1. May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Butterfly Wing Formation
In Bearing Steel
Sina Mobasher Moghaddam
PhD Research Assistant

2. 2
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Outlines
• Motivation
• Background
• Butterfly wing modeling:
– Stress solution
– Suggested theory
– Effect of inclusion depth
– Effect of inclusion size
– Effect of applied load
– S-N curve for butterfly formation
– Debonding at inclusion/ matrix interface
– Crack initiation
• Summary & conclusion

3. 3
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
RCF Failure Mechanisms
• Failure in rolling elements mostly
occurs due to two different
phenomena:
– Surface pitting
– Subsurface spalling
• If a bearing is well installed and
lubricated, and operates under the
right load, the main mode of failure
is subsurface spalling
• Cracks initiate underneath the
surface and grow to the surface to
cause the final failure Surface initiated crack observed by [1](top)
compared to subsurface initiated crack
observed at METL facilities (bottom)- Note
the difference in the crack depth
[1] A. OILA,S.J. BULL“Phase transformations associated with micropitting in rolling/sliding contacts”, JOURNAL OF MATERIALS
SCIENCE 40 (2005) 4767– 4774

4. 4
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Butterfly Wings
Detrimental Effect on RCF
• It has been frequently observed that
matrix microstructure alters in the
regions adjacent to the non-metallic
inclusions
• These material alteration is commonly
referred to as “Butterfly- Wings”
• Cracks often form in the vicinity of
butterfly wings
• 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)

5. 5
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Butterfly Wing Characteristics
• Butterfly structure is made of
highly saturated ultra fine ferrite
grains
• Two wings located along a line
which forms a 45° angle with
Over Rolling Direction (ORD)
• Subsurface cracks are frequently
observed to be initiated from
butterflies
• In this analysis, ORD is from
right to left in all cases
• Surface traction is set to 0.05
Schematic of a pair of butterfly
wings

6. 6
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Stress Concentration due to Inclusion
Presence
• Inclusion presence induces stress concentrations in the surrounding
matrix
• This stress concentration can culminate in microstructural alteration and
premature crack initiation
Comparison of centerline stresses for two domains with and without embedded inclusion
𝐷𝑖𝑛𝑐 = 16𝜇, b=100𝜇, 𝑃𝑚𝑎𝑥= 2.0 GPa

7. 7
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
x/b=-1.0 x/b=-0.5 x/b=0.0 x/b=0.5 x/b=1.0
Shear Stress Variation
During One Load Pass
Shear stress variation during Hertzian load approach and departure
• Shear stress contours at no single time step resemble the two- wing
butterfly shapes
• It is well known that wing formation is a cyclic phenomenon
• Hence, any stress based approach to model butterfly formation should
look at the loading history during each load pass

8. 8
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Effect of Surface Traction
Alternating and Mean Shear Stress
• Alternating shear stress
– There are four regions of
maximum alternating shear
stress around inclusion
– All these regions are equally
affected by surface traction
• Mean shear stress
– There are four regions of
maximum mean shear stress
around the inclusion
– Two of them are strongly
depended on surface traction

9. 9
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Damage Mechanics
Suggested Model for Butterfly Formation
• Butterfly formation is a fatigue
related phenomena alternating
shear stress should be considered
• Butterfly wing formation is a
depended on rolling direction
(surface traction) mean shear
stress should be considered
• The fatigue model should take both
alternating and mean shear stress
into account
• Suggested damage law is:
𝑑𝐷
𝑑𝑁
=
𝜏 𝑎
2
+ |𝜏 𝑚|
𝜎𝑟 1 − 𝐷
𝑚

10. 10
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Chronological Evolution
of Butterfly Wing
Butterfly Wing
Evolution
Color spectrum of
Butterfly Wing Formation

11. 11
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Butterfly Wing Shape
Comparison with Experiments
Butterfly wing orientation, direction, and size are consistent with
the experimental observations
Butterfly formation according
to METL model prediction
Butterfly formation
according to Grabulov[1]
[1] 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

12. 12
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
• Experimental Data by Nelias et. al.
[1] show butterfly formation
frequency versus depth
• Most of the researchers have
directly related butterfly formation
to stress level which does not match
over the whole span
• Damage Parameters obtained from
torsion fatigue match closely with
the experimental data
[1] Nelias. D, et. al.” Role of Inclusions, Surface Roughness and Operating Conditions on Rolling Contact Fatigue”, Transactions of the ASME,
April 1999, Vol. 121
Damage Parameter=
𝜏 𝑎+|𝜏 𝑚|
𝝈 𝒓(𝟏−𝑫)
𝒎
Effect of Depth on
Butterfly Occurrence Frequency

