “
Scale Effects in Friction in Single Asperity Contacts: Part II; Multiple-Dislocation-Cooperated Slip
,”
Proc. R. Soc. London, Ser. A
,
A455
, pp.
3385
3400
.
27.
Adams, G. G., Mu¨ftu¨, S., and Mohd Azhar, N., 2002, “A Nano-Scale Multi-Asperity Model for Contact and Friction,” Paper No. ASME 2002-TRIB-258.
You do not currently have access to this content.