A plane contact and partial slip model of an elastic layer with randomly rough surface were established by combining the Greenwood–Williamson (GW) rough contact model and the Cattaneo–Mindlin partial slip model. The rough surface of the elastic layer bonded to a rigid base is modeled as an ensemble of noninteracting asperities with identical radius of curvature and Gaussian-distributed heights. By employing the Hertzian solution and the Cattaneo–Mindlin solution to each individual asperity of the rough surface, we derive the total normal force, the real contact area, and the total tangential force for the rough surface, respectively, and then examine the normal contact and partial slip behaviors of the layer. An effective Coulomb coefficient is defined to account for interfacial friction properties. Furthermore, a typical stick–slip transition for the rough surface was also captured by distinguishing the stick and slip contacting asperities according to their respective indentation depths. Our analysis results show that an increasing layer thickness may result in a larger real contact area, a lower mean contact pressure, and a higher effective Coulomb coefficient.

References

References
1.
Bhushan
,
B.
,
1999
,
Principles and Applications of Tribology
,
Wiley
,
New York
.
2.
Wood
,
R. J.
,
2007
, “
Tribo-Corrosion of Coatings: A Review
,”
J. Phys. D: Appl. Phys.
,
40
(
18
), pp.
5502
5521
.10.1088/0022-3727/40/18/S10
3.
Holmberg
,
K.
, and
Mattews
,
A.
,
2001
, “
Tribological Properties of Metallic and Ceramic Coatings
,”
Modern Tribology Handbook
,
B.
Bhushan
, ed.,
CRC Press
,
New York
, Chap. 23.10.1201/9780849377877.ch23
4.
Ching
,
H. A.
,
Choudhury
,
D.
,
Nine
,
M. J.
, and
Osman
,
N. A. A.
,
2014
, “
Effects of Surface Coating on Reducing Friction and Wear of Orthopaedic Implants
,”
Sci. Technol. Adv. Mater.
,
15
(
1
), p.
014402
.10.1088/1468-6996/15/1/014402
5.
Meijers
,
P.
,
1968
, “
The Contact Problem of a Rigid Cylinder on an Elastic Layer
,”
Appl. Sci. Res.
,
18
(
1
), pp.
353
383
.10.1007/BF00382359
6.
Aleksandrov
,
V. M.
,
1969
, “
Asymptotic Solution of the Contact Problem for a Thin Layer
,”
PMM
,
33
(1), pp.
49
63
.10.1016/0021-8928(69)90113-0
7.
Alblas
,
J. B.
, and
Kuipers
,
M.
,
1970
, “
On the Two-Dimensional Problem of a Cylindrical Stamp Pressed Into a Thin Elastic Layer
,”
Acta Mech.
,
9
(
3–4
), pp.
292
311
.10.1007/BF01179827
8.
Greenwood
,
J. A.
, and
Barber
,
J. R.
,
2012
, “
Indentation of an Elastic Layer by a Rigid Cylinder
,”
Int. J. Solids Struct.
,
49
(
21
), pp.
2962
2977
.10.1016/j.ijsolstr.2012.05.036
9.
Komvopoulos
,
K.
, and
Gong
,
Z. Q.
,
2007
, “
Stress Analysis of a Layered Elastic Solid in Contact With a Rough Surface Exhibiting Fractal Behavior
,”
Int. J. Solids Struct.
,
44
(
78
), pp.
2109
2129
.10.1016/j.ijsolstr.2006.06.043
10.
Persson
,
B. N. J.
,
2006
, “
Contact Mechanics for Randomly Rough Surfaces
,”
Surf. Sci. Rep.
,
61
(
4
), pp.
201
227
.10.1016/j.surfrep.2006.04.001
11.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. London A
,
295
(1442), pp.
300
319
.10.1098/rspa.1966.0242
12.
Greenwood
,
J. A.
,
Putignano
,
C.
, and
Ciavarella
,
M.
,
2011
, “
A Greenwood & Williamson Theory for Line Contact
,”
Wear
,
270
(
3
), pp.
332
334
.10.1016/j.wear.2010.11.002
13.
Ciavarella
,
M.
,
Dibello
,
S.
, and
Demelio
,
G.
,
2008
, “
Conductance of Rough Random Profiles
,”
Int. J. Solids Struct.
,
45
(
3–4
), pp.
879
893
.10.1016/j.ijsolstr.2007.09.009
14.
Zhao
,
Y.
, and
Chang
,
L.
,
2002
, “
A Micro-Contact and Wear Model for Chemical–Mechanical Polishing of Silicon Wafers
,”
Wear
,
252
(
3–4
), pp.
