A model for the contact area and static friction of nominally flat rough surfaces and rough spherical surfaces is presented. The model extends previously published models, which are limited to plasticity index values below 8, to higher plasticity index values by accounting for fully plastically deformed asperities based on finite element results by Jackson and Green [2005, “A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat,” Trans. ASME, J. Tribol., 127, pp. 343–354]. The present model also corrects some deficiencies of the earlier models at very small plasticity index values below 0.5.

1.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
, 1966, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London, Ser. A
0950-1207,
295
, pp.
300
319
.
2.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
3.
Chang
,
W.
,
Etsion
,
I.
, and
Bogy
,
D.
, 1987, “
Elastic Plastic Model for the Contact of Rough Surfaces
,”
Trans. ASME, J. Tribol.
0742-4787,
109
, pp.
257
262
.
4.
Kogut
,
L.
, and
Etsion
,
I.
, 2002, “
Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat
,”
Trans. ASME, J. Appl. Mech.
0021-8936,
69
, pp.
657
662
.
5.
Kogut
,
L.
, and
Etsion
,
I.
, 2003, “
A Finite Element Based Elastic-Plastic Model for the Contact of Rough Surfaces
,”
Tribol. Trans.
1040-2004,
46
(
3
), pp.
383
390
.
6.
Jackson
,
R.
, and
Green
,
I.
, 2005, “
A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat
,”
Trans. ASME, J. Tribol.
0742-4787,
127
, pp.
343
354
.
7.
Jackson
,
R.
, and
Green
,
I.
, 2006, “
A Statistical Model of Elasto-Plastic Asperity Contact Between Rough Surfaces
,”
Tribol. Int.
0301-679X,
39
, pp.
906
914
.
8.
Pei
,
L.
,
Hyun
,
S.
,
Molinari
,
J.
, and
Robbins
,
M.
, 2005, “
Finite Element Modeling of Elasto-Plastic Contact Between Rough Surfaces
,”
J. Mech. Phys. Solids
0022-5096,
53
, pp.
2385
2409
.
9.
Abdo
,
J.
, and
Farhang
,
K.
, 2005, “
Elastic-Plastic Contact Model for Rough Contacts Based on Plastic Asperity Concept
,”
Int. J. Non-Linear Mech.
0020-7462,
40
, pp.
495
506
.
10.
Hariri
,
A.
, and
Mrad
,
R.
, 2006, “
Modeling of Elastic/Plastic Contact Between Nominally Flat Rough Surfaces Using an n-Point Asperity Model
,”
Trans. ASME, J. Tribol.
0742-4787,
128
, pp.
876
885
.
11.
Eid
,
H.
, and
Adams
,
G.
, 2007, “
An Elastic-Plastic Finite Element Analysis of Interacting Asperities in Contact With a Rigid Flat
,”
J. Phys. D: Appl. Phys.
0022-3727,
40
, pp.
7432
7439
.
12.
Wang
,
F. S.
,
Block
,
J. M.
,
Chen
,
W. W.
,
Martini
,
A.
,
Zhou
,
K.
,
Keer
,
L. M.
, and
Wang
,
Q. J.
, 2009, “
A Multilevel Model for Elastic-Plastic Contact Between a Sphere and a Flat Rough Surface
,”
Trans. ASME, J. Tribol.
0742-4787,
131
, p.
021409
.
13.
Yeo
,
C.
,
Katta
,
R.
, and
Polycarpou
,
A.
, 2009, “
Improved Elastic Contact Model Accounting for Asperity and Bulk Substrate Deformation
,”
Tribol. Lett.
1023-8883,
35
, pp.
191
203
.
14.
Ilincic
,
S.
,
Vorlaufer
,
G.
,
Fotiu
,
P. A.
,
Vernes
,
A.
, and
Franek
,
F.
, 2009, “
Combined Finite Element-Boundary Element Method Modeling of Elastic Multi-Asperity Contacts
,”
Proc. Inst. Mech. Eng., Part J: J. Eng. Tribol.
1350-6501,
223
(
5
), pp.
767
776
.
15.
Sepehri
,
A.
, and
Farhang
,
K.
, 2009, “
Closed-Form Equations for Three Dimensional Elastic-Plastic Contact of Nominally Flat Rough Surfaces
,”
Trans. ASME, J. Tribol.
0742-4787,
131
, p.
041402
.
16.
Dowson
,
D.
, 1979,
History of Tribology
,
Longman
,
New York
.
17.
Tabor
,
D.
, 1981, “
Friction—The Present State of Our Understanding
,”
ASME J. Lubr. Technol.
0022-2305,
103
, pp.
169
179
.
