1. Research Portfolio
Computational and experimental failure analysis (Wear and Fatigue)
Arnab Ghosh
PhD Candidate
Mechanical Engineering Tribology Laboratory
Purdue University
arnabjghosh@gmail.com

2. Outline
• Computational Modeling
– Contact Mechanics simulation (Stick-slip, Fretting)
– Surface Initiated Wear (Damage Mechanics + FEA)
– Subsurface Initiated Wear (Fracture Mechanics + FEA)
– Elastic-plastic model of third bodies in contact (Wear Debris)
– Fretting Fatigue Crack Propagation
– Three Dimensional flat on flat contact fretting wear (FEA, Increment Wear Model)
– Elastic-plastic rough surface model (FEA)
– Elastic-plastic surface roughness model (Analytical)
– A Novel Friction Model
• Experimental
– Pin on Disk experiments to characterize hard coatings
– Fretting wear experiments – Wear coefficient and wear maps
– Fretting fatigue experiments
– Analytical Wear Maps
– Optical Surface Profilometry
– Scanning Electron Microscope (SEM) images

3. Contact Mechanics Simulations
Hertzian Line Contact
• Plane Strain 2D
• Element Type: Linear Triangular
(CPE3)
• Deformable solids
• Slip Regime: based on Normal load and
applied displacement
• Augmented Lagrangian contact
algorithm Partial Slip
Gross Slip
Comparison of Hertzian Pressure profile with TheoryComparison of normalized shear stress with theory
FE (ABAQUS)
Theory (Continuum)
𝑄 = 𝑄 𝑚𝑎𝑥
𝑄 = −𝑄 𝑚𝑎𝑥
𝑄 = 0

4. Surface Initiated Wear (Stick Slip, Dry Contact, Smooth Surface)
𝑑𝐷
𝑑𝑁
=
𝑆 𝑢𝑠∆𝜏
2𝐸𝐻(1 − 𝐷)
Steel Microstructure Voronoi Tessellation FEA Mesh
2D Voronoi tessellations incorporate randomness in the microstructure and geometrically
simulate the grain morphology observed in reality.
D  Dc
Crack at grain
boundary
Grain removal
(Crack surrounds a
grain)
𝐷: Damage Variable
𝑁: Number of Cycles
Crack propagates along the hypothetical grain boundary
0 200 400 600 800 1000
0
500
1000
1500
2000
2500
3000
3500
Number of Cycles
WearVolume(m
2
/m)
No Wear Zone
Steady State Wear
(Archard’s Law)
𝑉𝑤 = −𝑉𝑤𝑜 + 𝑉𝑤𝑟 𝑁
𝑉𝑤𝑟
Simulation
Experiments
Comparison of Archard’s coefficients with simulationsWear Progression
HERTZIAN LINE
CONTACT
2D PLANE STRAIN

5. Sub-surface Initiated Wear (Delamination, Smooth Surface)
While surface initiated failure is predominantly observed in contact of brittle materials with high coefficient of friction, ductile failure is
initiated by formation of micro-cracks at the interface between precipitates in the subsurface
Define Initial Crack Tips- Refine Mesh
Apply boundary Conditions (Input File)
Run the FE model (ABAQUS)
Obtain Nodal Force and Displacement (C++)
Apply LEFM – Extend Crack (MATLAB)
Define new crack tips (MATLAB)
Adaptive mesh refinement around the crack tip
SIMULATIONRESULTS
Comparison of wear coefficients with
experiments
HERTZIAN LINE
CONTACT
2D PLANE STRAIN
Strain energy Release Rate:
𝑮 𝑰 =
𝟏
𝟐𝚫𝒂
𝑭 𝒚
𝒄
𝒖 𝒚
𝒂
− 𝒖 𝒚
𝒃
𝑮 𝑰𝑰 =
𝟏
𝟐𝚫𝒂
𝑭 𝒙
𝒄
𝒖 𝒙
𝒂
− 𝒖 𝒙
𝒃
For Plane Strain,
𝑲 =
𝑮𝑬
𝟏 − 𝝂 𝟐
Dissipated Energy:
𝑬 𝑫 = 𝝁𝑭 𝑵 𝟒𝜹𝑵
Wear Volume
𝑽 𝒘 = 𝜶𝑬 𝑫
𝛼: Wear Coefficient
Initial Crack Crack Propagation (Shear Stress criteria) Material Removal

