The document is a thesis defense presentation for a Masters degree in Mechanical Engineering. It discusses pre-sliding frictional analysis of a coated spherical asperity through finite element analysis (FEA) modeling in ABAQUS. Previous research on homogeneous and coated asperity models under normal and tangential loading are reviewed. The objective is to develop a 3D FEA model to analyze pre-sliding friction of coated asperities under combined loading and compare results. The methodology, FEA model development, verification studies, and results are presented.

1. Thesis defense presentation for the degree in
Masters of Engineering Science in Mechanical Engineering
Advisor: Dr. Ali Beheshti
Akshay Patel
Graduate Student
November 20th 2017
PRE-SLIDING FRICTIONAL ANALYSIS OF A
COATED SPHERICAL ASPERITY

2. Content
2
 Future Work Recommendation
 Conclusions
 Results
 Verification and Validation
 FEA Model
 Methodology
 Objective
 Previous Research
 Background

3. Background
3
Introduction- Friction
 Whenever two surfaces come in contact
with each other, friction comes into play.
 Friction with its many advantages and disadvantages, remains a complex
phenomenon till today.
Applied Force
Friction
Motion
Static Friction force
0 < 𝐹𝑠 ≤ 𝜇 𝑠 𝑁
Kinetic Friction force
𝐹𝑘 = 𝜇 𝑘 𝑁
Applied Tangential Force
FrictionalForce
𝐹𝑠 = 𝜇 𝑠 𝑁
𝐹𝑘 = 𝜇 𝑘 𝑁

4. Background
4
Motivation- Coatings
Magnetic disk drive
MEMS devices
 The components are in contact and
relative sliding.
 Experience friction, wear, adhesion
and high temperature.
 Coatings on the contacting surfaces
has proven highly effective for
tribological improvements.
 In absence of frictional study, solid
knowledge on the pre-sliding
behaviors of coated contact is
missing from the literature.
Cutting tools
Automobile engines
Biomedical prosthetics

5. Background
5
Solution- Coated Asperity
 Coating surfaces are also rough.
 Approach : Single asperity model is
extrapolated to all the asperities on
the surface.
 Available approach to explore
frictional behavior of asperity:
1. Indentation
2. Flattening
 Understanding the onset of sliding for coated asperity under combined
loading can help in selection of coatings.
Normal LoadingTangential
Loading

6. Previous Research
6
Homogeneous Asperity- Static Friction Model
 Chang, Etsion, and Bogy (1988): CEB model
 Plastic yield failure mechanism considered as sliding inception for the
shearing of small junction.
 Under an applied normal load 𝑃, the maximum static frictional force
𝑄 𝑚𝑎𝑥 is the tangential force, when local yielding occurred.
 Kogut and Etsion (2003): KE model
 When local yielding occurred, elastic material surrounding the plastic
zone in the contact area can sustain more tangential load.
 CEB and KE model underestimates the 𝑄 𝑚𝑎𝑥.

7.  Brizmer, Kligerman, and Etsion (2007): BKE Model
 By considering tangential stiffness criterion as sliding inception under
the full-stick contact condition.
(𝐾 𝑇)𝑖
(𝐾 𝑇)1
≤ 𝛼
Where, (𝐾 𝑇)𝑖=
𝜕𝑄
𝜕𝑢 𝑥 𝑖
≈
𝑄 𝑖−𝑄 𝑖−1
𝑢 𝑥 𝑖− 𝑢 𝑥 𝑖−1
′(𝐾 𝑇)𝑖′ Tangential contact stiffness at step 𝑖
′𝑄’ Tangential force
′𝑢 𝑥′ Tangential displacement of the rigid flat
′𝛼 ′ Pre-defined number
 Sliding initiate when the tangential contact stiffness drops to 𝛼, and
the corresponding value of 𝑄𝑖 becomes 𝑄 𝑚𝑎𝑥.
Previous Research
7
Homogeneous Asperity- Static Friction Model

8. Previous Research
8
Homogeneous Asperity- Static Friction Model
 Wu, Shi, and Polycarpou (2012):
 Maximum frictional shear stress criterion used for sliding inception.
𝜏 𝑐= 𝜎𝑠 /√3
Where, ′𝜏 𝑐′ Critical frictional shear stress
′𝜎𝑠′ Yield stress under uniaxial tension
 Once the frictional shear stress in contact area reaches the defined
critical shear stress, local sliding occurs at that point. When all the
points in contact area reach critical shear stress, the entire interface
starts sliding.
 The corresponding tangential loading, at that moment is maximum
static friction force 𝑄 𝑚𝑎𝑥.

