1. November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Sina Mobasher Moghaddam
Ph.D. Candidate
Farshid Sadeghi
Cummins Distinguished Professor of Mechanical Engineering
3D Simulation of Butterfly Wings
Formation in Bearing Steel

2. 2
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Outline
• Background and motivation
• 2D model
– Review
– Recent developments
• 3D model
– Theory
– Analytical results
– Experimental validation

3. 3
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Motivation:
Detriment of Butterfly Wings
• In some applications bearings may last
only 10% of their 𝐿10life [i.e. wind
turbines]
• The large costs associated with bearing
replacement (about 0.5 M$) makes clean
energy expensive
• Butterflies are believed to be one of the
major reasons for this premature failure
• Despite the extensive experimental
studies in the last 60 years, there is
almost no model capable of simulating
butterflies
[1] Vincent A., Lormand G., Lamagnere P., Gosset L., Girodin D., “From White Etching Areas Formed Around Inclusions To Crack Nucleation In Bearing Steels
Under Rolling Contact Fatigue”, ASTM International, 1998
[2] A. Grabulov, R. Petrov , H.W. Zandbergen , 2009, “EBSD investigation of the crack initiation and TEM/FIB analyses of the microstructural changes around the
cracks formed under Rolling Contact Fatigue (RCF)” International Journal of Fatigue 32 (2010) 576–583
Butterflies Observed by Vincent [1](top)
and Grabulov [2](Bottom)

4. 4
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
History & Background
- Styri (1947)
First Observation
1947
1992
45 years, more than 200 experimental papers- No Analytical solution
1996 2002 2014
- Salehizadeh (1992)
Residual stress
- Melander (1996)
Fracture mechanics
2006
-Vincent(2002)
Dislocation motion
- METL (2014)
Damage mechanics
- Alley (2009)
Plastic Strain
𝑑𝐷
𝑑𝑁
=
𝜏 𝑎 + |𝜏 𝑚|
𝜎𝑟 1 − 𝐷
𝑚
• The new model considers the effect of alternating and mean
components of shear stress in butterfly formation
• Butterfly shape, orientation, and appearance life were successfully
predicted with the model

5. 5
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Critical Damage Measurement
• Hardness tests are
conducted to obtain the
equivalent stiffness values
inside the wings using
Oliver and Parr method [1]
• Cracks are commonly
observed at the top of the
upper wing and bottom of
the lower wing [2]
[1] Oliver, W. C., and Pharr, G. M., 1992, “An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments.”
[2] Grabulov, a., Ziese, U., and Zandbergen, H. W., 2007, “TEM/SEM investigation of microstructural changes within the white etching area under rolling contact fatigue and 3-D crack
reconstruction by focused ion beam,” Scr. Mater., 57(7), pp. 635–638.
Average Stiffness ratio is 0.9041.
Critical damage value is set to 0.1
𝐷𝑐−𝐵𝑢𝑡𝑡𝑒𝑟𝑓𝑙𝑦 = 1 −
𝐸 𝐵𝑢𝑡𝑡𝑒𝑟𝑓𝑙𝑦
𝐸𝑆𝑡𝑒𝑒𝑙
𝐸 𝐵𝑢𝑡𝑡𝑒𝑟𝑓𝑙𝑦 = 𝐸𝑆𝑡𝑒𝑒𝑙(1 − 𝐷𝑐−𝐵𝑢𝑡𝑡𝑒𝑟𝑓𝑙𝑦)
Optical(top) and SEM(top-right) images of butterfly wings
formed in 8620 bearing steel. Nano-indentation marks (right)-
METL experimental facilities

6. 6
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
An Example of Spall Formation
Using Kill Element Approach
Half Contact
Width (µ)
Maximum Hertzian
Pressure (GPa)
Friction
Coefficient
Grain
Size(µ)
Matrix
Stiffness(GPa)
Domain
Length (µ)
Domain
Depth(µ)
100 2.0 0.05 10 200 1000 700
Animation of spall formation due to butterflies

7. 7
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Crack Maps & Spall Geometry
• Experimental observation indicate that cracks
tend to form on top of the upper wing and
bottom of the lower wing
• In 26/33 (~ 80%) of the investigated spalls,
cracks are observed at the corresponding
locations
Cracks

8. 8
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Effect of Inclusion Characteristics
Stiffness, Size, and Depth
Effect of inclusion depth on
centerline reversals
Effect of inclusion stiffness on
centerline reversals
Effect of inclusion size on
centerline reversals
Alternating shear stress
variation versus depth is
studied for different
cases