18.
Chang
,
W. R.
,
Etsion
,
I.
, and
Bogy
,
D. B.
, 1988, “
Static Friction Coefficient Model for Metallic Rough Surfaces
,”
Trans. ASME, J. Tribol.
0742-4787,
110
, pp.
57
63
.
19.
Kogut
,
L.
, and
Etsion
,
I.
, 2003, “
A Semi-Analytical Solution for the Sliding Inception of a Spherical Contact
,”
Trans. ASME, J. Tribol.
0742-4787,
125
, pp.
499
506
.
20.
Kogut
,
L.
, and
Etsion
,
I.
, 2004, “
A Static Friction Model for Elastic-Plastic Contacting Rough Surfaces
,”
Trans. ASME, J. Tribol.
0742-4787,
126
, pp.
34
40
.
21.
Brizmer
,
V.
,
Kligerman
,
Y.
, and
Etsion
,
I.
, 2006, “
Elastic-Plastic Spherical Contact Under Combined Normal and Tangential Loading in Full Stick
,”
Tribol. Lett.
1023-8883,
25
, pp.
61
70
.
22.
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.
0020-7683,
43
, pp.
5736
5749
.
23.
Brizmer
,
V.
,
Zait
,
Y.
,
Kligerman
,
Y.
, and
Etsion
,
I.
, 2006, “
The Effect of Contact Conditions and Material Properties on Elastic-Plastic Spherical Contact
,”
J. Mech. Mater. Struct.
1559-3959,
1
, pp.
865
879
.
24.
Cohen
,
D.
,
Kligerman
,
Y.
, and
Etsion
,
I.
, 2008, “
A Model for Contact and Static Friction of Nominally Flat Rough Surfaces Under Full Stick Contact Condition
,”
Trans. ASME, J. Tribol.
0742-4787,
130
, p.
031401
.
25.
Cohen
,
D.
,
Kligerman
,
Y.
, and
Etsion
,
I.
, 2009, “
The Effect of Surface Roughness on Static Friction and Junction Growth of an Elastic-Plastic Spherical Contact
,”
Trans. ASME, J. Tribol.
0742-4787,
131
, p.
021404
.
26.
Ovcharenko
,
A.
,
Halperin
,
G.
, and
Etsion
,
I.
, 2008, “
Experimental Study of Adhesive Static Friction in a Spherical Elastic-Plastic Contact
,”
Trans. ASME, J. Tribol.
0742-4787,
130
, p.
021401
.
27.
Yu
,
N.
,
Pergande
,
S.
, and
Polycarpou
,
A. A.
, 2004, “
Static Friction Model for Rough Surfaces With Asymmetric Distribution of Asperity Heights
,”
Trans. ASME, J. Tribol.
0742-4787,
126
, pp.
626
629
.
28.
Chang
,
L.
, and
Zhang
,
L.
, 2007, “
A Mathematical Model for Frictional Elastic-Plastic Sphere-on-Flat Contacts at Sliding Incipient
,”
Trans. ASME, J. Appl. Mech.
0021-8936,
74
, pp.
100
106
.
29.
Deladi
,
E. L.
,
de Rooij
,
M. B.
, and
Schipper
,
D. J.
, 2007, “
Modeling of Static Friction in Rubber-Metal Contact
,”
Tribol. Int.
0301-679X,
40
, pp.
588
594
.
30.
Jeng
,
Y.
, and
Peng
,
S.
, 2009, “
Static Friction Model of Elastic-Plastic Contact Behavior of Surface With Elliptical Asperities
,”
Trans. ASME, J. Tribol.
0742-4787,
131
, p.
021403
.
31.
Chen
,
W.
, and
Wang
,
Q.
, 2009, “
A Numerical Static Friction Model for Spherical Contacts of Rough Surfaces, Influence of Load, Material, and Roughness
,”
Trans. ASME, J. Tribol.
0742-4787,
131
, p.
021402
.
32.
Mindlin
,
R.
, 1949, “
Compliance of Elastic Bodies in Contact
,”
ASME Trans. J. Appl. Mech.
0021-8936,
16
, pp.
259
268
.
33.
Greenwood
,
J. A.
, and
Tripp
,
J. H.
, 1970, “
The Contact of Two Nominally Flat Rough Surfaces
,”
Proc. Inst. Mech. Eng.
0020-3483,
185
, pp.
625
634
.
34.
Greenwood
,
G. A.
, and
Tripp
,
J. H.
, 1967, “
The Elastic Contact of Rough Spheres
,”
ASME Trans. J. Appl. Mech.
0021-8936,
34
, pp.
153
159
.
You do not currently have access to this content.