9. Previous Research
9
Coated Asperity- Normal Loading
 Goltsberg, Etsion, and Davidi (2011):
 At Onset of plastic yielding, relation of the dimensionless coating
thickness 𝑡/𝑅 𝑝 provided by considering the material property.
 Typical location of onset of yielding found out.

10. Previous Research
10
Coated Asperity- Normal Loading
 Goltsberg, and Etsion (2015):
 Proposed universal model for the load-displacement relation in an
elastic coated spherical asperity for thin coating.
 Chen, Goltsberg, and Etsion (2016):
 Developed universal model for elastic-plastic coated spherical normal
contact for moderate to large coating thickness.
 Analyzed contact for 𝑡/𝑅 > 𝑡/𝑅 𝑃 under slip condition.
 Provided empirical expressions for first 𝜔 𝑐1 and second 𝜔 𝑐2 critical
interferences, corresponds the yield inception in coating and substrate
respectively.

11. Previous Research
11
Coated Asperity- Normal Loading
 Ronen, Goltsberg, and Etsion (2017):
 Provided the optimum coating thickness in stick condition 𝑡/𝑅 𝑝_𝑠𝑡.
 Coated contact analyzed for 𝑡/𝑅 > 𝑡/𝑅 𝑝_𝑠𝑡 and obtained the
expressions for first 𝛿 𝑐1 and second 𝛿 𝑐2 critical interference:
𝛿 𝑐1
𝜔𝑐_𝑐𝑜
= 6.82𝑣 − 7.83 𝑣2
+ 0.0586 1 + 0.007
𝐸𝑐𝑜
𝐸𝑠𝑢
− 1
0.646
𝑌𝑐𝑜
𝐸𝑐𝑜
0.244
𝑡
𝑅
−1.21
𝛿 𝑐2
𝜔𝑐_𝑐𝑜
=
𝑡
𝑅
1.17
𝐸𝑐𝑜
𝐸𝑠𝑢
− 1
−0.09
𝑌𝑐𝑜
𝐸𝑐𝑜
−1.93
𝑌𝑠𝑢
𝐸𝑠𝑢
0.89
Where, ′𝑣′ Poisson’s ratio Subscript,
′𝐸′ Young’s modulus ′𝑐′ Critical value
′𝑌′ Yield strength ′𝑐𝑜′ Coating
′𝜔′ Interference in slip ′𝑠𝑢′ Substrate

12. Objective
12
 To FE model of 3D coated asperity by using ABAQUS CAE.
 Verification of the FE model with available numerical and experimental
studies for normal and tangential loading.
 Analyze pre-sliding frictional behavior of coated asperity under combined
loading for various coating thickness ratios and coating to substrate
Young’s modulus ratios, and provide the comparison of:
 Von Mises stress and plastic strain
 Tangential frictional force
 Static friction coefficient

13. Methodology
13
 ABAQUS/Explicit quasi-static scheme is used to analyzed pre-sliding of
coated asperity.
 Normal loading is considered under the stick contact condition.
 Inspired by Wu et al.(2012), the maximum frictional shear stress
criterion is used for the sliding inception by considering the shear
strength of coating material.
𝜏 𝑐= 𝜎𝑠_𝑐𝑜 /√3
Where, ′𝜏 𝑐′ Critical frictional shear stress
′𝜎𝑆_𝑐𝑜′ Yield stress of coating

14. FE Model
14
Components
 Sphere:
o 3D Deformable
o Radius of sphere: 𝑅′
= 𝑅 + 𝑡
o Radius of substrate: 𝑅 = 10𝑚𝑚
o Thickness of coating: t
 Rigid flat plate:
o Analytical Rigid
o Dimensions: 3𝑅 × 𝑅

15. FE Model
15
Material Property- Coated Sphere
 The coating and the substrate material are defined as elastic-perfectly
plastic.
o Poisson's ratio: 𝑣 = 𝑣𝑠𝑢= 𝑣𝑐𝑜= 0.32
o Young's modulus of substrate: 𝐸𝑠𝑢 = 200GPa
o Young’s modulus of coating varies as: 2 ≤ 𝐸𝑐𝑜 𝐸𝑠𝑢 ≤ 10
o Young’s modulus to yield strength to ratio for substrate and coating:
𝐸𝑠𝑢 𝑌𝑠𝑢 = 𝐸𝑐𝑜 𝑌𝑐𝑜 = 1000

16. FE Model
16
Contact Interaction
 Surface to surface (Explicit)
o Master surface: Rigid flat plate
o Slave surface: Deformable sphere
 Contact interaction property:
o Normal loading: “Hard” contact pressure-overclosure used and
separation of the contact is not allowed.
o Tangential loading: The value of local friction coefficient is defined
as 1000 and shear stress limit is given by considering the coating
material.

