Abstract

A finite element analysis of a rigid sphere contact with a deformable elastic–plastic plat called indentation model is studied. The numerical results are applied on the rough surfaces contact of the Greenwood-Williamson (G-W) model. A series of the relationships of the rough surfaces contact parameters are obtained. The contact parameters of the indentation model and the flattening model are compared in detail, and the reasons for their differences are analyzed. In the case of single asperity contact, for ω/ωc > 1, the indentation model reaches the initial plastic yield while the flattening model is $ω/ωc=1$. In $ω/ωc=10$, the plastic yield reaches the contact surface for the first time, and the corresponding point of the flattening model is relatively earlier in $ω/ωc=6$. The contact parameters of the rough surface in different plasticity indexes are compared again. On the point of ψ = 0.5, the contact parameters of the flattening model and the indentation model coincide perfectly. For 0.5 < ψ < 4, the difference between the parameters curves become larger and larger. To the point of ψ = 4, when the distance difference reaches the maximum, it begins to decrease until the two curves are close to coincide again. The dimensionless elastic–plastic contact hardness is introduced. The relation between the real contact area and the contact pressure of the indentation model can be acquired quickly. The results show that the geometric shape of deformable contact parts has an important effect on the contact parameters, especially for the extension of the plastic deformation region within a specific range of plasticity index.

