Research Papers: Applications

Cyclic Constitutive Response and Effective S–N Diagram of M50 NiL Case-Hardened Bearing Steel Subjected to Rolling Contact Fatigue

[+] Author and Article Information
Abir Bhattacharyya, Anup Pandkar, Ghatu Subhash

Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611

Nagaraj Arakere

Department of Mechanical and
Aerospace Engineering,
University of Florida,
Gainesville, FL 32611
e-mail: nagaraj@ufl.edu

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received October 29, 2014; final manuscript received May 21, 2015; published online July 3, 2015. Assoc. Editor: Xiaolan Ai.

J. Tribol 137(4), 041102 (Oct 01, 2015) (15 pages) Paper No: TRIB-14-1266; doi: 10.1115/1.4030689 History: Received October 29, 2014; Revised May 21, 2015; Online July 03, 2015

A combined experimental and numerical method is developed to estimate the continuously evolving cyclic plastic strain amplitudes in plastically deformed subsurface regions of a case-hardened M50 NiL steel rod subjected to rolling contact fatigue (RCF) over several hundred million cycles. The subsurface hardness values measured over the entire plastically deformed regions and the elastoplastic von Mises stresses determined from the three-dimensional (3D) Hertzian contact finite element (FE) model have been used in conjunction with Neuber's rule to estimate the evolved cyclic plastic strain amplitudes at various points within the RCF-affected zone. The cyclic stress–strain plots developed as a function of case depth revealed that cyclic hardening exponent of the material is greater than the monotonic strain-hardening exponent. Effective S–N diagram for the RCF loading of the case-hardened steel has been presented and the effect of compressive mean stress on its fatigue strength has been explained using Haigh diagram. The compressive mean stress correction according to Haigh diagram predicts that the allowable fatigue strength of the steel increases by a factor of two compared to its fatigue limit before mean stress correction, thus potentially allowing the rolling element bearings to operate over several hundred billion cycles. The methodology presented here is generalized and can be adopted to obtain the constitutive response and S–N diagrams of both through- and case-hardened steels subjected to RCF.

