The multiple normal loading-unloading process of an elastic-plastic sphere by a rigid flat is analyzed using finite element method for stick contact condition and both kinematic and isotropic hardening models. The behavior of the global contact parameters as well as the stress field within the sphere tip is presented for several loading cycles. It was found that under stick contact condition, secondary plastification occurs even after the second loading cycle and that the hardening model used has little effect on the loading-unloading process. The cyclic loading process gradually converges into elastic shakedown.

1.
Kadin
,
Y.
,
Kligerman
,
Y.
, and
Etsion
,
I.
, 2006, “
Unloading of Elastic-Plastic Contact of Rough Surfaces
,”
J. Mech. Phys. Solids
0022-5096,
54
, pp.
2652
2674
.
2.
Johnson
,
K. L.
, 1985,
Contact Mechanics
,
Cambridge University Press
,
Cambridge
.
3.
Jackson
,
R.
,
Chusoipin
,
I.
, and
Green
,
I.
, 2005, “
A Finite Element Study of the Residual Stress and Deformation in Hemispherical Contacts
,”
ASME J. Tribol.
0742-4787,
127
, pp.
484
493
.
4.
Etsion
,
I.
,
Kligerman
,
Y.
, and
Kadin
,
Y.
, 2005, “
Unloading of an Elastic-Plastic Loaded Spherical Contact
,”
Int. J. Solids Struct.
0020-7683,
42
, pp.
3716
3729
.
5.
Du
,
Y.
,
Chen
,
L.
,
McGruer
,
N. E.
,
Adams
,
G. G.
, and
Etsion
,
I.
, 2007, “
A Finite Element Model of Loading and Unloading of an Asperity Contact With Adhesion and Plasticity
,”
J. Colloid Interface Sci.
0021-9797,
312
, pp.
522
528
.
6.
Kral
,
E. R.
,
Komvopoulos
,
K.
, and
Bogy
,
D. B.
, 1993, “
Elastic-Plastic Finite Element Analysis of Repeated Indentation of a Half-Space by a Rigid Sphere
,”
ASME J. Appl. Mech.
0021-8936,
60
, pp.
829
841
.
7.
Kadin
,
Y.
,
Kligerman
,
Y.
, and
Etsion
,
I.
, 2006, “
Multiple Loading-Unloading of an Elastic-Plastic Spherical Contact
,”
Int. J. Solids Struct.
0020-7683,
43
, pp.
7119
7127
.
8.
Kadin
,
Y.
,
Kligerman
,
Y.
, and
Etsion
,
I.
, 2008, “
Loading-Unloading of an Elastic-Plastic Adhesive Spherical Microcontact
,”
J. Colloid Interface Sci.
0021-9797,
321
, pp.
242
250
.
9.
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
.
10.
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
.
11.
Zait
,
Y.
,
Kligerman
,
Y.
, and
Etsion
,
I.
, 2010, “
Unloading of an Elastic-Plastic Spherical Contact Under Stick Contact Condition
,”
Int. J. Solids Struct.
0020-7683,
47
, pp.
990
997
.
12.
Parker
,
R.
, and
Hatch
,
D.
, 1950, “
The Static Friction Coefficient and the Area of Contact
,”
Proc. Phys. Soc. London
0370-1328,
B63
, pp.
185
197
.
13.
Aymerich
,
F.
, and
Pau
,
M.
, 2004, “
Assessment of Nominal Contact Area Parameters by Means of Ultrasonic Waves
,”
ASME J. Tribol.
0742-4787,
126
, pp.
639
645
.
14.
Ovcharenko
,
A.
,
Halperin
,
G.
,
Verberne
,
G.
, and
Etsion
,
I.
, 2007, “
In Situ Investigation of the Contact Area in Elastic-Plastic Spherical Contact During Loading-Unloading
,”
Tribol. Lett.
1023-8883,
25
, pp.
153
160
.
15.
Ovcharenko
,
A.
,
Halperin
,
G.
, and
Etsion
,
I.
, 2008, “
In Situ and Real-Time Optical Investigation of Junction Growth in Spherical Elastic-Plastic Contact
,”
Wear
0043-1648,
264
, pp.
1043
1050
.
16.
McGuiggan
,
P. M.
, 2008, “
Stick Slip Mechanics Between Dissimilar Materials: Effect of Charging and Large Friction
,”
Langmuir
0743-7463,
24
, pp.
3970
3976
.
17.
Jirásek
,
M.
, and
Bazant
,
Z. P.
, 2002,
Inelastic Analysis of Structures
,
Wiley
,
Chichester
.
18.
Feng
,
X. Q.
, and
Liu
,
X. S.
, 1996, “
On Shakedown of Three Dimensional Elastoplastic Strain Hardening Structures
,”
Int. J. Plast.
0749-6419,
12
, pp.
1241
1256
.
19.
Ambrico
,
J. M.
, and
Begley
,
M. S.
, 2000, “
Plasticity in Fretting Contact
,”
J. Mech. Phys. Solids
0022-5096,
48
, pp.
2391
2417
.
20.
Chen
,
W. W.
,
Wang
,
Q. J.
,
Wang
,
F.
,
Keer
,
L. M.
, and
Cao
,
J.
, 2008, “
Three-Dimensional Repeated Elasto-Plastic Point Contacts, Rolling, and Sliding
,”
Trans. ASME, J. Appl. Mech.
0021-8936,
75
, p.
021021
.
21.
Kadin
,
Y.
,
Kligerman
,
Y.
, and
Etsion
,
I.
, 2008, “
Cyclic Loading of an Elastic-Plastic Adhesive Spherical Microcontact
,”
J. Appl. Phys.
0021-8979,
104
, p.
073522
.
22.
Etsion
,
I.
, 2010, “
“Revisiting the Cattaneo–Mindlin Concept of Interfacial Slip in Tangentially Loaded Compliant Bodies
,”
ASME J. Tribol.
0742-4787,
132
, p.
020801
.
You do not currently have access to this content.