Effect of Mean Stress on Rolling Contact Fatigue

1. Effect of Mean Stress on Rolling Contact Fatigue SinaMobasherMoghaddam Ph.D. Research Assistant

2. Outlines • Butterfly-wing formation in bearing steel • Background and Motivation • Stress Analysis • METL suggested theory • Results comparison and validation • Effect of compressive stress on torsion fatigue • Instrument Design • Fatigue life reduction • Failure mode change • FEM simulation

3. Butterfly WingsDetrimental Effect on RCF • In some applications bearings may last only 10% of their life [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 Butterflies Observed by Vincent [1](top) and Grabulov [2](Bottom) [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

4. ORD 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 Wing Span Debonded Region Coarse Grains 50-100 nm Schematic of a pair of butterfly wings Crack Fine Grains 5-10 nm

5. Stress Analysis • Inclusion presence induces stress concentrations in the surrounding matrix • When dealing with fatigue problems, it is important to consider stress history Comparison of centerline stresses for two domains with and without embedded inclusion , b=100= 2.0 GPa Damage Equation

6. Butterfly Wing Evolution Butterfly wing orientation, direction, and size are consistent with the experimental observations Color spectrum of butterfly wing formation Butterfly formation according to Grabulov[1] Butterfly formation according to METL model prediction [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

7. Effect of Depth on Butterfly Growth 0.38 b 0.4 b 0.42 b 0.7 b 0.5 0.6 b 0.8 b Secondary upper wing 1.1 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

8. S-N Curve for Butterfly Formation Damage equation is calibrated by curve fitting to Torsion Fatiguedata Integration from to S-N curve for butterfly formation [1]TakemuraH, et al. , “ Development of New Life Equation for Ball and Roller Bearings”, NSK Motion & Control No. 11 (October 2001)

9. Effect of Inclusion Size on Butterfly Wing Span • For comparison, the wingspan to inclusion diameter ratio is compared • The model results lie within the bounds of the experimental results and show the same trend Butterflies around a 16 inclusion Butterflies around a 2 inclusion [1] Lewis , Tomkins, ” A fracture mechanics interpretation of rolling bearing fatigue“, ProcIMechE Part J: J Engineering Tribology,(2012)

10. Debonding on Inclusion/ Matrix Interface To find the debonding regions, stresses should be resolved along the inclusion/ matrix interface Stress transformation formulas in 2D are employed for this purpose Schematic showing the reversal of shear in presence of compressive stress along the inclusion- matrix interface METL Model prediction (bold, black arches show the debonding areas) Areas of debonding (A & B) and deformation (C) observed by (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

11. Prediction of Crack Initiation Locations • Cracks are commonly observed on top of the upper wing and bottom of the lower wing • Mode I loading is suggested as the main factor for crack development in vicinity of the inclusion • FEM results show maximum tensile stress during loading history is higher on top of the upper wing and bottom of the lower wing Maximum tensile stress resolved along the butterfly edges [1] Lewis , Tomkins, ” A fracture mechanics interpretation of rolling bearing fatigue“, ProcIMechE Part J: J Engineering Tribology,(2012)

12. Effect of Compressive Stress on Torsion Fatigue • RCF is a shear dominated phenomena • There is a large compressive stress present in the contact zone • A custom made set of clamps are designed to apply high compressive stress (up to 2.5 GPa) on torsion specimens to better simulate RCF failure Stress history at 0.5b Custom made clamps: a) exploded view b) as they appear after assembly Schematic of Hertzian contact zone in clamp/ specimen interface

13. Effect of Compressive Stress on Torsion Fatigue Life • Application of compressive clamps reduced the torsion fatigue life • The reduction is up to in one order of magnitude in high cycle fatigue Steel B Steel C Steel E

14. Effect of Compressive Stress on Fracture Mode • As opposed to helical fracture surfaces for pure torsion tests, broken specimens form cup & cone pairs • Initiation cracks are due to torsion while multiple cracks grow in the propagation stage 0.8 0.6 0.4 0.3 0.5 0.6 0.5 0.7 0.9 Propagation cracks Initiation cracks Initiation and propagation cracks in sample failed specimens Sample failed specimens at different load levels

15. FEM ModelLife Prediction and Failure Simulation • A user defined subroutine is developed to apply a Hertzian pressure profile at the center of the specimen • FEM results show similar crack patterns to experiments • Life prediction is successful implementing the damage mechanics Without compressive stress With compressive stress S-N Curve: Experiment vs. FEM

16. Summary and Future Work • Summary • Damage mechanics is used to model butterfly wing formation in bearing steel • 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 • Effect of compressive stress on torsion fatigue life and fracture mode is studied • Future Work • Explore capabilities of damage mechanics to model DERs, WEBs, and WECs in bearings • Conduct RCF tests to expand a data base for different types of microstructural changes in bearings • Experimental and analytical investigation of effect of steel cleanliness on torsion fatigue and RCF