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Sina Mobasher MoghaddamPh.D. CandidateFarshid SadeghiCummins Distinguished Professor of Mechanical Engineering

3D Simulation of Butterfly Wings Formation in Bearing Steel

November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

OutlineBackground and motivation2D modelReviewRecent developments3D modelTheoryAnalytical resultsExperimental validation

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

Motivation:Detriment of Butterfly Wings

[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) 576583

Butterflies Observed by Vincent [1](top) and Grabulov [2](Bottom)

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

History & Background

- Styri (1947)First Observation19471992 45 years, more than 200 experimental papers- No Analytical solution199620022014- Salehizadeh (1992)Residual stress - Melander (1996)Fracture mechanics

2006-Vincent(2002)Dislocation motion- METL (2014)Damage mechanics- Alley (2009)Plastic Strain

The new model considers the effect of alternating and mean components of shear stress in butterfly formationButterfly shape, orientation, and appearance life were successfully predicted with the model

#November 13, 2014Mechanical 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. 635638.Average Stiffness ratio is 0.9041. Critical damage value is set to 0.1

Optical(top) and SEM(top-right) images of butterfly wings formed in 8620 bearing steel. Nano-indentation marks (right)-METL experimental facilities

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

An Example of Spall FormationUsing Kill Element ApproachHalf Contact Width ()Maximum Hertzian Pressure (GPa)Friction CoefficientGrain Size()Matrix Stiffness(GPa)Domain Length ()Domain Depth()1002.00.05102001000700

Animation of spall formation due to butterflies

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

Domain # 08

Crack Maps & Spall GeometryExperimental observation indicate that cracks tend to form on top of the upper wing and bottom of the lower wingIn 26/33 (~ 80%) of the investigated spalls, cracks are observed at the corresponding locations

Domain # 13Domain # 22

Cracks

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

Effect of Inclusion Characteristics Stiffness, Size, and DepthEffect 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

#November 13, 2014Mechanical 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

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

Wings Without Inclusion!A 2D plain strain model does not count for the globular or ellipsoidal form of the inclusionsDuring the optical microscopy of M50 rods, features similar to pairs of wings without inclusion appearedA detailed study of butterfly wing shape in 3D was necessary to better understand these features

ORDORD

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

3D FEM ModelTheory & AssumptionsTo save computational time, half contact width is reduced from 100 (for 2D model) to 50 for the 3D modelY-Plane experiences the largest reversal valueShear 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

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

3D Butterfly Model

Contact TypeLine ContactHalf Contact Width (b)50 Maximum Hertzian Pressure2.0 GpaFriction Coefficient0.05Inclusion Stiffness300 GPaMatrix Stiffness200 GPaDomain Length500 Domain Depth350 Domain Width50

Animation of 3D Butterfly ProgressionIt took more than 10 days of continues FEM simulation to complete this model!!

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

Analytical Serial Sectioning of Butterflies

Animation illustrating the cut cross sections in 3DSerial sectioning of a fully formed pair of wingsDuring fractography, we can only access 2D sections of butterflies Serial sectioning is necessary to reconstruct a 3D map out of 2D sections

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

Lateral Extension of Butterfly WingsAnalytical serial sectioning shows that wings can develop laterally beyond the inclusion extents Final confirmation would be possible after experimental serial sectioning

Modeled Inclusion-less WingsExperimentally Observed Inclusion-less Wings

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

3 Ball on Rod RCF Tester

Rotational fixtureTransducerSample

Schematic of the rigSchematic of the contactTest specimenUltrasonic inspection of inclusions (image courtesy: Sonoscan, Inc.)

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Ultrasonic Detection of InclusionsC-Scan of Sample

Length of the SpecimenNoise from airMarker

360 Degree

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Image Processing on C-Scan

Studied inclusionSpecimen MaterialMajor Axis()Minor Axis()Maximum Hertzian Pressure (GPa)Test Speed(rpm)Spalling Life8620 (5% RA)2361302.0360032.2E7

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

Experimental Serial Sectioning of Butterflies

123456789101112131415Sections 1, 2, and 11-15 show the presence of wings without inclusion

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

Wing Span to Radius RatioClosed Form Solution

Wings without inclusions

4R (Observed wingspan)2RdObserved inclusion diameterCut planeThe wing span to inclusion ratio is observed to be about 2.0 at the mid cross sectionSerial sectioning results show that the wingspan is approximately the same in all the section while the observed inclusion diameter varies

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

Wing Span to Radius Ratio2D vs. 3D

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)

SummaryCritical damage is measured inside butterfliesEffect of inclusion characteristics is studied on wing formation and RCF lifeButterflies is studied as a 3D objectA 3D model is used to simulate butterfly formation using damage mechanicsLateral expansion of wings is confirmed with analytical and experimental serial sectioningClosed form solution for wingspan to inclusion ratio in 3D is suggested

#November 13, 2014Mechanical Engineering Tribology Laboratory (METL)