0
Research Papers: Applications

A New Approach for Fatigue Damage Modeling of Subsurface-Initiated Spalling in Large Rolling Contacts

[+] Author and Article Information
Aditya A. Walvekar

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: awalveka@purdue.edu

Neil Paulson

School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: npaulson@purdue.edu

Farshid Sadeghi

Fellow ASME
Cummins Distinguished Professor
of Mechanical Engineering,
School of Mechanical Engineering,
Purdue University,
West Lafayette, IN 47907
e-mail: sadeghi@purdue.edu

Nick Weinzapfel

Engine Components and Chassis Systems,
Schaeffler Group USA, Inc.,
Troy, MI 48083
e-mail: nick.weinzapfel@schaeffler.com

Martin Correns

Rolling Bearing Fundamentals,
Schaeffler Technologies GmbH & Co. KG,
Industriestraße 1-3,
Herzogenaurach 91074, Germany,
e-mail: corremnt@schaeffler.com

Markus Dinkel

Materials Development,
Schaeffler Technologies GmbH & Co. KG,
Georg-Schäfer-Straße 30,
Schweinfurt 97421, Germany
e-mail: markus.dinkel@schaeffler.com

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received September 1, 2015; final manuscript received February 8, 2016; published online July 14, 2016. Assoc. Editor: Dong Zhu.

J. Tribol 139(1), 011101 (Jul 14, 2016) (15 pages) Paper No: TRIB-15-1324; doi: 10.1115/1.4033054 History: Received September 01, 2015; Revised February 08, 2016

Large bearings employed in wind turbine applications have half-contact widths that are usually greater than 1 mm. Previous numerical models developed to investigate rolling contact fatigue (RCF) require significant computational effort to study large rolling contacts. This work presents a new computationally efficient approach to investigate RCF life scatter and spall formation in large bearings. The modeling approach incorporates damage mechanics constitutive relations in the finite element (FE) model to capture fatigue damage. It utilizes Voronoi tessellation to account for variability occurring due to the randomness in the material microstructure. However, to make the model computationally efficient, a Delaunay triangle mesh was used in the FE model to compute stresses during a rolling contact pass. The stresses were then mapped onto the Voronoi domain to evaluate the fatigue damage that leads to the formation of surface spall. The Delaunay triangle mesh was dynamically refined around the damaged elements to capture the stress concentration accurately. The new approach was validated against previous numerical model for small rolling contacts. The scatter in the RCF lives and the progression of fatigue spalling for large bearings obtained from the model show good agreement with experimental results available in the open literature. The ratio of L10 lives for different sized bearings computed from the model correlates well with the formula derived from the basic life rating for radial roller bearing as per ISO 281. The model was then extended to study the effect of initial internal voids on RCF life. It was found that for the same initial void density, the L10 life decreases with the increase in the bearing size.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.