17. FE Model
17
Mesh- Partition
 Partitioning of sphere.
o Coating: Shielded only 20% of
radius of substrate sphere.
o Substrate: Rest of the sphere
 Coating –Substrate Zones:
Zone Partition Size
I 0.2t
II 0.7t
III 0.05R
IV 0.1R
V 0.2R
VI 0.22R

18. FE Model
18
Mesh- Elements
Zone
Element
type
Order
Element
shape
Meshing
Technique
I, II, III, IV
and V
C3D8R Linear Hex Structured
VI and
rest
C3D10M Quadratic Tet Free
 Mesh element size at contact
region is maintained 0.0003R.
 According t/R, number of
mesh elements varies between
around 400K to 800K.

19. FE Model
19
Loading and Boundary Conditions
 ENCASTRE at bottom of sphere
U1=U2=U3=UR1=UR2=UR3=0
 XY-plane symmetry
𝑍𝑆𝑌𝑀𝑀(𝑈𝑧 = 𝑈𝑅 𝑥 = 𝑈𝑅 𝑦 = 0)
 Reference point
Normal displacement in Y and
tangential displacement in X.

20. Verification and Validation
20
 Verification of Model under Normal Loading
 Homogeneous model under elastic normal loading
 Coated model under elastic normal loading
 Coated model under elastic-plastic normal loading
 Verification and Validation (experimental comparison) of Model under
Elastic-perfectly Plastic Combined Normal and Tangential Loading

21. Verification
21
Homogeneous ( 𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟏) Model under Elastic Normal Loading
0
2
4
6
8
10
12
0 0.0002 0.0004 0.0006 0.0008 0.001
Load,P(N)
Interference, δ (mm)
Hertz Analytical
FEM
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0 0.002 0.004 0.006 0.008 0.01
P/E*
δ/aH
Hertz Analytical
FEM
 Hertz Model
𝒕/𝑹 = 𝟎. 𝟎𝟎𝟗 𝒕/𝑹 = 𝟎. 𝟎𝟎𝟗

22. Verification
22
Coated Model under Elastic Normal Loading
 Goltsberg and Etsion (2015)
0
1
2
3
4
5
6
0 0.00005 0.0001 0.00015 0.0002
Load,P(N)
Interference, ω (mm)
Goltsberg and Etsion (2015)
t/R=0.009 FEM
t/R=0.007 FEM
t/R=0.005 FEM
t/R=0.003 FEM
t/R=0.001 FEM
𝑬 𝒄𝒐/𝑬 𝒔𝒖 = 𝟒

23. Verification
23
Coated Model under Elastic-plastic Normal Loading
 Ronen, Goltsberg, and Etsion (2017)
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
DimensionlesscontatcLoad,L/Lc2
Dimensionless Interference, δ/δc2
t/R=0.05
Ronen et al. (2017)
Eco/Esu=10 FEM
Eco/Esu=8 FEM
Eco/Esu=6 FEM
Eco/Esu=4 FEM
Eco/Esu=2 FEM
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
DimensionlesscontatcArea,Ast/Ac2_st
Dimensionless Interference, δ/δc2
t/R=0.05
Ronen et al. (2017)
Eco/Esu=10 FEM
Eco/Esu=8 FEM
Eco/Esu=6 FEM
Eco/Esu=4 FEM
Eco/Esu=2 FEM

24. Verification
24
Homogeneous ( 𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟏) Model under Combined Loading
 Wu, Shi, and Polycarpou (2012)
0
0.1
0.2
0.3
0.4
0 0.2 0.4 0.6 0.8 1
Q/Pc
ux/ωc
ω=0.5ωc
Wu et al. (2012)
FEM
0
0.5
1
1.5
2
2.5
0 0.5 1 1.5 2 2.5 3
Q/Pc
ux/ωc
ω=3ωc
Wu et al. (2012)
FEM
0
3
6
9
12
0 3 6 9 12 15
Q/Pc
ux/ωc
ω=12ωc
Wu et al. (2012)
FEM
0
20
40
60
80
100
0 10 20 30 40 50
Q/Pc
ux/ωc
ω=72ωc
Wu et al. (2012)
FEM
𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟐

