The local yield maps for the identification of the yield initiation positions of hard coating on three-dimensional (3D) elastic half space under sliding contact were developed. In this study, the semi-analytical method (SAM), which is based on the conjugate gradient method (CGM) and the discrete convolution and fast Fourier transform (DC-FFT) technique, was employed to analyze the contact problem. By using this method, the von Mises stress distributions for various combinations of coating thicknesses, friction coefficients, and elastic moduli of the coating and substrate were calculated. Then, the positions of yield initiation were found with the calculated results by comparing the critical maximum contact pressure Pmax,c for von Mises yielding at or in the different positions (surface, coating, interface, and substrate), and the 3D-local yield maps were introduced in relation to the yield strength ratio of the coating to the substrate (Yf/Yb) and the ratio of the coating thickness to the Hertzian contact radius (t/a0). Finally, the effect of critical friction coefficient on the transition of yielding positions was discussed.

References

References
1.
Posti
,
E.
, and
Niemiuen
,
I.
, 1989, “
Influence of Coating Thickness on the TiN-Coated High Speed Cutting Tools
,”
Wear
,
129
, pp.
273
283
.
2.
Holmberg
,
K.
, 1992, “
A Concept for Friction Mechanisms of Coated Surface
,”
Surf. Coat. Technol.
,
56
, pp.
1
10
.
3.
Holmberg
,
K.
,
Matthews
,
A.
, and
Ronkainen
,
H.
, 1998, “
Coatings Tribology—Contact Mechanisms and Surface Design
,”
Tribol. Int.
,
31
(
1–3
), pp.
107
120
.
4.
Treutler
,
C. P. O.
, 2005, “
Industrial Use of Plasma-deposited Coatings for Components of Automotive Fuel Injection Systems
,”
Surf. Coat. Technol.
,
200
, pp.
1969
1975
.
5.
Erdemir
,
A.
, and
Donnet
,
C.
, 2006, “
Tribology of Diamond-Like Carbon Films: Recent Progress and Future Prospects
,”
J. Phys. D: Appl. Phys.
,
39
, pp.
R311
R327
.
6.
Diao
,
D. F.
,
Kato
,
K.
, and
Hokkirigawa
,
K.
, 1994, “
Fracture Mechanisms of Ceremic Coatings in Indentation
,”
ASME J. Tribol.
116
, pp.
860
869
.
7.
Oliveira
,
S. A. G.
, and
Bower
,
A. F.
, 1996, “
An Analysis of Fracture and Delamination in Thin Coatings Subjected to Contact Loading
,”
Wear
,
198
, pp.
15
32
.
8.
Cheng
,
W.
, and
Cheng
,
H. S.
, 1997, “
Semi-Analytical Modeling of Crack Initiation Dominant Contact Fatigue Life for Roller Bearing
,”
ASME J. Tribol.
,
119
, pp.
233
240
.
9.
Bhomwick
,
S.
,
Kale
,
A. N.
,
Jayaram
,
V.
, and
Biswas
,
S. K.
, 2003, “
Contact Damage in TiN Coatings Steel
,”
Thin Solid Films
,
436
, pp.
250
258
.
10.
Roman
,
K. Z.
, and
Gabriel
,
R.
, 2010, “
Stresses in Hard Coating Due to a Rigid Spherical Indenter on a Layered Elastic Half-Space
,”
Tribol. Int.
,
43
, pp.
1592
1601
.
11.
Keer
,
L. M.
, and
Worden
,
R. E.
, 1990, “
A Qualitative Model to Describe the Microchipping Wear Model in Ceramic Rollers
,”
Tribol. Trans.
,
33
, pp.
411
417
.
12.
Chen
,
S. Y.
,
Farris
,
T. N.
, and
Chandrasckar
,
S.
, 1991, “
Sliding Microindentation Fracture of Brittle Materials
,”
Tribol. Trans.
,
34
, pp.
161
168
.
13.
Keer
,
L. M.
, and
Kuo
,
C. H.
, 1992, “
Cracking in a Loaded Brittle Elastic Half-Space
,”
Int. J. Solids Struct.
,
29
, pp.
1819
1826
.
14.
Bower
,
A. F.
, and
Fleck
,
N. A.
, 1994, “
Brittle Fracture Under a Sliding Line Contact
,”
J. Mech. Phys. Solids
,
42
, pp.
1375
1396
.
15.
Ahmed
,
A.
, and
Hadfield
,
M.
, 1999, “
Failure Modes of Plasma Sprayed WC–15% Co Coated Rolling Elements
,”
Wear
,
230
(
1
), pp.
35
39
.
16.
Zhou
,
K.
,
Keer
,
L. M.
,
Wang
,
Q. J.
, and
Hua
,
D. Y.
, 2011, “
Size Prediction of Particles Caused by Chipping Wear of Hard Coatings
,”
Wear
,
271
, pp.
1203
1206
.
17.
Nowell
,
D.
, and
Hills
,
D. A.
, 1988, “
Contact Problems Incorporating Elastic Layers
,”
Int. J. Solids Struct.
,
24
(
1
), pp.
105
115
.
18.
King
,
R. B.
, and
O’Sullivan
,
T. C.
, 1988, “
Sliding Contact Stress Field Due to a Spherical Indenter on a Layered Elastic Half-space
,”
ASME J. Tribol.
,
109
, pp.
223
231
.
19.