References

Harris, T. A. , 2001, Rolling Bearing Analysis, Wiley, New York.
Littmann, W. E. , 1969, “ The Mechanism of Contact Fatigue,” NASA Special Report, Report No. SP-237.
Littmann, W. E. , and Widner, R. L. , 1966, “ Propagation of Contact Fatigue From Surface and Subsurface Origins,” ASME J. Basic Eng., 88(3), pp. 624–636. [CrossRef]
Bower, A. F. , 1988, “ The Influence of Crack Face Friction and Trapped Fluid on Surface Initiated Rolling Contact Fatigue Cracks,” ASME J. Tribol., 110(4), pp. 704–711. [CrossRef]
Lundberg, G. , and Palmgren, A. , 1949, “ Dynamic Capacity of Rolling Bearings,” ASME J. Appl. Mech., 16(2), pp. 165–172.
Ioannides, E. , and Harris, T. A. , 1985, “ A New Fatigue Life Model for Rolling Bearings,” ASME J. Tribol., 107(3), pp. 367–377. [CrossRef]
Sadeghi, F. , Jalalahmadi, B. , Slack, T. S. , Raje, N. , and Arakere, N. K. , 2009, “ A Review of Rolling Contact Fatigue,” ASME J. Tribol., 131(4), p. 041403. [CrossRef]
Alley, E. S. , and Neu, R. W. , 2010, “ Microstructure-Sensitive Modeling of Rolling Contact Fatigue,” Int. J. Fatigue, 32(5), pp. 841–850. [CrossRef]
Panasyuk, V. V. , Datsyshyn, O. P. , and Marchenko, H. P. , 1995, “ The Crack Propagation Theory Under Rolling Contact,” Eng. Fract. Mech., 52(1), pp. 179–191. [CrossRef]
Keer, L. M. , and Bryant, M. D. , 1983, “ A Pitting Model for Rolling Contact Fatigue,” ASME J. Tribol., 105(2), pp. 198–205.
Miyashita, Y. , Yoshimura, Y. , Xu, J. Q. , Horikoshi, M. , and Mutoh, Y. , 2003, “ Subsurface Crack Propagation in Rolling Contact Fatigue of Sintered Alloy,” JSME Int. J. Ser. A, 46(3), pp. 341–347. [CrossRef]
Miller, K. J. , 1999, “ A Historical Perspective of the Important Parameters of Metal Fatigue and Problems for the Next Century,” Seventh International Fatigue Congress, Beijing, pp. 15–39.
Espinosa, H. D. , and Zavattieri, P. D. , 2003, “ A Grain Level Model for the Study of Failure Initiation and Evolution in Polycrystalline Brittle Materials—Part I: Theory and Numerical Implementation,” Mech. Mater., 35(3–6), pp. 333–364. [CrossRef]
Jalalahmadi, B. , and Sadeghi, F. , 2009, “ A Voronoi Finite Element Study of Fatigue Life Scatters in Rolling Contacts,” ASME J. Tribol., 131(2), p. 022203. [CrossRef]
Raje, N. , Sadeghi, F. , and Rateick, R. G., Jr. , 2008, “ A Statistical Damage Mechanics Model for Subsurface Initiated Spalling in Rolling Contacts,” ASME J. Tribol., 130(4), p. 042201. [CrossRef]
Jalalahmadi, B. , and Sadeghi, F. , 2010, “ A Voronoi FE Fatigue Damage Model for Life Scatter in Rolling Contacts,” ASME J. Tribol., 132(2), p. 021404. [CrossRef]
Slack, T. , and Sadeghi, F. , 2010, “ Explicit Finite Element Modeling of Subsurface Initiated Spalling in Rolling Contacts,” Tribol. Int., 43(9), pp. 1693–1702. [CrossRef]
Weinzapfel, N. , and Sadeghi, F. , 2013, “ Numerical Modeling of Sub-Surface Initiated Spalling in Rolling Contacts,” Tribol. Int., 59, pp. 210–221. [CrossRef]
Bomidi, J. A. , Weinzapfel, N. , Sadeghi, F. , Liebel, A. , and Weber, J. , 2013, “ An Improved Approach for 3D Rolling Contact Fatigue Simulations With Microstructure Topology,” Tribol. Trans., 56(3), pp. 385–399. [CrossRef]
Lemaître, J. , 1992, A Course on Damage Mechanics, Springer-Verlag, Berlin.
Kim, T. H. , Olver, A. V. , and Pearson, P. K. , 2001, “ Fatigue and Fracture Mechanisms in Large Rolling Element Bearings,” Tribol. Trans., 44(4), pp. 583–590. [CrossRef]
Shewchuk, J. R. , 1996, “ Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator,” Applied Computational Geometry Towards Geometric Engineering, Springer, Berlin, pp. 203–222.
Ito, O. , and Fuller, E. R. , 1993, “ Computer Modelling of Anisotropic Grain Microstructure in Two Dimensions,” Acta Metall. Mater., 41(1), pp. 191–198. [CrossRef]
Warhadpande, A. , Jalalahmadi, B. , Slack, T. , and Sadeghi, F. , 2010, “ A New Finite Element Fatigue Modeling Approach for Life Scatter in Tensile Steel Specimens,” Int. J. Fatigue, 32(4), pp. 685–697. [CrossRef]
Bomidi, J. A. , Weinzapfel, N. , Wang, C. P. , and Sadeghi, F. , 2012, “ Experimental and Numerical Investigation of Fatigue of Thin Tensile Specimen,” Int. J. Fatigue, 44, pp. 116–130. [CrossRef]
Przybyla, C. P. , and McDowell, D. L. , 2010, “ Microstructure-Sensitive Extreme Value Probabilities for High Cycle Fatigue of Ni-Base Super Alloy IN100,” Int. J. Plast., 26(3), pp. 372–394. [CrossRef]
Slack, T. S. , Leonard, B. D. , and Sadeghi, F. , 2013, “ Estimating Life Scatter in Fretting Fatigue Crack Initiation,” Tribol. Trans., 56(4), pp. 531–535. [CrossRef]
Mücklich, F. , Ohser, J. , and Schneider, G. , 1997, “ The Characterization of Homogeneous Polyhedral Microstructures Applying the Spatial Poisson-Voronoi Tessellation Compared to the Standard DIN 50601,” Z. Metallkd., 88(1), pp. 27–32.
Callister, W. D., Jr. , 2000, Material Science and Engineering: An Introduction, 5th ed., Wiley, New York, pp. 51–52.
Kachanov, L. M. , 1958, “ Time of the Rupture Process Under Creep Conditions,” Isv. Akad. Nauk. SSR. Otd Tekh. Nauk, 8, pp. 26–31.
Bolotin, V. V. , and Belousov, I. L. , 2001, “ Early Fatigue Crack Growth as the Damage Accumulation Process,” Probab. Eng. Mech., 16(4), pp. 279–287. [CrossRef]
Styri, H. , 1951, “ Fatigue Strength of Ball Bearing Races and Heat-Treated 52100 Steel Specimens,” Proc. ASTM, 51, pp. 682–700.
Lemaitre, J. , 1985, “ A Continuous Damage Mechanics Model for Ductile Fracture,” ASME J. Eng. Mater. Technol., 107(1), pp. 83–89. [CrossRef]
Bomidi, J. A. , Weinzapfel, N. , Slack, T. , Moghaddam, S. M. , Sadeghi, F. , Liebel, A. , Weber, J. , and Kreis, T. , 2013, “ Experimental and Numerical Investigation of Torsion Fatigue of Bearing Steel,” ASME J. Tribol., 135(3), p. 031103. [CrossRef]
Barnsby, R. M. , ed., 2003, Life Ratings for Modern Rolling Bearings: A Design Guide for the Application of International Standard ISO 281/2, Vol. 1, American Society of Mechanical Engineers, New York.
Tallian, T. E. , 1999, Failure Atlas for Hertz Contact Machine Elements, American Society of Mechanical Engineers, New York.
Lou, B. , Han, L. , Lu, Z. , Liu, S. , and Shen, F. , 1990, “ The Rolling Contact Fatigue Behaviors in Carburized and Hardened Steel,” Fourth International Conference on Fatigue and Fatigue Thresholds, Honolulu, HI, pp. 627–632.
Harris, T. A. , and Barnsby, R. M. , 2001, “ Life Ratings for Ball and Roller Bearings,” Proc. Inst. Mech. Eng., Part J, 215(6), pp. 577–595. [CrossRef]
Ai, X. , 2015, “ A Comprehensive Model for Assessing the Impact of Steel Cleanliness on Bearing Performance,” ASME J. Tribol., 137(1), p. 011101. [CrossRef]
Chen, Q. , Shao, E. , Zhao, D. , Guo, J. , and Fan, Z. , 1991, “ Measurement of the Critical Size of Inclusions Initiating Contact Fatigue Cracks and Its Application in Bearing Steel,” Wear, 147(2), pp. 285–294. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Random material microstructure generated using a Voronoi tessellation. The Voronoi cell boundaries represent the weak planes in the material microstructure.