25. Verification
25
Homogeneous ( 𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟏) Model under Combined Loading
 Wu, Shi, and Polycarpou (2012)
0
0.3
0.6
0.9
1.2
1.5
1.8
-5 5 15 25 35 45 55 65 75
Staticfrictiuoncoefficient,µs
Dimensionless normal loading, ω/ωc_su
Wu et al. (2012)
Current FEM, Eco/Esu=1

26. Validation
26
Homogeneous ( 𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟏) Model under Combined Loading
 Ovcharenko et al. (2008)
0
0.3
0.6
0.9
1.2
1.5
1.8
-5 5 15 25 35 45 55 65 75 85 95 105
Staticfrictiuoncoefficient,µs
Dimensionless normal load, P/Pc_su
Cu D=5mm, Ovcharenko et al. (2008)
Current FEM, Eco/Esu=1

27. Results
27
Coated Model under Combined Loading
 Stress and Strain
 Frictional Force
 Static Friction
Input Parameters of Coating-Substrate model
Radius of substrate sphere, 𝑹 10 𝑚𝑚
Dimensionless coating thickness, 𝒕/𝑹 0.005, 0.025, 0.05
Young’s modulus of rigid surface, 𝑬 ∞
Young’s modulus of substrate, 𝑬 𝒔𝒖 200 𝐺𝑃𝑎
Coating to substrate ratio, 𝑬 𝒄𝒐/𝑬 𝒔𝒖 1,2,4
Young’s modulus to yield strength to
ratio for substrate and coating,
𝑬 𝒔𝒖/𝒀 𝒔𝒖 = 𝑬 𝒄𝒐/𝒀 𝒄𝒐
1000
Poisson’s ratio, 𝒗 0.32

28. Results
28
Selection of Range for study
0
2
4
6
8
10
12
0 0.01 0.02 0.03 0.04 0.05
δc1/ωc_su
t/R
Eco/Esu=2
Eco/Esu=4
Eco/Esu=6
Eco/Esu=8
Eco/Esu=10
0
5
10
15
20
25
30
35
40
45
0 0.01 0.02 0.03 0.04 0.05
δc2/ωc_su
t/R
Eco/Esu=2
Eco/Esu=4
Eco/Esu=6
Eco/Esu=8
Eco/Esu=10
 Coating thickness ratio
0.005 ≤ 𝑡/𝑅 ≤ 0.05
 Normal loading
0 ≤ 𝛿 𝜔𝑐_𝑠𝑢 ≤ 60
 𝛿 𝜔𝑐_𝑠𝑢 = 1, 10, 30 𝑎𝑛𝑑 60

29. Results
29
Stress and Strain, 𝜹 𝝎 𝒄_𝒔𝒖 = 𝟏, t/R=0.005
 In the tangential loading,
the maximum stress area
moves to the surface,
reaching the yield stress,
and yielding covers the
whole contact area
gradually. At that moment
𝑄 becomes 𝑄 𝑚𝑎𝑥.
 No yielding during the
normal loading because of
𝛿 < 𝛿 𝑐1 .

30. Results
30
Stress and Strain, 𝜹 𝝎 𝒄_𝒔𝒖 = 𝟏𝟎
 When, 𝛿 𝑐1 < 𝛿 < 𝛿 𝑐2 , yielding of
the coating can be seen during the
normal loading.
 For 𝑡/𝑅 = 0.005 , 𝛿 > 𝛿 𝑐2 ,
yielding of substrate occurred
during normal loading.
 Plastic strain development shrinks
in the coating with increment of
the Young’s modulus ratios.

31. Results
31
Stress and Strain, 𝜹 𝝎 𝒄_𝒔𝒖 = 𝟏𝟎
 Higher coating thickness ratio
t/R, protects the substrate
from yielding.