6. Third body simulation (Elastic-plastic, Fretting, Wear Debris)
ELKP Material Model Contact Pressure (1 particle) Deformation under normal load leading to a platelet shape
-1 -0.5 0 0.5 1
-80
-60
-40
-20
0
20
40
60
80
Displacement (m)
ShearForce,Q(mN)
Cycle 1
Cycle 2
Cycle 3
No 3rd Body
Evolution of fretting loops for an
elastic-plastic contact in presence of
third bodies
Comparison of fretting loops obtained
with multiple third bodies in contact
with first bodies
𝑄/𝑄 𝑚𝑎𝑥 = 1.001 𝑛−0.06237
𝑠/𝑠 𝑚𝑎𝑥 = 0.748𝑛0.09515

7. Fretting Fatigue Crack Propagation (LEFM, XFEM)
HERTZIAN LINE
CONTACT
2D PLANE STRAIN
Linear Elastic Fracture Mechanics
Mode I crack propagation
Paris’ Law (R=0)
0 100 200 300 400 500 600 700 800 900 1000
0
100
200
300
400
500
600
700
x (m)
y(m)
0.74/6578
0.74/6246
0.71/5775
0.50/7123
0.48/9380
Crack Propagation in Fretting Fatigue (𝜎 𝑦𝑦 stress profiles)
𝜎 𝑦𝑦 stress state
Crack paths for different locations and angles
of initial crack

8. Three Dimensional Flat on Flat Fretting Contact Wear Simulation
P=100 N, δ=50µm P=200 N, δ=200µm P=400 N, δ=100µm
Pressure
Worn Surface
Profile
ABAQUS Geometry and Mesh
Contact Pressure Profile Slip Parallel to sliding
Wear Depth = Coefficient * Pressure * Slip

9. 600 700 800 900 1000 1100 1200 1300 1400
1380
1385
1390
1395
1400
1405
1410
1415
1420
x (m)
y(m)
x106
5
10
15
20
25
30
35
40
45
Elastic Plastic Wear Model over Rough Surfaces (FEA)
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
-5
-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
-0.5
0
Time (s)
Displacement(m)
Elastic
Elastic-Plastic (M=100 GPa)
Elastic-Plastic (M=10 GPa)
PlasticDeformation
RIGID BODY
DEFORMABLE BODY
Continuous Remeshing Algorithm (CRA) with Increment Wear
Model (Deeper wear scars, Better convergence)
Vertical displacement of the asperity tip
Evolution of Surface (E=210 GPa, M=10 GPa)

10. Semi analytical Elastic-plastic wear model over rough surfaces
Asperity in contact at depth d recorded Three points recorded
Circle constructed, Radius &
Deformation obtained
ELASTIC
𝐹 =
4
3
𝐸∗ 𝑅1/2 𝑑3/2 𝑃 =
3𝐹
2𝜋𝑎2
ELASTIC-PLASTIC : FEA
Multiple asperity approximation method
Apply vertical displacement
Evaluate radius and
deformation of each asperity
Evaluate pressure, contact area
Evaluate total contact force
Convergence Criteria:
Ftot − Fapp < 10−4
Wear depth, ℎ 𝑤 =
𝑘𝑃𝛿
𝐻
+ 𝛿 𝑝
Displace surface nodes, obtain
worn surface topography
FORCEBALANCE
Axisymmetric FE model (sphere on flat) Force Displacement Curve
Critical deformation:
𝜹 𝒄 =
𝝅𝑺 𝒚
𝟐𝑬
𝟐
𝑹
𝟏 + 𝟒𝝁 𝟐
Contact Pressure:
𝑷/𝑷 𝒄 = 𝒇
𝜹
𝜹 𝒄
, 𝑴, 𝒌
Contact Area:
𝑨/𝑨 𝒄 = 𝒇
𝜹
𝜹 𝒄
, 𝑴, 𝒌
Wear Volume
𝒉 𝒘 =
𝒌𝑷𝒔
𝑯
+ 𝜹 𝒑
Wear Depth vs Number of cycles
RUNNING-IN
STEADY STATE
𝜖 𝑦𝑦

11. A Novel Friction Model
𝐹𝑛
𝐹𝑦
x
y
 
2 1 2
1
2
0
Boundary c
,
2
(
ondition:
At 0 0; 0 Fixeden
t
d
) anh
y
y
F
c c
ER
F x x
w x
ER R R
w
x w
x



  
  
    
 

  




max max
Maximumdeflection at :
2 3
3 2
y
y
x R
F
w F ERw
ER



  
* 1/2 3/2
max
FromHertziansolution forspherecontact:
4
3
nF E R 
 
 
max
2 1/2 max
1/2 3/2 3/2
max max
2
Coefficient of friction:
3
92 1
2 4
3 1
y
n
ERwF w
R
ERF
 
