Abstract

The complexity of modeling friction between rough surfaces has prompted many researchers to use Greenwood and Tripp’s sum surface assumption to simplify the analysis. This assumption approximates the contact between two rough surfaces as contact between their equivalent sum surface and a rigid plane. In this work, we develop detailed finite element models to test the sum surface assumption for surfaces with Gaussian and exponential autocorrelation functions. We consider surfaces with differing surface roughness and correlation length values. For each case, we conduct simulations of two rough surfaces interacting in compression followed by shear, and a corresponding equivalent surface model based on the sum surface assumption. Multiple realizations of each parameter combination are simulated to obtain a statistical picture of the responses. We find that (a) the sum surface assumption consistently under-predicts the static coefficient of friction and (b) the equivalent surface model is less accurate for surfaces with differing correlation length-to-surface roughness ratios.

Issue Section:
Contact Mechanics
Keywords:
friction, equivalent surface, finite element modeling, rough surfaces‌
Topics:
Compression, Displacement, Friction, Shear (Mechanics), Simulation, Surface roughness, Testing, Stress, Finite element analysis, Modeling

References

1.
Greenwood
,
J. A.
, and
Williamson
,
J.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. Lond. A: Math. Phys. Eng. Sci.
,
295
(
1442
), pp.
300
–
319
.
2.
Greenwood
,
J. A.
, and
Tripp
,
J. H.
,
1970
, “
The Contact of Two Nominally Flat Rough Surfaces
,”
Tribol. Group
,
185
(
1
), pp.
625
–
633
.
3.
Jackson
,
R. L.
,
2005
, “
A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat
,”
ASME J. Tribol.
,
127
(
2
), pp.
343
–
354
. 10.1115/1.1866166
4.
Chatterjee
,
B.
, and
Sahoo
,
P.
,
2012
, “
Effect of Strain Hardening on Elastic-Plastic Contact of a Deformable Sphere Against a Rigid Flat Under Full Stick Contact Condition
,”
Adv. Tribol.
,
2012
, pp.
1
–
8
. 10.1155/2012/472794
5.
Kogut
,
L.
, and
Etsion
,
I.
,
2004
, “
A Static Friction Model for Elastic-Plastic Contacting Rough Surfaces
,”
ASME J. Tribol.
,
126
(
1
), pp.
34
–
40
. 10.1115/1.1609488
6.
Karpenko
,
Y. A.
, and
Akay
,
A.
,
2001
, “
A Numerical Model of Friction Between Rough Surfaces
,”
Tribol. Int.
,
34
(
8
), pp.
531
–
545
. 10.1016/S0301-679X(01)00044-5
7.
Hu
,
Y.
,
Cheng
,
H. S.
,
Arai
,
T.
,
Kobayashi
,
Y.
, and
Aoyama
,
S.
,
1994
, “
Numerical Simulation of Piston Ring in Mixed Lubrication—A Nonaxisymmetrical Analysis
,”
ASME J. Tribol.
,
116
(
3
), pp.
470
–
478
. 10.1115/1.2928867
8.
Sista
,
B.
, and
Vemaganti
,
K.
,
2015
, “
A Computational Study of Dry Static Friction Between Elastoplastic Surfaces Using a Statistically Homogenized Microasperity Model
,”
ASME J. Tribol.
,
137
(
2
), p.
021601
. 10.1115/1.4028998
9.
Cohen
,
D.
,
Kligerman
,
Y.
, and
Etsion
,
I.
,
2008
, “
A Model for Contact and Static Friction of Nominally Flat Rough Surfaces Under Full Stick Contact
,”
ASME J. Tribol.
,
130
(
3
), p.
031401
. 10.1115/1.2908925
10.
Li
,
L.
,
Etsion
,
I.
, and
Talke
,
F. E.
,
2010
, “
Contact Area and Static Friction of Rough Surfaces With High
,”
ASME J. Tribol.
,
132
(
3
), p.
031401
. 10.1115/1.4001555
11.
Zolotarevskiy
,
V.
,
Kligerman
,
Y.
, and
Etsion
,
I.
,
2011
, “
The Evolution of Static Friction for Elastic-Plastic Spherical Contact in Pre-sliding
,”
ASME J. Tribol.
,
133
(
3
), p.
034502
. 10.1115/1.4004304
12.
Sahli
,
R.
,
Pallares
,
G.
,
Ducottet
,
C.