32. Results
32
Strain ( 𝛿 𝜔𝑐_𝑠𝑢 = 1), 𝜹 < 𝜹 𝒄𝟏 , 𝒕/𝑹 = 𝟎. 𝟎𝟎𝟓, 𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟐

33. Results
33
Strain ( 𝛿 𝜔𝑐_𝑠𝑢 = 10), 𝜹 𝒄𝟏< 𝜹 < 𝜹 𝒄𝟐 , 𝒕/𝑹 = 𝟎. 𝟎𝟐𝟓, 𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟐 and 𝟒
𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟐 𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟒

34. Results
34
Plastic Strain ( 𝛿 𝜔𝑐_𝑠𝑢 = 10), 𝜹 > 𝜹 𝒄𝟐 , 𝒕/𝑹 = 𝟎. 𝟎𝟎𝟓, 𝑬 𝒄𝒐/𝑬 𝒔𝒖 = 𝟐 and 4
𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟐 𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟒

35. Results
35
Plastic Strain ( 𝛿 𝜔𝑐_𝑠𝑢 = 30), 𝜹 > 𝜹 𝒄𝟐 , 𝒕/𝑹 = 𝟎. 𝟎𝟐𝟓, 𝑬 𝒄𝒐/𝑬 𝒔𝒖 = 𝟐 and 4
𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟐 𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟒

36. Results
36
Plastic Strain ( 𝛿 𝜔𝑐_𝑠𝑢 = 60), 𝜹 > 𝜹 𝒄𝟐 , 𝒕/𝑹 = 𝟎. 𝟎𝟓, 𝑬 𝒄𝒐/𝑬 𝒔𝒖 = 𝟐 and 4
𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟐 𝑬 𝒄𝒐 𝑬 𝒔𝒖 = 𝟒

37. Results
37
Tangential Frictional Force vs. Tangential Displacement for 𝑡/𝑅 = 0.005
0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 1
Q/Pc_su
ux/ωc_su
δ=1ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4
0
5
10
15
20
25
30
35
0 2 4 6 8 10
Q/Pc_su
ux/ωc_su
δ=10ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4
0
20
40
60
80
100
120
0 5 10 15 20 25 30
Q/Pc_su
ux/ωc_su
δ=30ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4
0
50
100
150
200
250
0 10 20 30 40 50 60
Q/Pc_su
ux/ωc_su
δ=60ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4
 As Young’s modulus ratio
increases, it delays the
stiffness softening.
 Coated asperity can sustain
much higher loads before the
onset of sliding.
 Ability to sustain higher
friction force increases with
increment of 𝐸𝑐𝑜/𝐸𝑠𝑢.

38. Results
38
Tangential Frictional Force vs. Tangential Displacement for 𝑡/𝑅 = 0.025
 As Young’s modulus ratio
increases, it delays the
stiffness softening.
 Coated asperity can sustain
much higher loads before the
onset of sliding.
 Ability to sustain higher
friction force increases with
increment of 𝐸𝑐𝑜/𝐸𝑠𝑢
0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 1
Q/Pc_su
ux/ωc_su
δ=1ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4
0
5
10
15
20
25
30
35
0 2 4 6 8 10
Q/Pc_su
ux/ωc_su
δ=10ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4
0
20
40
60
80
100
120
0 5 10 15 20 25 30
Q/Pc_su
ux/ωc_su
δ=30ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4
0
50
100
150
200
250
0 10 20 30 40 50 60
Q/Pc_su
ux/ωc_su
δ=60ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4

39. Results
39
Tangential Frictional Force vs. Tangential Displacement for 𝑡/𝑅 = 0.05
 As Young’s modulus ratio
increases, it delays the
stiffness softening of contact.
 Coated asperity can sustain
much higher loads before the
onset of sliding.
 Ability to sustain higher
friction force increases with
increment of 𝐸𝑐𝑜/𝐸𝑠𝑢
0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 1
Q/Pc_su
ux/ωc_su
δ=1ωc_suEco/Esu=1
Eco/Esu=2
Eco/Esu=4
0
5
10
15
20
25
30
35
0 2 4 6 8 10
Q/Pc_su
ux/ωc_su
δ=10ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4
0
20
40
60
80
100
120
0 5 10 15 20 25 30
Q/Pc_su
ux/ωc_su
δ=30ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4
0
50
100
150
200
250
0 10 20 30 40 50 60
Q/Pc_su
ux/ωc_su
δ=60ωc_su
Eco/Esu=1
Eco/Esu=2
Eco/Esu=4

40. Results
40
Tangential Frictional Force vs. Tangential Displacement for 𝛿 𝜔𝑐_𝑠𝑢 = 1
 At same 𝐸𝑐𝑜/𝐸𝑠𝑢, higher t/R is
suitable to resist stiffness
softening of the coated contact.
0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 1
Q/Pc_su
ux/ωc_su
Eco/Esu=1
Eco/Esu=2, t/R=0.05
Eco/Esu=2, t/R=0.025
Eco/Esu=2, t/R=0.005