 
 

   

NEW
OLD
Asperity
Using this approach, friction will continuously evolve with the
surface and won’t be assumed constant
   
2
2
22 2
Shear force:
where,
4
y
d d w
EI F
dx dx
I x R x

 
 
 
 

12. Multilayer Ceramic & Hard Coating Wear Test
Pin on Disk Rig
Optical Profilometer – To measure
Wear Volume
SiN Ceramic Balls TiCN/TiN Multilayer B Disk
TiCN/TiN Multilayer A Disk
TiN Single Layer Disk
TiCN Single Layer Disk
0 200 400 600 800 1000 1200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sliding Distance (m)
FrictionCoefficient:Ft
/Fn
TiN: Disk 1, Side 2
400 (m)
800 (m)
1200 (m)
0 200 400 600 800 1000 1200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sliding Distance (m)
FrictionCoefficient:Ft
/Fn
TiCN: Disk 5, Side 1
400 (m)
800 (m)
1200 (m)
0 200 400 600 800 1000 1200
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sliding Distance (m)
FrictionCoefficient:Ft
/Fn
TiCN/TiN: Disk 13, Side 1
400 (m)
800 (m)
1200 (m)
Evolution of COF
0 0.5 1 1.5 2 2.5 3
-5
-4
-3
-2
-1
0
1
x (mm)
y(m)
Disk 1, Side 2, Track 19
0 0.5 1 1.5 2 2.5 3
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
x (mm)
y(m)
Disk 5, Side 1, Track 19
0 0.5 1 1.5 2 2.5 3
-7
-6
-5
-4
-3
-2
-1
0
1
x (mm)
y(m)
Disk 13, Side 1, Track 19
Worn Surface Profile

13. Fretting Wear Experiments (coatings, Wear coefficients, maps, in-situ)
Flat on Flat Contact Fretting Rig
In-situ observation of Fretting Contact
Effect of Displacement amplitude on
Fretting Loops
Evolution of partial slip fretting wear and observation of debris (in-situ)
Uncoated Ni Superalloy (ambient) Uncoated Ni Superalloy (220 C)
-40 -30 -20 -10 0 10 20 30 40
-40
-30
-20
-10
0
10
20
30
40
Displacement (m)
FrictionForce(N)
0 500 1000 1500 2000 2500 3000 3500
1
2
3
4
5
6
7
8
x 10
8
Dissipated Energy (J)
WearVolume(m3)
ROUGH: V = 2e+04*E + 5.027e+06
SMOOTH: V = 2e+05*E + 4.87e+07
αROUGH = 2 x 104 µm3/J
αROUGH = 2 x 105 µm3/J
Smooth vs Rough (NiCr-CrC)
0 1 2 3 4 5
0
1
2
3
4
5
6
7
Normalized Dissipated Energy (E/E0
)
NormalizedWearVolume(W/W
0
)
Steel
Nickel Alloy
Coated Nickel
Comparison of wear rates

14. Fretting Fatigue Experiments
Apparatus developed for fretting fatigue Experiments on MTS Load Frame
Zoomed-in view of the contact specimensFretting and bulk stress vs. life curves obtained from experiments
Figure 1: Pictures of the crack growth taken as the test is running for test #7 (red line
denotes the effective crack length).
1 2
3 4
5
7 8
9
6
Observation of crack propagation

15. Analytical Wear Maps
Rq=1 µm Rq=0.5 µm Rq=0.05 µm
Effect of Modulus of Elasticity
Rq=1 µm Rq=0.5 µm Rq=0.05 µm
Effect of Applied Load
Obtain wear
coefficients from
experiments
Use wear
coefficients as input
in computational
wear model
Obtain wear rates
for different sets of
input parameters
Create Wear Maps
over a range of
parameters

16. Surface Profilometry
Wear Volume Measurement
Analyze Surface Topography

17. SEM Images (Effect of Polishing on NiCr-CrC wear resistant coatings)
Worn and Unworn Regions
NiCr-CrC Unpolished
Unworn Region (porous coating) Worn Region (Pitting, Delamination)
Unworn, Polished regionWorn and Unworn Regions Cross Section view of the wear scar
(Delamination)
NiCr-CrC Polished

18. “ Change means movement. Movement means friction. Only in the
frictionless vacuum of a nonexistent abstract world can movement
or change occur without that abrasive friction of conflict.”
~Saul Alinsky