,
Ali
,
I. E. B.
,
Akhrass
,
S. A.
,
Guibert
,
M.
, and
Scheibert
,
J.
,
2018
, “
Evolution of Real Contact Area Under Shear and the Value of Static Friction of Soft Materials
,”
Proc. Natl. Acad. Sci. U. S. A.
,
115
(
3
), pp.
471
–
476
. 10.1073/pnas.1706434115
13.
Wang
,
X.
,
Xu
,
Y.
, and
Jackson
,
R. L.
,
2019
, “
Theoretical and Finite Element Analysis of Static Friction Between Multi-Theoretical and Finite Element Analysis of Static Friction Between Multi-Scale Rough Surfaces
,”
Tribol. Lett.
,
66
(
4
), p.
146
. 10.1007/s11249-018-1099-6
14.
Ghaednia
,
H.
,
Wang
,
X.
,
Saha
,
S.
,
Sharma
,
A.
,
Xu
,
Y.
, and
Jackson
,
R. L.
,
2018
, “
A Review of Elastic-Plastic Contact Mechanics
,”
ASME Appl. Mech. Rev.
,
69
(
6
), p.
060804
. 10.1115/1.4038187
15.
Persson
,
B. N. J.
,
2001
, “
Theory of Rubber Friction and Contact Mechanics
,”
J. Chem. Phys.
,
115
(
8
), pp.
3840
–
3861
. 10.1063/1.1388626
16.
Persson
,
B. N. J.
,
Bucher
,
F.
, and
Chiaia
,
B.
,
2002
, “
Elastic Contact Between Randomly Rough Surfaces: Comparison of Theory With Numerical Results
,”
Phys. Rev. B
,
65
(
18
), p.
184106
. 10.1103/PhysRevB.65.184106
17.
Persson
,
B. N. J.
,
2008
, “
On the Elastic Energy and Stress Correlation in the Contact Between Elastic Solids With Randomly Rough Surfaces
,”
J. Phys.: Condens. Matter
,
20
(
31
), pp.
1
–
3
.
18.
Scaraggi
,
M.
, and
Persson
,
B. N. J.
,
2015
, “
General Contact Mechanics Theory for Randomly Rough Surfaces With Application to Rubber Friction
,”
J. Chem. Phys.
,
143
(
22
), pp.
1
–
9
.
19.
Afferrante
,
L.
,
Bottiglione
,
F.
,
Persson
,
B. N. J.
, and
Putignano
,
C.
,
2018
, “
Elastic Contact Mechanics of Randomly Rough Surfaces: An Assessment of Advanced Asperity Models and Persson’s Theory
,”
Tribol. Lett.
,
66
(
2
), pp.
1
–
13
. 10.1007/s11249-018-1026-x
20.
Carbone
,
G.
, and
Bottiglione
,
F.
,
2011
, “
Contact Mechanics of Rough Surfaces: a Comparison Between Theories
,”
Meccanica
,
46
(
3
), pp.
557
–
565
. 10.1007/s11012-010-9315-y
21.
Gupta
,
P. K.
,
1970
, “
Discussion on JA Greenwood and JH Tripp
,”
Tribology Group
,
185
(
1
), pp.
245
–
246
.
22.
Tran
,
I. T.
,
Robbe-Valloire
,
F.
, and
Quillien
,
M.
,
2013
, “
Validity of Sum Surface Assumption in the Case of Static Contact Between Rough Periodic Surfaces
,”
World Tribology Congress
.
23.
Shi
,
X.
, and
Zou
,
Y.
,
2018
, “
A Comparative Study on Equivalent Modeling of Rough Surfaces Contact
,”
ASME J. Tribol.
,
140
(
4
), p.
041402
. 10.1115/1.4039231
24.
Sista
,
B.
,
2014
, “
Dry Static Friction in Metals: Experiments and Micro-Asperity Based Modeling
,”
Ph.D. thesis
,
University of Cincinnati
,
Cincinnati, Ohio
.
25.
Bergström
,
D.
,
2014
, “
Rough Surface Generation and Analysis
,” http://www.mysimlabs.com/
26.
Garcia
,
N.
, and
Stoll
,
E.
,
1984
, “
Monte Carlo Calculation for Electromagnetic-Wave Scattering From Random Rough Surfaces
,”
Phys. Rev. Lett.
,
52
(
20
), pp.
1798
–
1801
. 10.1103/PhysRevLett.52.1798
27.
Ansys
,
2018
,
ANSYS 18 User Manual
.