41. Results
41
Tangential Frictional Force vs. Tangential Displacement for 𝛿 𝜔𝑐_𝑠𝑢 = 1
 At same 𝐸𝑐𝑜/𝐸𝑠𝑢, higher t/R is
suitable to resist stiffness
softening of the coated contact.
 Combination of higher 𝐸𝑐𝑜/𝐸𝑠𝑢
with higher t/R can present
good tribological performance
of the coated contact for high
load applications. 0
0.5
1
1.5
2
2.5
3
0 0.2 0.4 0.6 0.8 1
Q/Pc_su
ux/ωc_su
Eco/Esu=1
Eco/Esu=4, t/R=0.05
Eco/Esu=4, t/R=0.025
Eco/Esu=4, t/R=0.005

42. Results
42
Static Friction
 Higher 𝐸𝑐𝑜/𝐸𝑠𝑢 predicts
slightly more µs.
0
0.3
0.6
0.9
1.2
1.5
0 10 20 30 40 50 60 70 80 90 100
Staticfrictiuoncoefficient,µs
Dimensionless normal load, P/Pc_su
t/R=0.005 Eco/Esu=1
Eco/Esu=2
Eco/Esu=4

43. Results
43
Static Friction
 Higher 𝐸𝑐𝑜/𝐸𝑠𝑢 predicts
slightly more µs.
 With the increase of the t/R
from 0.005 to 0.05 the static
friction deviates for chosen
𝐸𝑐𝑜/𝐸𝑠𝑢.
0
0.3
0.6
0.9
1.2
1.5
0 10 20 30 40 50 60 70 80 90 100
Staticfrictiuoncoefficient,µs
Dimensionless normal load, P/Pc_su
t/R=0.025 Eco/Esu=1
Eco/Esu=2
Eco/Esu=4

44. Results
44
Static Friction
 Higher 𝐸𝑐𝑜/𝐸𝑠𝑢 predicts
slightly more µs.
 With the increase of the t/R
from 0.005 to 0.05 the static
friction deviates for chosen
𝐸𝑐𝑜/𝐸𝑠𝑢.
0
0.3
0.6
0.9
1.2
1.5
0 10 20 30 40 50 60 70 80 90 100
Staticfrictiuoncoefficient,µs
Dimensionless normal load, P/Pc_su
t/R=0.05 Eco/Esu=1
Eco/Esu=2
Eco/Esu=4

45. Conclusions
45
 A 3D spherical coated model is developed upon the verification and
validation against the available numerical and experimental studies.
 Von Mises stress and strain distribution are studied, and failure
mechanisms for coating and substrate are observed for 𝛿 < 𝛿 𝑐1 ,
𝛿 𝑐1 < 𝛿 < 𝛿 𝑐2 and 𝛿 > 𝛿 𝑐2 under combined loading.
 It is found that,
For 𝛿 < 𝛿 𝑐2 , higher 𝑡/𝑅 with higher 𝐸𝑐𝑜/𝐸𝑠𝑢 shows good resistance
against the yield failure of coating.
For 𝛿 > 𝛿 𝑐2 , higher 𝑡/𝑅 with lower 𝐸𝑐𝑜/𝐸𝑠𝑢 shows good resistance
against the yield failure of substrate.

46. Conclusions
46
 Under the same normal displacement pre-load,
 Coated asperity can sustain much higher loads before the onset of
sliding.
 Ability to protect the coated contact from the softening is increased
with the increment of 𝐸𝑐𝑜/𝐸𝑠𝑢 and t/R.
 For the load control model, increase of 𝐸𝑐𝑜/𝐸𝑠𝑢 and t/R results in slightly
higher friction coefficient.

47. Future Work Recommendation
47
 Different failure criterion can be used to analyze coating contact interface
based on yield failure and stiffness failure criterion.
 Similar study can be conducted for soft coatings. Moreover, it can be
further expanded for multi-layer and functionally graded coating
materials.
 For a large range of coating thickness ratio and material property study
can be extended and solid empirical relation for the friction coefficient
can be developed in terms of frictional force, material properties and
coating thickness ratio.
 Study can be extended to different geometries such as Cylindrical and
Sinusoidal shapes.

48. Acknowledgement
48
 I would like to thank my advisor, Dr. Ali Beheshti, for his encouragement
and constant kind support.
 I also thankful to my committee members Dr. Xuejun Fan and Dr. Jenny
Zhou, for their time from busy schedules.
 I appreciate all the tidbits of knowledge, care, and motivation provided
by my colleagues at the µTCM.

49. 49

50. 50
Thank You