Copyright © 2015 by ASME
Topics: Stress , Cycles , Fatigue , Steel
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Bhattacharyya, A., Subhash, G., and Arakere, N., 2014, “Evolution of Subsurface Plastic Zone Due to Rolling Contact Fatigue of M-50 NiL Case Hardened Bearing Steel,” Int. J. Fatigue, 59, pp. 102–113. [CrossRef]
McDowell, D. L., 1995, “Stress State Dependence of Cyclic Ratcheting Behavior of Two Rail Steels,” Int. J. Plast., 11(4), pp. 397–421. [CrossRef]
Vincent, A., 1998, “From White Etching Areas Around Inclusions to Crack Nucleation in Bearing Steels Under Rolling Contact Fatigue,” Bearing Steels: Into the 21st Century, J. J. C.Hoo and W. B.Green, eds., American Society for Testing and Materials, West Conshohocken, PA, pp. 109–123.
Voskamp, A. P., Osterlund, R., Becker, P. C., and Vingsbo, O., 1980, “Gradual Changes in Residual Stress and Microstructure During Rolling Contact Fatigue in Ball Bearings,” Met. Technol., 7(1), pp. 14–21. [CrossRef]
Vingsbo, O., and Osterlund, R., 1980, “Phase Changes in Fatigued Ball Bearings,” Metall. Trans. A, 11(5), pp. 701–707. [CrossRef]
Voskamp, A. P., 1985, “Material Response to Rolling Contact Loading,” ASME J. Tribol., 107(3) pp. 359–364. [CrossRef]
Voskamp, A. P., and Mittemeijer, E. J., 1997, “The Effect of the Changing Microstructure on the Fatigue Behavior During Cyclic Rolling Contact Loading,” Z. Metallkd., 88, pp. 310–319.
Barrow, A. T. W., and Rivera-Díaz-del-Castillo, P. E. J., 2011, “Nanoprecipitation in Bearing Steels,” Acta Mater., 59(19), pp. 7155–7167. [CrossRef]
Swahn, H., Becker, P. C., and Vingsbo, O., 1976, “Martensite Decay During Rolling Contact Fatigue in Ball Bearings,” Metall. Trans. A, 7(8), pp. 1099–1110. [CrossRef]
Bhadeshia, H. K. D. H., 2012, “Steels for Bearings,” Prog. Mater. Sci., 57(2), pp. 268–435. [CrossRef]
Steindorf, H., Broszeit, E., and Kloos, K. H., 1987, “Gefüge Und Anlaßverhalten Von Weißen Bändern,” Materialwiss. Werkstofftech., 18(12), pp. 428–435. [CrossRef]
Reis, L., Li, B., and de Freitas, M., 2014, “A Multiaxial Fatigue Approach to Rolling Contact Fatigue in Railways,” Int. J. Fatigue, 67, pp. 191–202. [CrossRef]
Reis, L., Li, B., and De Freitas, M., 2006, “Analytical and Experimental Studies on Fatigue Crack Path Under Complex Multi-Axial Loading,” Fatigue Fract. Eng. Mater. Struct., 29(4), pp. 281–289. [CrossRef]
Smith, K., Topper, T., and Watson, P., 1970, “A Stress–Strain Function for the Fatigue of Metals (Stress–Strain Function for Metal Fatigue Including Mean Stress Effect),” J. Mater., 5, pp. 767–778.
Stephens, R. I., Fatemi, A., and Stephens, R. R., 2000, Metal Fatigue in Engineering, Wiley, New York.
Klecka, M. A., Subhash, G., and Arakere, N. K., 2013, “Microstructure–Property Relationships in M50-NiL and P675 Case-Hardened Bearing Steels,” Tribol. Trans., 56(6), pp. 1046–1059. [CrossRef]
Glover, D., 1982, “A Ball–Rod Rolling Contact Fatigue Tester,” Rolling Contact Fatigue Testing of Bearing Steels, Vol. 771, ASTM STP, West Conshohocken, PA, pp. 107–125.
Branch, N. A., Subhash, G., and Arakere, N. K., 2011, “A New Reverse Analysis to Determine the Constitutive Response of Plastically Graded Case Hardened Bearing Steels,” Int. J. Solids Struct., 48(3–4), pp. 584–591. [CrossRef]
Klecka, M. A., 2011, Microstructure Property Relationships and Constitutive Response of Plastically Graded Case Hardened Steels, University of Florida, Gainesville, FL.
Johnson, K. L., and Johnson, K. L., 1987, Contact Mechanics, Cambridge University Press, Cambridge, UK.
Kang, G., and Liu, Y., 2008, “Uniaxial Ratchetting and Low-Cycle Fatigue Failure of the Steel With Cyclic Stabilizing or Softening Feature,” Mater. Sci. Eng.: A, 472(1–2), pp. 258–268. [CrossRef]
Sadeghi, F., Jalalahmadi, B., and Slack, T. S., 2009, “A Review of Rolling Contact Fatigue,” ASME J. Tribol., 131(4), p. 041403. [CrossRef]
Neuber, H., 1946, Theory of Notch Stresses, J. W.Edwards Co, Ann Arbor, MI.
Tabor, D., 1970, “The Hardness of Solids,” Rev. Phys. Technol., 1(3), p. 145. [CrossRef]
Boehmer, H., Ebert, F., and Trojahn, W., 1992, “M50NiL Bearing Material: Heat Treatment, Material Properties and Performance in Comparison With M50 and RBD,” Lubr. Eng., 48(1), pp. 28–35.
Budynas, R. N. K., 2011, Shigley's Mechanical Engineering Design, McGraw-Hill, New York.
Harris, T., and Barnsby, R., 2001, “Life Ratings for Ball and Roller Bearings,” Proc. Inst. Mech. Eng., Part J, 215(6), pp. 577–595. [CrossRef]
Fuchs, H., 1965, “A Set of Fatigue Failure Criteria,” ASME J. Fluids Eng., 87(2), pp. 333–342. [CrossRef]
Wehner, T., and Fatemi, A., 1991, “Effects of Mean Stress on Fatigue Behaviour of a Hardened Carbon Steel,” Int. J. Fatigue, 13(3), pp. 241–248. [CrossRef]


Grahic Jump Location
Fig. 1

(a) Schematic of a typical three-ball-on-rod test, (b) Tracks on the surface of a RCF tested M-50 NiL rod, (c) RCF track after 38.7 M cycles, and (d) Spalled RCF track after 171.8 M cycles

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Fig. 2

Polished and etched (a) radial and (b) longitudinal sectional views of RCF-affected plastic zone in M50-NiL. Inset of (a) shows gradation in carbide distribution from case region to the core in a virgin material.

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Fig. 3

(a) A FEA contact model of a quarter section of an M50-NiL rod and a Si3N4 ball, (b) The contact pressure distribution on the surface of the rod, (c) The von Mises stress distribution in XY and YZ planes of the rod, and (d) The monotonic stress–strain graphs of various case layers and the core region of M-50 NiL steel. The depths of the corresponding case layers are provided. The strain-hardening exponents (n) of all the case layers are 0.056.

