Finite element (FE) simulations were performed to study yielding in single and bilayer (BL) film systems using a “yield zone map” approach. Onset of yielding was observed at the interface, substrate, surface, and film in HfB2/silicon and HfB2/stainless steel systems. The interface yield zone in HfB2/stainless steel system was found to be larger due to the dominant effect of interfacial stress gradients. Based on the FE simulations, empirical equations were derived for the maximum contact pressure required to initiate yield at the interface. For BL/substrate systems, onset of yield at the lower film/substrate interface occurred when film thickness ratio was in the range 0.5–5. The maximum contact pressure associated with the initial yielding at this interface is minimum compared to other locations. From the design point of view, for a BL system the preferable film thickness ratio was found to be 20, whereas the optimum hardness ratio ranges from 2 to 4. For these values, maximum contact pressure is very high (∼30 GPa), and thus, yield onset can be avoided at lower film/substrate interfaces. In addition, based on the obtained results, the advantages and disadvantages of using a BL film as compared to a single film and their relevance to practical applications are discussed.

References

References
1.
Vossen
,
J. L.
, and
Kern
,
W.
,
1991
,
Thin Film Processes II
,
Academic
,
Boston, MA
.
2.
Bhushan
,
B.
,
1999
,
Handbook of Micro/Nanotribology
,
CRC
,
Boca Raton, FL
.
3.
Grill
,
A.
,
1993
, “
Review of the Tribology of Diamond-Like Carbon
,”
Wear
,
168
(
1–2
), pp.
143
153
.
4.
Dearnaley
,
G.
, and
Arps
,
J. H.
,
2005
, “
Biomedical Applications of Diamond-Like Carbon (DLC) Coatings: A Review
,”
Surf. Coat. Technol.
,
200
(
7
), pp.
2518
2524
.
5.
Lee
,
K. M.
,
Yeo
,
C. D.
, and
Polycarpou
,
A. A.
,
2007
, “
Nanomechanical Property and Nanowear Measurements for Sub-10-nm Thick Films in Magnetic Storage
,”
Exp. Mech.
,
47
(
1
), pp.
107
121
.
6.
Komvopoulos
,
K.
,
2000
, “
Head-Disk Interface Contact Mechanics for Ultrahigh Density Magnetic Recording
,”
Wear
,
238
(
1
), pp.
1
11
.
7.
Ferrari
,
A. C.
,
2004
, “
Diamond-Like Carbon for Magnetic Storage Disks
,”
Surf. Coat. Technol.
,
180–181
, pp.
190
206
.
8.
Erdemir
,
A.
, and
Donnet
,
C.
,
2006
, “
Tribology of Diamond-Like Carbon Films: Recent Progress and Future Prospects
,”
J. Phys. D: Appl. Phys.
,
39
(
18
), pp.
R311
R327
.
9.
Fu
,
Y. Q.
,
Du
,
H. J.
,
Huang
,
W. M.
,
Zhang
,
S.
, and
Hu
,
M.
,
2004
, “
TiNi-Based Thin Films in MEMS Applications: A Review
,”
Sens. Actuators A
,
112
(
2–3
), pp.
395
408
.
10.
Bull
,
S. J.
,
Rickerby
,
D. S.
,
Robertson
,
T.
, and
Hendry
,
A.
,
1988
, “
The Abrasive Wear-Resistance of Sputter Ion Plated Titanium Nitride Coatings
,”
Surf. Coat. Technol.
,
36
(
3–4
), pp.
743
754
.
11.
Bull
,
S. J.
,
1999
, “
Can Scratch Testing be Used as a Model for the Abrasive Wear of Hard Coatings?
,”
Wear
,
233–235
, pp.
412
423
.
12.
Diao
,
D. F.
,
Kato
,
K.
, and
Hokkirigawa
,
K.
,
1994
, “
Fracture Mechanisms of Ceramic Coatings in Indentation
,”
ASME J. Tribol.
,
116
(
4
), pp.
860
869
.
13.
Kulchytsky-Zhyhailo
,
R.
, and
Rogowski
,
G.
,
2010
, “
Stresses in Hard Coating Due to a Rigid Spherical Indenter on a Layered Elastic Half-Space
,”
Tribol. Int.