Komvopoulos
,
K.
,
Saka.
N.
, and
Suh
,
N. P.
, 1987, “
The Role of Hard Layers in Lubricated and Dry Sliding
,”
ASME J. Tribol.
,
109
, pp.
223
231
.
20.
Komvopoulos
,
K.
, 1988, “
Finite Element Analysis of a Layered Elastic Solid in Normal Contact With a Rigid Surface
,”
ASME J. Tribol.
,
110
, pp.
477
485
.
21.
Komvopoulos
,
K.
, 1989, “
Elastic-Plastic Finite Element Analysis of Indented Layered Media
,”
ASME J. Tribol.
,
111
, pp.
430
439
.
22.
Plumet
,
S.
, and
Dubourg
,
M. C.
, 1998, “
A 3-D Model for a Multilayered Body Loaded Normally and Tangentially against a Rigid Body: Application to Specific Coatings
,”
ASME J. Tribol.
,
120
, pp.
668
676
.
23.
Stephens
,
L. S.
,
Liu
,
Y.
, and
Meletis
,
E. I.
, 2000, “
Finite Element Analysis of the Initial Yielding Behavior of a Hard Coating-Substrate System With Functionally Graded Interface Under Indentation and Friction
,”
ASME J. Tribol.
,
122
(
2
), pp.
381
387
.
24.
Michler
,
J.
, and
Blank
,
E.
, 2001, “
Analysis of Coating Fracture and Substrate Plasticity Induced by Spherical Indentors: Diamond and Diamond-Like Carbon Layers on Steel Substrates
,”
Thin Solid Films
,
381
, pp.
119
134
.
25.
Holmberg
,
K.
,
Laukkanen
,
A.
,
Ronkainen
,
H.
, and
Wallin
,
K.
, 2005, “
Tribological Analysis of Fracture in Thin Surface Coatings by 3D FEM Modeling and Stress Simulations
,”
Tribol. Int.
,
38
, pp.
1035
1049
.
26.
Lin
,
W.
, and
Keer
,
L. M.
, 1989, “
Three-Dimensional Analysis of Cracks in Layered Transversely Isotropic Media
,”
Proc. R. Soc. London, Ser. A
,
424
, pp.
307
322
.
27.
Kuo
,
C. H.
, and
Keer
,
L. M.
, 1995, “
Three-Dimensional Analysis of Cracking in a Multilayered Composite
,”
ASME J. Appl. Mech.
,
62
, pp.
273
281
.
28.
Polonsky
,
I. A.
, and
Keer
,
L. M.
, 2001, “
Stress Analysis of Layered Elastic Solids With Cracks Using the Fast Fourier Transform and Conjugate Gradient Techniques
,”
ASME J. Appl. Mech.
,
68
(
5
), pp.
708
714
.
29.
Nogi
,
T.
, and
Kato
,
T.
, 1997, “
Influence of a Hard Surface Layer on the Limit of Elastic Contact—Part I: Analysis Using a Real Surface Model
,”
ASME J. Tribol.
,
119
, pp.
493
500
.
30.
Polonsky
,
I. A.
, and
Keer
,
L. M.
, 1999, “
A Numerical Method for Solving Rough Contact Problems Based on the Multi-Level Multi-Summation and Conjugate Gradient Techniques
,”
Wear
,
231
, pp.
206
219
.
31.
Liu
,
S. B.
,
Wang
,
Q.
, and
Liu
,
G.
, 2000, “
A Versatile Method of Discrete Convolution and FFT (DC-FFT) for Contact Analyses
,”
Wear
,
243
, pp.
101
111
.
32.
Boucly
,
V.
,
Nélias
,
D.
,
Liu
,
S. B.
,
Wang
,
Q. J.
, and
Keer
,
L. M.
, 2005, “
Contact Analyses for Bodies With Frictional Heating and Plastic Behavior
,”
ASME J. Tribol.
,
127
, pp.
355
364
.
33.
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
, p.
021403
.
34.
Chen
,
W. W.
,
Zhou
,
K.
,
Keer
,
L. M.
, and
Wang
,
Q. J.
, 2010, “
Modeling Elasto-Plastic Indentation on Layered Materials Using the Equivalent Inclusion Method
,”
Int. J. Solids Struct.
,
47
, pp.
2841
2854
.
35.
Diao
,
D. F.
,
Kato
,
K.
, and
Hayashi
,
K.
, 1992, “
The Local Yield Map of Hard Coating under Siding Contact
,” Proceedings of the 19th Leeds-Lyon Symposium on Tribology,
Elsevier
,
Amsterdam
, pp.
419
427
.
36.
Diao
,
D. F.
, and
Kato
,
K.
, 1994, “
Interface Yield Map of a Hard Coating Under Sliding Contact
,”
Thin Solid Films
,
245
, pp.
115
121
.
37.
Diao
,
D. F.
, and
Ito
,
K.
, 1999, “
Local Yield Map and Elastic-Plastic Deformation Map of Hard Coating With Lubricative Particles Under Sliding
,”
Surf. Coat. Technol.
,
115
, pp.
193
200
.
38.
Diao
,
D. F.
, and
Kandori
,
A.
, 2006, “
Finite Element Analysis of the Effect of Interfacial Roughness and Adhesion Strength on the Local Delamination of Hard Coating Under Sliding Contact
,”
Tribol. Int.
,
39
, pp.
849
855
.
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