Abstract

Understanding the contact characteristics of rough surfaces is essential to explain engineering phenomenon in interface. In order to improve accuracy of contact model, a novel simplified fully plastic contact model of sphere asperity was proposed considering material properties based on fractal theory. First, based on Von Mises yield criteria, maximum contact pressure factor was derived. Second, relationships taking into consideration strain hardening effects were proposed to describe contact area based on the fully plastic contact area index and contact pressure. Then, the critical interference at inception of fully plastic deformation was derived. Lastly, validations were conducted for different materials. The results show that the present work is remarkably consistent with experimental results and has higher accuracy than other models.

References

1.
Greenwood
,
J. A.
, and
Williamson
,
J. B. P.
,
1966
, “
Contact of Nominally Flat Surfaces
,”
Proc. R. Soc. A: Math. Phys. Eng. Sci.
,
295
(
1442
), pp.
300
319
.
2.
Abbott
,
E. J.
, and
Firestone
,
F. A.
,
1933
, “
Specifying Surface Quality—A Method Based on Accurate Measurement and Comparison
,”
J. Mech. Eng.
,
55
, pp.
569
572
.
3.
Meyer
,
E.
,
1908
, “
Investigations of Hardness Testing and Hardness
,”
Z. Phys.
,
9
, pp.
66
74
.
4.
Tabor
,
D.
,
1951
,
The Hardness of Metals
,
Clarendon Press
,
Oxford, UK
.
5.
Ishlinskii
,
A.
,
1944
, “
The Problem of Plasticity With Axial Symmetry and Brinell’s Test
,”
J. Appl. Math. Mech.
,
8
, pp.
201
224
.
6.
Shlinsky
,
A. J.
,
1943
, “
The Stressed State of a Cylinder at Large Angles of Torsion
,”
Appl. Math. Mech. [Akad. Nauk SSSR. Prikl. Mat. Mech.]
,
7
, pp.
223
225
.
7.
Matthews
,
J. R.
,
1980
, “
Indentation Hardness and hot Pressing
,”
Acta Metall.
,
28
(
3
), pp.
311
318
.
8.
Johnson
,
K. L.
,
1968
, “An Experimental Determination of the Contact Stresses Between Plastically Deformed Cylinders and Spheres,”
Engineering Plasticity
,
J.
Heyman
and
F. A.
Leckie
, eds.,
Cambridge University Press
,
Cambridge, UK
, pp.
341
361
.
9.
Chaudhri
,
M. M.
,
Hutchings
,
I. M.
, and
Makin
,
P. L.
,
1984
, “
Plastic Compression of Spheres
,”
Philos. Mag. A
,
49
(
4
), pp.
493
503
.
10.
Chaudhri
,
M. M.
,
1987
, “
The Plastic Deformation of Single Asperities by Hard Flats
,”
Proc. Inst. Mech. Eng.
,
158
, pp.
1003
1012
.
11.
Jamari
,
J.
, and
Schipper
,
D. J.
,
2006
, “
Experimental Investigation of Fully Plastic Contact of a Sphere Against a Hard Flat
,”
ASME J. Tribol.
,
128
(
2
), pp.
230
235
.
12.
Pawlus
,
P.
,
Zelasko
,
W.
,
Dzierwa
,
A.
,
Prucnal
,
S.
, and
Wieczorowski
,
M.
,
2018
, “
Experimental Investigation of a Hemisphere Contact With a Hard Flat
,”
Philos. Tech. Gaz.
,
25
(
1
), pp.
40
46
.
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.
Mesarovic
,
S. D.
, and
Fleck
,
N. A.
,
1999
, “
Spherical Indentation of Elastic–Plastic Solids
,”
Proc. R. Soc. London A
,
455
(
1987
), pp.
2707
2728
.
15.
Mesarovic
,
S. D.
, and
Fleck
,
N. A.
,
2000
, “
Frictionless Indentation of Dissimilar Elastic-Plastic Spheres
,”
Int. J. Solids Struct.
,
37
(
46–47
), pp.
7071
7091
.
16.
Ye
,
N.
, and
Komvopoulos
,
K.
,
2003
, “
Indentation Analysis of Elastic-Plastic Homogeneous and Layered Media: Criteria for Determining the Real Material Hardness
,”
ASME J. Tribol.
,
125
(
4
), pp.
685
691
.
17.
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
.
18.
Ghaednia
,
H.
,
Pope
,
S. A.
,
Jackson
,
R. L.
, and
Marghitu
,
D. B.
,
2016
, “
A Comprehensive Study of the Elasto-Plastic Contact of a Sphere and a Flat
,”
Tribol. Int.
,
93
, pp.
78
90
.
19.