,
43
(
9
), pp.
1592
1601
.
14.
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
(
7–8
), pp.
1203
1206
.
15.
Zhang
,
P. Y.
,
Diao
,
D. F.
, and
Wang
,
Z. J.
,
2012
, “
Three-Dimensional Local Yield Maps of Hard Coating Under Sliding Contact
,”
ASME J. Tribol.
,
134
(
2
), p.
021301
.
16.
Hamilton
,
G. M.
, and
Goodman
,
L. E.
,
1966
, “
Stress Field Created by a Circular Sliding Contact
,”
ASME J. Appl. Mech.
,
33
(
2
), pp.
371
376
.
17.
King
,
R. B.
, and
Osullivan
,
T. C.
,
1987
, “
Sliding Contact Stresses in a Two-Dimensional Layered Elastic Half-Space
,”
Int. J. Solids Struct.
,
23
(
5
), pp.
581
597
.
18.
Kral
,
E. R.
, and
Komvopoulos
,
K.
,
1996
, “
Three-Dimensional Finite Element Analysis of Surface Deformation and Stresses in an Elastic-Plastic Layered Medium Subjected to Indentation and Sliding Contact Loading
,”
ASME J. Appl. Mech.
,
63
(
2
), pp.
365
375
.
19.
Diao
,
D. F.
,
1999
, “
Finite Element Analysis on Local Yield Map and Critical Maximum Contact Pressure for Yielding in Hard Coating With an Interlayer Under Sliding Contact
,”
Tribol. Int.
,
32
(
1
), pp.
25
32
.
20.
Tian
,
H.
, and
Saka
,
N.
,
1991
, “
Finite-Element Analysis of an Elastic-Plastic 2-Layer Half-Space—Sliding Contact
,”
Wear
,
148
(
2
), pp.
261
285
.
21.
Diao
,
D. F.
, and
Koji
,
K.
,
1994
, “
Interface Yield Map of a Hard Coating Under Sliding Contact
,”
Thin Solid Films
,
245
(
1–2
), pp.
115
121
.
22.
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
(
9
), pp.
849
855
.
23.
Cai
,
T. X.
,
Zhang
,
P. Y.
, and
Diao
,
D. F.
,
2013
, “
Evolution of Maximum Contact Stresses in Amorphous Carbon Coated Silicon During Sliding Wear Against Si3N4 Ball
,”
ASME J. Tribol.
,
135
(
2
), p.
021401
.
24.
Holmberg
,
K.
,
Laukkanen
,
A.
,
Ronkainen
,
H.
, and
Wallin
,
K.
,
2005
, “
Tribological Analysis of Fracture Conditions in Thin Surface Coatings by 3D FEM Modelling and Stress Simulations
,”
Tribol. Int.
,
38
(
11–12
), pp.
1035
1049
.
25.
Goltsberg
,
R.
,
Etsion
,
I.
, and
Davidi
,
G.
,
2011
, “
The Onset of Plastic Yielding in a Coated Sphere Compressed by a Rigid Flat
,”
Wear
,
271
(
11–12
), pp.
2968
2977
.
26.
Song
,
W. P.
,
Li
,
L. Q.
,
Ovcharenko
,
A.
,
Jia
,
D.
,
Etsion
,
I.
, and
Talke
,
F. E.
,
2012
, “
Plastic Yield Inception of an Indented Coated Flat and Comparison With a Flattened Coated Sphere
,”
Tribol. Int.
,
53
, pp.
61
67
.
27.
Huang
,
X.
,
Kasem
,
H.
,
Shang
,
H. F.
,
Shao
,
T. M.
, and
Etsion
,
I.
,
2012
, “
Experimental Study of a Potential Weakening Effect in Spheres With Thin Hard Coatings
,”
Wear
,
296
(
1–2
), pp.
590
597
.
28.
Goltsberg
,
R.
, and
Etsion
,
I.
,
2013
, “
A Model for the Weakening Effect of Very Thin Hard Coatings
,”
Wear
,
308
(
1–2
), pp.
10
16
.
29.
Song
,
W. P.
,
Li
,
L. Q.
,
Etsion
,
I.