13. 13
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
0.7 b
0.8 b
0.38 b
0.42 b
1.1 b
0.4 b
𝑑𝑖𝑛𝑐 < 0.5
Larger lower wing
0.5 𝑏 < 𝑑𝑖𝑛𝑐< 1.0 𝑏
Larger upper wing
1.0 𝑏 < 𝑑𝑖𝑛𝑐
Secondary upper wing
0.6 b
1.1b
[1] M.-H.Evans,etal.,”Effect of Hydrogen on Butterfly and White Etching Crack (WEC) Formation under Rolling Contact Fatigue
(RCF),Wear(2013), http://dx.doi.org/10.1016/j.wear.2013.03.008i
Effect of Depth on Butterfly Shape

14. 14
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Effect of Inclusion Size on Butterfly
Wing Span
[1] Lewis , Tomkins, ” A fracture mechanics interpretation of rolling bearing fatigue“, Proc IMechE Part J: J Engineering Tribology,(2012)
• For comparison, the wingspan to inclusion diameter ratio is compared
• Simulations show that the relative wingspan to inclusion size increases as the
inclusion diameter decreases
Butterflies around a
16 𝜇 inclusion
Butterflies around a
2 𝜇 inclusion

15. 15
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Effect of Inclusion Size
Comparison with Experimental Data
[1] Lewis , Tomkins, ” A fracture mechanics interpretation of rolling bearing fatigue“, Proc IMechE Part J: J Engineering Tribology,(2012)
• The model is exercised for
different inclusions diameters
• The results are compared with
experimental data provided in
[1]
• The model results lie within
the bounds of the
experimental results and show
the same trend

16. 16
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Effect of Load Level on Wing
Formation
• Simulation results show that
Butterfly shape, size and
orientation are very similar for
different loading conditions
• Number of cycles for butterfly
appearance is drastically affected
by the amount of applied load
(note the color spectrums)
• Butterflies are believed to appear
at about 10−3 of final RCF life [1]
• Butterfly appearance has been
used as a method to predict very
long RCF lives [1]
[1] Takemura H, et al. , “ Development of New Life Equation for Ball and Roller Bearings”, NSK Motion & Control No. 11 (October 2001)
Color spectrum indicating butterfly
formation at different load levels

17. 17
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
S-N Curve for Butterfly Formation
Damage equation is calibrated by
curve fitting to Torsion Fatigue
data
𝒅𝑫
𝒅𝑵
=
𝜏 𝑎
2
+ |𝜏 𝑚|
𝝈 𝒓 𝟏 − 𝑫
𝒎
𝑵 𝒂𝒑𝒑𝒆𝒂𝒓𝒂𝒏𝒄𝒆 =
𝟏
𝟏 + 𝒎
𝝈 𝒓
𝜏 𝑎
2
+ |𝜏 𝑚|
𝒎
Integration from
𝑫 𝒑𝒓𝒊𝒔𝒕𝒊𝒏𝒆 to 𝑫 𝒄𝒓𝒊𝒕𝒊𝒄𝒂𝒍
S-N curve for butterfly formation
[1] Takemura H, et al. , “ Development of New Life Equation for Ball and Roller Bearings”, NSK Motion & Control No. 11 (October 2001)

18. 18
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Schematic showing the reversal of shear
in presence of compressive stress along
the inclusion- matrix interface
Debonding on Inclusion/ Matrix Interface
Stress Transformation
[1] 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
• It is suggested that debonding at inclusion/ matrix interface can be the
reason for crack initiation[1]
• To find the debonding regions, stresses should be resolved along the
inclusion/ matrix interface
Stress transformation formulas in
2D are employed for this purpose

19. 19
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Debonding on Inclusion/ Matrix Interface
Simulation vs. Experiments
[1] 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
Areas of debonding (A & B) and
deformation (C) observed by
(Grabulov[1])
METL Model prediction (bold,
black arches show the
debonding areas)
Resolved shear stress along the inclusion matrix interface has for maxima
regions corresponding to debonding areas observed by [1]

20. 20
May 22, 2015
Mechanical Engineering Tribology Laboratory (METL)
Summary & Conclusion
• Damage mechanics is used to model butterfly wing formation
in bearing steel
• Alternating and mean shear stress are suggested to be effective
in butterfly wing formation
• The model predicts butterfly shape and size with respect to
inclusion diameter and depth successfully
• S-N curve for wing development is in corroboration with
experiments