Ghaednia
,
H.
,
Brake
,
M. R. W.
,
Berryhill
,
M.
, and
Jackson
,
R. L.
,
2019
, “
Strain Hardening From Elastic-Perfectly Plastic to Perfectly Elastic Flattening Single Asperity Contact
,”
ASME J. Tribol.
,
141
(
3
), p.
031402
.
20.
Megalingam
,
A.
, and
Hanumanth Ramji
,
K. S.
,
2021
, “
A Complete Elastic-Plastic Spherical Asperity Contact Model With the Effect of Isotropic Strain Hardening
,”
Proc. Inst. Mech. Eng. J: J. Eng. Tribol.
,
235
(
4
), pp.
820
829
.
21.
Chen
,
J.
,
Zhang
,
W.
,
Wang
,
C.
,
Liu
,
D.
, and
Zhu
,
L.
,
2022
, “
An Accurate Solution of a Hemisphere Contact Against a Rigid Flat Under Varying Elastic Moduli and Yield Strengths and Comparison With Previous Model
,”
J. Mech. Sci. Technol.
,
36
(
9
), pp.
4615
4624
.
22.
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
.
23.
Jackson
,
R. L.
, and
Green
,
I.
,
2003
, “
A Finite Element Study of Elasto-Plastic Hemispherical Contact
,”
Proceeding of 2003 STLE/ASME Joint Tribology Conference
, ASME Paper No. 2003TRIB-268.
24.
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
.
25.
Brake
,
M. R.
,
2012
, “
An Analytical Elastic-Perfectly Plastic Contact Model
,”
Int. J. Solids Struct.
,
49
(
22
), pp.
3129
3141
.
26.
Jackson
,
R. L.
,
Ghaednia
,
H.
, and
Pope
,
S.
,
2015
, “
A Solution of Rigid–Perfectly Plastic Deep Spherical Indentation Based on Slip-Line Theory
,”
Tribol. Lett.
,
58
(
3
), pp.
1
7
.
27.
Majumdar
,
A.
, and
Bhushan
,
B.
,
1991
, “
Fractal Model of Elastic-Plastic Contact Between Rough Surfaces
,”
ASME J. Tribol.
,
113
(
1
), pp.
1
11
.
28.
Yan
,
W.
, and
Komvopoulos
,
K.
,
1998
, “
Contact Analysis of Elastic-Plastic Fractal Surfaces
,”
J. Appl. Phys.
,
84
(
7
), pp.
3617
3624
.
29.
Yu
,
R.
,
Chen
,
W.
, and
Gachot
,
C.
,
2018
, “
Fractal Modeling of Elastic-Plastic Contact Between Three-Dimensional Rough Surfaces
,”
Ind. Lubr. Tribol.
,
70
(
2
), pp.
290
300
.
30.
Xiao
,
H.
,
Sun
,
Y.
, and
Chen
,
Z.
,
2019
, “
Fractal Modeling of Normal Contact Stiffness for Rough Surface Contact Considering the Elastic–Plastic Deformation
,”
J. Braz. Soc. Mech. Sci. Eng.
,
41
(
11
).
31.
Zhao
,
Y.
,
Maietta
,
D. M.
, and
Chang
,
L.
,
2000
, “
An Asperity Microcontact Model Incorporating the Transition From Elastic Deformation to Fully Plastic Flow
,”
ASME J. Tribol.
,
122
(
1
), pp.
86
93
.
32.
Lin
,
L. P.
, and
Lin
,
J. F.
,
2005
, “
An Elasto-Plastic Asperity Contact Model for Metallic Materials
,”
ASME J. Tribol.
,
127
(
3
), pp.
666
672
.
33.
Brake
,
M.
,
2015
, “
An Analytical Elastic Plastic Contact Model With Strain Hardening and Frictional Effects for Normal and Oblique Impacts
,”
Int. J. Solids Struct.
,
62
, pp.
104
123
.
34.
Olsson
,
E.
, and
Larsson
,
P. L.
,
2016
, “
A Unified Model for the Contact Behaviour Between Equal and Dissimilar Elastic–Plastic Spherical Bodies
,”
Int. J. Solids Struct.
,
81
, pp.
23
32
.
35.
Hertz
,
H.
,
1882
, “
On the Contact of Elastic Solids
,”
J. für die Reine und Angew. Math.
,
92
(
3
), pp.
156
171
.
36.
Xu
,
J.
,
Zhu
,
J.
,
Xia
,
W.
, and
Liu
,
B.
,
2022
, “
Asperity Contact Area Considering Strain Hardening for Metallic Materials
,”
ASME J. Tribol.
,
144
(
4
), p.
041503
.
37.
Alcalá
,
J.
,
Giannakopoulos
,
A. E.
, and
Suresh
,
S.
,
1998
, “
Continuous Measurements of Load-Penetration Curves With Spherical Microindenters and the Estimation of Mechanical Properties
,”
J. Mater. Res.
,
13
(
5
), pp.
1390
1400
.
38.
Satound
,
S.
, and
Okoshi
,
N.
,
1981
, “
Tensile and Hardness Tests of Various Aluminum Alloys
,”
J. Jpn. Inst. Light Met.
,
31
(
6
), pp.
401
409
.
You do not currently have access to this content.