9. 9
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Weibull Distribution of Fatigue Lives
• The combined results show Weibull slope values of 2.5 and
2.9 for butterfly formation and final failure respectively.
• These values fall between the Weibull slope range for ball
and roller bearings which is known to be from 0.51 to 5.7 for
52100 bearing steel [1]
[1] Harris, T. A., 2001, Rolling bearing analysis, Wiley, New York, NY.
33 randomly generated domains are considered for each scenario

10. 10
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Wings Without Inclusion!
• A 2D plain strain model does not count for the
globular or ellipsoidal form of the inclusions
• During the optical microscopy of M50 rods,
features similar to pairs of wings without
inclusion appeared
• A detailed study of butterfly wing shape in 3D
was necessary to better understand these
features

11. 11
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
3D FEM Model
Theory & Assumptions
• To save computational time, half contact width is reduced from 100µ (for 2D model) to 50µ
for the 3D model
• Y-Plane experiences the largest reversal value
• Shear stresses on this plane are selected for damage calculation
[1] Weinzapfel, N., Sadeghi, F., Bakolas, V., & Liebel, A. (2011). A 3D finite element study of fatigue life dispersion in rolling line contacts. Journal of Tribology, 133(4), 042202.
Critical shear stress reversals experienced by elements according to the orientation of the
grain boundary on which they occur [1]
(a) single RVE
(b) composite results of
several RVEs
(c) bounding contours by percentage of
the largest critical shear stress reversal

12. 12
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
3D Butterfly Model
Contact Type
Line
Contact
Half Contact Width
(b)
50 µ
Maximum Hertzian
Pressure
2.0 Gpa
Friction Coefficient 0.05
Inclusion Stiffness 300 GPa
Matrix Stiffness 200 GPa
Domain Length 500 µ
Domain Depth 350 µ
Domain Width 50µ
Animation of 3D Butterfly Progression
It took more than 10 days of
continues FEM simulation to
complete this model!!

13. 13
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Analytical Serial Sectioning of
Butterflies
Animation illustrating the cut
cross sections in 3D
Serial sectioning of a fully
formed pair of wings
• During fractography, we can only access 2D sections of butterflies
• Serial sectioning is necessary to reconstruct a 3D map out of 2D sections

14. 14
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Lateral Extension of Butterfly Wings
• Analytical serial sectioning shows that
wings can develop laterally beyond
the inclusion extents
• Final confirmation would be possible
after experimental serial sectioning
Modeled
Inclusion-less Wings
Experimentally Observed
Inclusion-less Wings

15. 15
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
3 Ball on Rod RCF Tester
Rotational
fixture
Transducer
Sample
Schematic of the rig Schematic of the contact
Test specimen Ultrasonic inspection of inclusions
(image courtesy: Sonoscan, Inc.)

16. 16
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Ultrasonic Detection of Inclusions
C-Scan of Sample
Length of the Specimen
Noise from airMarker
360Degree

17. 17
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Image Processing on C-Scan
Studied
inclusion
Specimen
Material
Major
Axis(µ)
Minor
Axis(µ)
Maximum Hertzian
Pressure (GPa)
Test
Speed(rpm)
Spalling
Life
8620 (5% RA) 236 130 2.0 3600 32.2E7

18. 18
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Experimental Serial Sectioning
of Butterflies
1 2 3 4 5 6 7 8
9 10 11 12 13 14 15
Sections 1, 2, and 11-15 show the presence of wings without inclusion

19. 19
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Wing Span to Radius Ratio
Closed Form SolutionWings without inclusions
4R (Observed wingspan)
2R
d
Observed inclusion diameter
Cut plane
𝑹𝒂𝒕𝒊𝒐 𝒅 =
𝟐
𝟏 −
𝒅
𝑹
𝟐
𝟎 < 𝒅 < 𝑹
• The wing span to inclusion ratio is observed to be
about 2.0 at the mid cross section
• Serial sectioning results show that the wingspan is
approximately the same in all the section while the
“observed” inclusion diameter varies

20. 20
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Wing Span to Radius Ratio
2D vs. 3D

21. 21
November 13, 2014
Mechanical Engineering Tribology Laboratory (METL)
Summary
– Critical damage is measured inside butterflies
– Effect of inclusion characteristics is studied on wing
formation and RCF life
– Butterflies is studied as a 3D object
o A 3D model is used to simulate butterfly formation
using damage mechanics
o Lateral expansion of wings is confirmed with analytical
and experimental serial sectioning
o Closed form solution for wingspan to inclusion ratio in
3D is suggested