,
Ovcharenko
,
A.
, and
Talke
,
F. E.
,
2014
, “
Yield Inception of a Soft Coating on a Flat Substrate Indented by a Rigid Sphere
,”
Surf. Coat. Technol.
,
240
, pp.
444
449
.
30.
Goltsberg
,
R.
, and
Etsion
,
I.
,
2015
, “
A Universal Model for the Load-Displacement Relation in an Elastic Coated Spherical Contact
,”
Wear
,
322
, pp.
126
132
.
31.
Huang
,
X.
,
Etsion
,
I.
, and
Shao
,
T.
,
2015
, “
Effects of Elastic Modulus Mismatch Between Coating and Substrate on the Friction and Wear Properties of TiN and TiAlN Coating Systems
,”
Wear
,
338
, pp.
54
61
.
32.
Jayaraman
,
S.
,
Gerbi
,
J. E.
,
Yang
,
Y.
,
Kim
,
D. Y.
,
Chatterjee
,
A.
,
Bellon
,
P.
,
Girolami
,
G. S.
,
Chevalier
,
J. P.
, and
Abelson
,
J. R.
,
2006
, “
HfB2 and Hf-B-N Hard Coatings by Chemical Vapor Deposition
,”
Surf. Coat. Technol.
,
200
(
22–23
), pp.
6629
6633
.
33.
Chatterjee
,
A.
,
Jayaraman
,
S.
,
Gerbi
,
J. E.
,
Kumar
,
N.
,
Abelson
,
J. R.
,
Bellon
,
P.
,
Polycarpou
,
A. A.
, and
Chevalier
,
J. P.
,
2006
, “
Tribological Behavior of Hafnium Diboride Thin Films
,”
Surf. Coat. Technol.
,
201
(
7
), pp.
4317
4322
.
34.
Chatterjee
,
A.
,
Kumar
,
N.
,
Abelson
,
J. R.
,
Bellon
,
P.
, and
Polycarpou
,
A. A.
,
2008
, “
Nanoscratch and Nanofriction Behavior of Hafnium Diboride Thin Films
,”
Wear
,
265
(
5–6
), pp.
921
929
.
35.
Chatterjee
,
A.
,
Kumar
,
N.
,
Abelson
,
J. R.
,
Bellon
,
P.
, and
Polycarpou
,
A. A.
,
2010
, “
Nanowear of Hafnium Diboride Thin Films
,”
Tribol. Trans.
,
53
(
5
), pp.
731
738
.
36.
Chatterjee
,
A.
,
Polycarpou
,
A. A.
,
Abelson
,
J. R.
, and
Bellon
,
P.
,
2010
, “
Nanoscratch Study of Hard HfB2 Thin Films Using Experimental and Finite Element Techniques
,”
Wear
,
268
(
5–6
), pp.
677
685
.
37.
ABAQUS
,
2007
,
Analysis: User's Manual
,
ABAQUS, Version 6.7.1 Documentation
,
Simulia, Providence, RI
.
38.
Bhattacharya
,
A. K.
, and
Nix
,
W. D.
,
1988
, “
Analysis of Elastic and Plastic-Deformation Associated With Indentation Testing of Thin-Films on Substrates
,”
Int. J. Solids Struct.
,
24
(
12
), pp.
1287
1298
.
39.
Chen
,
X.
,
Xiang
,
Y.
, and
Vlassak
,
J. J.
,
2006
, “
Novel Technique for Measuring the Mechanical Properties of Porous Materials by Nanoindentation
,”
J. Mater. Res.
,
21
(
3
), pp.
715
724
.
40.
Lee
,
K. M.
,
Yeo
,
C. D.
, and
Polyearpou
,
A. A.
,
2008
, “
Relationship Between Scratch Hardness and Yield Strength of Elastic Perfectly Plastic Materials Using Finite Element Analysis
,”
J. Mater. Res.
,
23
(
8
), pp.
2229
2237
.
41.
Veprek
,
S.
, and
Argon
,
A. S.
,
2002
, “
Towards the Understanding of Mechanical Properties of Super- and Ultrahard Nanocomposites
,”
J. Vac. Sci. Technol. B
,
20
(
2
), pp.