ANSYS Inc
.,
Canonsburg, PA
.
28.
Thompson
,
M. K.
,
2006
, “
Methods for Generating Rough Surfaces in ANSYS
,”
International ANSYS Users Conference and Exhibition
,
Pittsburgh, PA
,
ANSYS, Inc
.
29.
Hypermesh
,
2013
,
Hypermesh User Manual v13.0
,
Altair Hyperworks
,
Johnston, RI
, https://www.researchgate.net/publication/237566348_Methods_for_Generating_ Rough_Surfaces_in_ANSYS
30.
ABAQUS/CAE
,
2017
,
ABAQUS User Manual
,
Dassault Systèmes
,
Troy, MI
.
31.
Cohen
,
D.
,
Kligerman
,
Y.
, and
Etsion
,
I.
,
2009
, “
The Effect of Surface Roughness on Static Friction and Junction Growth of An Elastic-Plastic
,”
ASME J. Tribol.
,
131
(
3
), p.
021404
. 10.1115/1.3075866
32.
Johnson
,
G. R.
, and
Cook
,
W. H.
,
1985
, “
Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures
,”
Eng. Fract. Mech.
,
21
(
1
), pp.
31
–
48
. 10.1016/0013-7944(85)90052-9
33.
Akram
,
S.
,
Husain
,
S.
,
Jaffery
,
I.
,
Khan
,
M.
,
Fahad
,
M.
,
Mubashar
,
A.
, and
Ali
,
L.
,
2018
, “
Numerical and Experimental Investigation of Johnson–Cook Material Models for Aluminum (Al 6061-T6) Alloy Using Orthogonal Machining Approach
,”
Adv. Mech. Eng.
,
10
(
9
), pp.
1
–
14
. 10.1177/1687814018797794
34.
Center
,
O. S.
,
1987
, “
Ohio Supercomputer Center
,” http://osc.edu/ark:/19495/f5s1ph73.
35.
Müser
,
M. H.
,
Dapp
,
W. B.
,
Bugnicourt
,
R.
,
Sainsot
,
P.
,
Lesaffre
,
N.
,
Lubrecht
,
T. A.
,
Persson
,
B. N. J.
,
Harris
,
K.
,
Bennett
,
A.
,
Schulze
,
K.
,
Rohde
,
S.
,
Ifju
,
P.
,
Sawyer
,
W. G.
,
Angelini
,
T.
,
Ashtari Esfahani
,
H.
,
Kadkhodaei
,
M.
,
Akbarzadeh
,
S.
,
Wu
,
J.-J.
,
Vorlaufer
,
G.
,
Vernes
,
A.
,
Solhjoo
,
S.
,
Vakis
,
A. I.
,
Jackson
,
R. L.
,
Xu
,
Y.
,
Streator
,
J.
,
Rostami
,
A.
,
Dini
,
D.
,
Medina
,
S.
,
Carbone
,
G.
,
Bottiglione
,
F.
,
Afferrante
,
L.
,
Monti
,
J.
,
Pastewka
,
L.
,
Robbins
,
M. O.
, and
Greenwood
,
J. A.
,
2017
, “
Meeting the Contact-Mechanics Challenge
,”
Tribol. Lett.
,
65
(
4
), p.
118
. 10.1007/s11249-017-0900-2
36.
Bhagwat
,
P.
,
Sista
,
B.
, and
Vemaganti
,
K.
,
2017
, “
A Computational Study of the Effects of Strain Hardening in Micro-Asperity Friction Models
,”
Tribol. Lett.
,
65
(
4
), p.
154
. 10.1007/s11249-017-0939-0
37.
Mulvihill
,
D. M.
,
Kartal
,
M. E.
,
Nowell
,
D.
, and
Hills
,
D. A.
,
2011
, “
An Elastic–Plastic Asperity Interaction Model for Sliding Friction
,”
Tribiol. Int.
,
44
(
12
), pp.
1679
–
1694
. 10.1016/j.triboint.2011.06.018
38.
Jackson
,
R. L.
,
Ghaednia
,
H.
,
Lee
,
H.
,
Rostami
,
A.
, and
Wang
,
X.
,
2013
, “Contact Mechanics,”
Tribology for Scientist and Engineers
,
P. L.
Menezes
,
S. P.
Ingole
,
M.
Nosonovsky
,
S. V.
Kailas
,
M. R.
Lovell
, eds.,
Springer
,
US
, pp.
295
–
389
.
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