220
226
.10.1016/S0043-1648(01)00871-7
15.
Morrow
,
C.
,
Lovell
,
M. R.
, and
Ning
,
X.
,
2003
, “
A JKR-DMT Transition Solution for Adhesive Rough Surface Contact
,”
J. Phys. D: Appl. Phys.
,
36
(5), pp.
534
540
.10.1088/0022-3727/36/5/317
16.
Zhang
,
W.
,
Jin
,
F.
,
Guo
,
X.
, and
Zhang
,
S.
,
2014
, “
Adhesive Contact on Randomly Rough Surfaces Based on the Double-Hertz Model
,”
ASME J. Appl. Mech.
,
81
(
5
), p.
051008
.10.1115/1.4026019
17.
Jones
,
R. E.
,
2007
, “
A Greenwood-Williamson Model of Small-Scale Friction
,”
ASME J. Appl. Mech.
,
74
(
1
), pp.
31
40
.10.1115/1.2172269
18.
Cattaneo
,
C.
,
1938
, “
Sul contatto di due corpi elastici: Distribuzione locale degli sforzi
,”
R. C. Accad. Naz. Lincei
,
27
, pp.
474
478
.
19.
Mindlin
,
R. D.
,
1949
, “
Compliance of Elastic Bodies in Contact
,”
ASME J. Appl. Mech.
,
16
, pp.
259
268
.
20.
Etsion
,
I.
,
2008
, “
Discussion: ‘A Greenwood-Williamson Model of Small-Scale Friction’
,”
ASME J. Appl. Mech.
,
75
(4), p.
045501
.10.1115/1.2870267
21.
Corwin
,
A. D.
,
Street
,
M. D.
,
Carpick
,
R. W.
,
Ashurst
,
W. R.
, and
de Boer
,
M. P.
,
2004
, “
Pre-Sliding Tangential Deflection Can Govern Friction in MEMS Devices
,”
ASME
Paper No. TRIB2004-64360. 10.1115/TRIB2004-64360
22.
Peng
,
W.
, and
Bhushan
,
B.
,
2001
, “
Three-Dimensional Contact Analysis of Layered Elastic/Plastic Solids With Rough Surfaces
,”
Wear
,
249
(
9
), pp.
741
760
.10.1016/S0043-1648(01)00692-5
23.
Peng
,
W.
, and
Bhushan
,
B.
,
2002
, “
Sliding Contact Analysis of Layered Elastic/Plastic Solids With Rough Surfaces
,”
ASME J. Tribol.
,
124
(
1
), pp.
46
61
.10.1115/1.1401018
24.
Nowell
,
D.
, and
Hills
,
D. A.
,
1998
, “
Contact Problems Incorporating Elastic Layers
,”
Int. J. Solids Struct.
,
24
(
1
), pp.
105
115
.10.1016/0020-7683(88)90102-3
25.
Wang
,
Z. J.
,
Wang
,
W. Z.
,
Wang
,
H.
,
Zhu
,
D.
, and
Hu
,
Y. Z.
,
2010
, “
Partial Slip Contact Analysis on Three-Dimensional Elastic Layered Half-Space
,”
ASME J. Tribol.
,
132
(
2
), p.
021403
.10.1115/1.4001011
26.
Chen
,
P.
, and
Chen
,
S.
,
2013
, “
Partial Slip Contact Between a Rigid Punch With an Arbitrary Tip-Shape and an Elastic Graded Solid With a Finite Thickness
,”
Mech. Mater.
,
59
(
1
), pp.
24
35
.10.1016/j.mechmat.2012.12.003
27.
Chen
,
P.
,
Chen
,
S.
, and
Peng
,
Z.
,
2012
, “
Thermo-Contact Mechanics of a Rigid Cylindrical Punch Sliding on a Finite Graded Layer
,”
Acta Mech.
,
223
(
12
), pp.
2647
2665
.10.1007/s00707-012-0732-y
28.
Chen
,
P.
, and
Chen
,
S.
,
2013
, “
Thermo-Mechanical Contact Behavior of a Finite Graded Layer Under a Sliding Punch With Heat Generation
,”
Int. J. Solids Struct.
,
50
(
7–8
), pp.
1108
1119
.10.1016/j.ijsolstr.2012.12.007
29.
Johnson
,
K. L.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
30.
Kesari
,
H.
,
Doll
,
J.
,
Pruitt
,
B.
,
Wei
,
C.
, and
Lew
,
A.
,
2010
, “
The Role of Surface Roughness During Adhesive Elastic Contact
,”
Philos. Mag. Lett.
,
90
(
12
), pp.
891
902
.10.1080/09500839.2010.521204
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