Grahic Jump Location
Fig. 2

Voronoi cell divided into Voronoi elements and stresses resolved along the grain boundaries

Grahic Jump Location
Fig. 3

S–N curve for bearing steel AISI 52100 in completely reversed torsional fatigue [32]

Grahic Jump Location
Fig. 4

Computational domain used in FE simulation

Grahic Jump Location
Fig. 5

Comparison of number of elements in the Voronoi (a) and Delaunay (b) mesh for b = 100 μm and b = 400 μm

Grahic Jump Location
Fig. 6

Flowchart for the procedure to couple Delaunay mesh with fatigue damage model

Grahic Jump Location
Fig. 7

State of stress for the Delaunay mesh (a) obtained from FE simulation and stresses mapped onto the Voronoi mesh (b)

Grahic Jump Location
Fig. 9

Remeshing procedure: Critically damaged Voronoi elements are shown in black and surrounding Voronoi elements are highlighted. (a) Delaunay mesh and (b) Voronoi mesh

Grahic Jump Location
Fig. 10

Progression of the Delaunay mesh at various stages of simulation (b = 200 μm). The spall pattern is shown in black color. The Voronoi mesh is depicted in (I).

Grahic Jump Location
Fig. 11

Weibull probability plots for (a) initiation and (b) final lives for different contact sizes

Grahic Jump Location
Fig. 12

Relationship between L10 lives and size factor fs obtained from the model results and Eq.(23) derived from basic life rating for radial roller bearing as per ISO 281

Grahic Jump Location
Fig. 13

Typical spall patterns obtained from the model for different contact sizes: (I) b = 100 μm, (II) b = 200 μm, (III) b = 400 μm, and (IV) b = 1000 μm

Grahic Jump Location
Fig. 14

Experimentally observed spall patterns: (I) Tallian [36] and (II) Lou et al. [37]

Grahic Jump Location
Fig. 15

Spalls obtained from the model by continuing the simulation after the first crack reaches the surface (b = 400 μm)

Grahic Jump Location
Fig. 16

Types of initial voids randomly placed in the microstructure topology region. Elasticity modulus of highlighted elements is set to zero.

Grahic Jump Location
Fig. 17

Weibull probability plots for final lives for different simulation conditions (b = 100 μm)

Grahic Jump Location
Fig. 18

Typical spall pattern for randomly placed (a) small and (b) large initial void for b = 100 μm. The initial void is highlighted.

Grahic Jump Location
Fig. 19

Examples of spalls obtained for different simulation condition. (a) Four small initial voids randomly placed in the domain with b = 400 μm and (b) four large initial voids randomly placed in the domain with b = 400 μm. The initial voids are highlighted.

Grahic Jump Location
Fig. 20

Weibull probability plots for final lives for different contact sizes having same initial void density

Tables

Errata

Discussions

Related

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In