650
664
.
42.
Petersen
,
K. E.
,
1982
, “
Silicon as a Mechanical Material
,”
Proc. IEEE
,
70
(
5
), pp.
420
457
.
43.
Knapp
,
J. A.
,
Follstaedt
,
D. M.
,
Myers
,
S. M.
,
Barbour
,
J. C.
, and
Friedmann
,
T. A.
,
1999
, “
Finite-Element Modeling of Nanoindentation
,”
J. Appl. Phys.
,
85
(
3
), pp.
1460
1474
.
44.
Knapp
,
J. A.
,
Follstaedt
,
D. M.
,
Myers
,
S. M.
,
Barbour
,
J. C.
,
Friedmann
,
T. A.
,
Ager
,
J. W.
,
Monteiro
,
O. R.
, and
Brown
, I
. G.
,
1998
, “
Finite-Element Modeling of Nanoindentation for Evaluating Mechanical Properties of MEMS Materials
,”
Surf. Coat. Technol.
,
104
, pp.
268
275
.
45.
Bolshakov
,
A.
,
Oliver
,
W. C.
, and
Pharr
,
G. M.
,
1996
, “
Influences of Stress on the Measurement of Mechanical Properties Using Nanoindentation.2. Finite Element Simulations
,”
J. Mater. Res.
,
11
(
3
), pp.
760
768
.
46.
Hay
,
J. C.
,
Bolshakov
,
A.
, and
Pharr
,
G. M.
,
1999
, “
A Critical Examination of the Fundamental Relations Used in the Analysis of Nanoindentation Data
,”
J. Mater. Res.
,
14
(
6
), pp.
2296
2305
.
47.
Katta
,
R. R.
,
Nunez
,
E. E.
,
Polycarpou
,
A. A.
, and
Lee
,
S. C.
,
2009
, “
Plane Strain Sliding Contact of Multilayer Magnetic Storage Thin-Films Using the Finite Element Method
,”
Microsyst. Technol. Micro- Nanosyst. Inf. Storage Process. Syst.
,
15
(
7
), pp.
1097
1110
.
48.
Katta
,
R. R.
,
Polycarpou
,
A. A.
,
Lee
,
S. C.
, and
Suk
,
M.
,
2010
, “
Experimental and FEA Scratch of Magnetic Storage Thin-Film Disks to Correlate Magnetic Signal Degradation With Permanent Deformation
,”
ASME J. Tribol.
,
132
(
2
), p.
021902
.
49.
Etsion
,
I.
,
2015
, “
Comment on Leonardo da Vinci's Friction Experiments: An Old Story Acknowledged and Repeated
,”
Tribol. Lett.
,
58
(
2
), pp.
1
2
.
50.
Jungk
,
J. M.
,
Michael
,
J. R.
, and
Prasad
,
S. V.
,
2008
, “
The Role of Substrate Plasticity on the Tribological Behavior of Diamond-Like Nanocomposite Coatings
,”
Acta Mater.
,
56
(
9
), pp.
1956
1966
.
51.
Djabella
,
H.
, and
Arnell
,
R. D.
,
1993
, “
Finite-Element Comparative-Study of Elastic Stresses in Single, Double-Layer and Multilayered Coated Systems
,”
Thin Solid Films
,
235
(
1–2
), pp.
156
162
.
52.
Tayebi
,
N.
,
Conry
,
T. F.
, and
Polycarpou
,
A. A.
,
2004
, “
Reconciliation of Nanoscratch Hardness With Nanoindentation Hardness Including the Effects of Interface Shear Stress
,”
J. Mater. Res.
,
19
(
11
), pp.
3316
3323
.
53.
Lee
,
K. M.
, and
Polycarpou
,
A. A.
,
2006
, “
Shear Strength Determination Using the Nanoscratch Technique and Its Application to Thin Solid Films
,”
J. Mater. Res.
,
21
(
9
), pp.
2304
2313
.
54.
Suk
,
M.
, and
Gillis
,
D.
,
1998
, “
Effect of Slider Burnish on Disk Damage During Dynamic Load/Unload
,”
ASME J. Tribol.
,
120
(
2
), pp.
332
338
.
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