References

1.
Polycarpou
,
A. A.
, and
Etsion
,
I.
,
2000
, “
A Model for the Static Sealing Performance of Compliant Metallic Gas Seals Including Surface Roughness and Rarefaction Effects
,”
Tribol. Trans.
,
43
(
2
), pp.
237
244
.
2.
Jiang
,
X.
,
Cheng
,
H. S.
, and
Hua
,
D. Y.
,
2000
, “
A Theoretical Analysis of Mixed Lubrication by Macro Micro Approach: Part I—Results in a Gear Surface Contact
,”
Tribol. Trans.
,
43
(
4
), pp.
689
699
.
3.
Wang
,
Y.
,
Zhang
,
C.
,
Wang
,
Q. J.
, and
Lin
,
C.
,
2002
, “
A Mixed-TEHD Analysis and Experiment of Journal Bearings Under Severe Operating Conditions
,”
Tribol. Int.
,
35
(
6
), pp.
395
407
.
4.
Tabor
,
D.
,
1951
,
The Hardness of Metals
,
Clarendon Press
,
Oxford, UK
.
5.
Johnson
,
K. L.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
6.
Hardy
,
C.
,
Baronet
,
C. N.
, and
Tordion
,
G. V.
,
2010
, “
The Elasto-Plastic Indentation of a Half-Space by a Rigid Sphere
,”
Int. J. Numer. Methods Eng.
,
3
(
4
), pp.
451
462
.
7.
Giannakopoulos
,
A. E.
,
,
P. L.
, and
Vestergaard
,
R.
,
2015
, “
Analysis of Vickers Indentation
,”
Int. J. Solids Struct.
,
31
(
19
), pp.
2679
2708
.
8.
Komvopoulos
,
K.
, and
Ye
,
N.
,
2001
, “
Three-Dimensional Contact Analysis of Elastic-Plastic Layered Media With Fractal Surface Topographies
,”
ASME J. Tribol.
,
123
(
3
), pp.
632
640
.
9.
Kogut
,
L.
, and
Komvopoulos
,
K.
,
2004
, “
Analysis of the Spherical Indentation Cycle for Elastic–Perfectly Plastic Solids
,”
J. Mater. Res.
,
19
(
12
), pp.
3641
3653
.
10.
Park
,
Y. J.
, and
Pharr
,
G. M.
,
2004
, “
Nanoindentation With Spherical Indenters: Finite Element Studies of Deformation in the Elastic–Plastic Transition Regime
,”
Thin Solid Films
,
447
, pp.
246
250
.
11.
Mesarovic
,
S. D.
, and
Fleck
,
N. A.
,
1999
, “
Spherical Indentation of Elastic-Plastic Solids
,”
Proc. R. Soc. A
,
455
(
1987
), pp.
2707
2728
.
12.
Chang
,
W. R.
,
Etsion
,
I.
, and
Bogy
,
D. B.
,
1987
, “
An Elastic-Plastic Model for the Contact of Rough Surfaces
,”
ASME J. Tribol.
,
109
(
2
), pp.
257
263
.
13.
Kogut
,
L.
, and
Etsion
,
I.
,
2002
, “
Elastic-Plastic Contact Analysis of a Sphere and a Rigid Flat
,”
ASME J. Appl. Mech.
,
69
(
5
), pp.
657
662
.
14.
Jackson
,
R. L.
, and
Green
,
I.
,
2005
, “
A Finite Element Study of Elasto-Plastic Hemispherical Contact Against a Rigid Flat
,”
ASME J. Tribol.
,
127
(
2
), pp.
343
354
.
15.
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.
,
43
(
18–19
), pp.
5736
5749
.
16.
Jackson
,
R. L.
, and
Kogut
,
L.
,
2006
, “
A Comparison of Flattening and Indentation Approaches for Contact Mechanics Modeling of Single Asperity Contacts
,”
ASME J. Tribol.
,
128
(
1
), pp.
209
212
.
17.
Cha
,
P. R.
,
Srolovitz
,
D. J.
, and
Vanderlick
,
T. K.
,
2004
, “
Molecular Dynamics Simulation of Single Asperity Contact
,”
Acta Mater.
,
52
(
13
), pp.
3983
3996
.
18.
Jeng
,
Y. R.
,
Kao
,
W. C.
, and
Tsai
,
P. C.
,
2007
, “
Investigation Into the Mechanical Contact Behavior of Single Asperities Using Static Atomistic Simulations
,”
Appl. Phys. Lett.
,
91
(
9
), pp.
10
24
.
19.
Jeng
,
Y. R.
, and
Peng
,
S. R.
,
2009
, “
Investigation Into the Lateral Junction Growth of Single Asperity Contact Using Static Atomistic Simulations
,”
Appl. Phys. Lett.
,
94
(
16
), p.
378
.
20.
Greenwood
,
J. A.
, and
Williamson
,
J.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. A
,
295
(
1442
), pp.
300
319
.
21.
Biwa
,
S.
, and
Storkers
,
B.
,
1995
, “
An Analysis of Fully Plastic Brinell Indentation
,”
J. Mech. Phys. Solids
,
43
(
8
), pp.
1303
1333
.
22.
,
J.
,
Biwa
,
S.
, and
Storakers
,
B.
,
1999
, “
Inelastic Flattening of Rough Surfaces
,”
Mech. Mater.
,
31
(
1
), pp.
29
41
.
23.
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
,”
ASME J. Tribol.
,
130
(
3
), pp.
117
139
.
24.
Jeng
,
Y. R.
, and
Peng
,
S. R.
,
2009
, “
Static Friction Model of Elastic-Plastic Contact Behavior of Surface With Elliptical Asperities
,”
ASME J. Tribol.
,
131
(
2
), p.
021403
.
25.
McCool
,
J. I.
,
1986
, “
Predicting Microfracture in Ceramics Via a Microcontact Model
,”
ASME J. Tribol.
,
108
(
3
), pp.
380
385
.
26.
Etsion
,
I.
, and
Amit
,
M.
,
1993
, “
The Effect of Small Normal Loads on the Static Friction Coefficient for Very Smooth Surfaces
,”
ASME J. Tribol.
,
115
(
3
), pp.
406
410
.
27.
Kogut
,
L.
, and
Etsion
,
I.
,
2003
, “
A Finite Element Based Elastic-Plastic Model for the Contact of Rough Surfaces
,”
Tribol. Trans.
,
46
(
3
), pp.
383
390
.