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Fig. 4

Profiles of the RCF tracks for five different test cycles. Both the width and depth of plastically deformed regions increase with RCF cycles. The variation of track width is shown as a function of cycles in the inset. A plateau region is observed in between 38.7 M cycles and 158.4 M cycles.

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Fig. 5

(a) Hardness profile of the virgin material and after 246 × 106 cycles along the centerline of the RCF-affected zone as a function of depth from surface. Note considerable increase in hardness within 450 μm from the surface at 246 M cycles followed by a decrease in hardness compared to the virgin material. (b) Hardness distribution in the RCF-affected zone after 246 M cycles. Regions of softening are shaded.

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Fig. 6

The measured maximum hardness change as a function of RCF cycles. No increase in hardness was observed until track widening started (at around 43,000 cycles). Considerably high hardness was measured after 13.5 M cycles. The rate of hardening decreases significantly beyond 38.7 M cycles. Also shown on the plot is the variation of contact pressure with RCF cycles, where the pressure decreases with cycles due to increase in track width.

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Fig. 7

Schematic of the proposed method to estimate strain amplitudes and construct cyclic stress–strain response of various case regions of a case-hardened material. Each material point at a given depth is subjected to a unique far-field von Mises stress amplitude (ΔSVM/2) that causes strain amplitude to evolve over millions of RCF cycles. The ΔSVM/2 is plotted with respect to Δɛ/2 at two different depths where the correspondence between hardness and cyclic stress–strain response is illustrated.

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Fig. 8

Analogy between a cyclically loaded carbide particle and a notched fatigue specimen. (a) A magnified view of a material point inside the RCF-affected region is equivalent to combined cyclic loading of a carbide particle surrounded by a steel matrix. The far-field cyclic normal stress ranges are ΔS1 and ΔS2, and the cyclic shear stress range is Δτ. (b) The stresses are replaced with an equivalent von Mises stress ΔSVM. The stress concentration in the vicinity of the carbide is accounted for by Kt. (c) Schematic of a notched specimen subjected to uniaxial cyclic loading. The global cyclic stress and strain ranges are ΔSVM and ΔeVM, but the magnified local strains at the notched root are ΔσVM and ΔɛVM, respectively. The fatigue stress concentration factor (Kf) at the notch root is assumed to be same as Kt.

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Fig. 9

Distribution of the far-field equivalent von Mises stress along the width of the plastic zone after a single static contact. The stress decreases with depth. The von Mises stress is greater near the center of the region and decreases at distances away from the central region. The stress also saturates over a certain region in the width direction within the plastic zone until 225 μm depth, beyond which no saturation is observed. The inset shows a schematic of the plastic zone.

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Fig. 10

(a) The variation of fully reversed applied far field and local strain amplitudes due to application of far-field stress amplitude at 75 μm depth. The local strain amplitudes are greater than applied far-field strain amplitudes that are elastic. (b) The variation of local plastic strain amplitude as a function of the width of the hardened region. The regions at the center of the width are subjected to higher plastic strain reversals than the regions away from the center.

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Fig. 11

The monotonic and cyclic flow curves at four different case depths inside the RCF-affected plastic zone

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Fig. 12

(a) Comparison of cyclic stress–strain responses at four different depths of M50 NiL. The cyclic yield strength increases with depth. (b) Cyclic plastic strain amplitude versus equivalent fully reversed von Mises stress amplitude (R = −1) at four different depths. The cyclic strain-hardening exponent decreases with depth.

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Fig. 13

S–N diagram of M50-NiL steel

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Fig. 14

Haigh diagram revealing the effect of compressive mean stress on allowable alternating stress amplitude in M50-NiL steel. Any combination of mean and alternating stress outside the shaded area GCK represents gross yielding. The variation of allowable alternating stress in presence of compressive mean stress is shown by the solid lines BH and HE. The continuous boundary BHE shows that compressive mean stress (Sm) increases the tolerable alternating stress (Sa) significantly.

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Fig. 15

Effect of compressive mean stress through SaNf diagram. Fatigue strength is increased from 539 MPa for R = −1 to 1087 MPa in the presence of Sm = −1471 MPa.

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Fig. 16

Mesh sensitivity analysis showing: (a) force–displacement response of ball-on-rod contact FE model for three different mesh sizes. Note that all three curves are essentially same and lie on each other. (b) The Hertzian contact pressure and maximum von Mises stress as a function of mesh size. The variation in the magnitudes of contact pressure and von Mises stress is less than 1%.



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