This paper presents a rolling contact fatigue life prediction model for bearing steel. In the initial stage of rolling contact, the gradient structure appears in the subsurface region of bearing steel and the hardness shows a gradient distribution along the contact depth direction due to the roller compaction effect. This indicates that the fatigue resistance of bearing steel varies in the subsurface region. Besides, each subsurface material volume element is subject to different stress cycles. Based on Weibull theory, the survival possibility of subsurface volume elements is formulated. Then the rolling contact fatigue life is evaluated considering the stress state and anti-fatigue performance of each elementary volume of the subsurface material. According to the phenomenon and assumption, the model proposed for gradient material was applied in the rolling contact fatigue life prediction of the bearing steel GCr15 and validated with the fatigue experiment data in the open literature. Furthermore, the accuracy of the proposed model results was compared with the traditional empirical rolling contact fatigue life prediction models.
ArakereNKSubhashG (2012)
Work hardening response of M50-NiL case hardened bearing steel during shakedown in rolling contact fatigue. Materials Science and Technology28(1): 34–38.
2.
AverbeckSKerscherE (2017a)
Critical plane analysis of multiaxial fatigue experiments leading to white etching crack formation. Journal of Physics: Conference Series843: 012028.
3.
AverbeckSKerscherE (2017b)
Influence of multiaxial fatigue loading conditions on white etching crack formation. Engineering Fracture Mechanics174: 180–195.
4.
CaoZLiuTYuF, et al. (2020)
Carburization induced extra-long rolling contact fatigue life of high carbon bearing steel. International Journal of Fatigue131: 105351.
5.
CarpinteriASpagnoliAVantadoriS (2009)
Multiaxial fatigue life estimation in welded joints using the critical plane approach. International Journal of Fatigue31(1): 188–196.
6.
EvansMH (2012)
White structure flaking (WSF) in wind turbine gearbox bearings: effects of ‘butterflies’ and white etching cracks (WECs). Materials Science and Technology28(1): 3–22.
7.
FangTHLiWLTaoNR, et al. (2011)
Revealing extraordinary intrinsic tensile plasticity in gradient nano-grained copper. Science (New York, N.Y.)331(6024): 1587–1590.
8.
FatemiAShamsaeiN (2011)
Multiaxial fatigue: an overview and some approximation models for life estimation. International Journal of Fatigue33(8): 948–958.
9.
FatemiASocieDF (1988)
A critical plane approach to multiaxial fatigue damage including out-of-phase loading. Fatigue & Fracture of Engineering Materials & Structures11(3): 149–165.
10.
FeiH (2017) Numerical computation of rolling contact fatigue of components with strength gradient surface layer. MS Thesis, University of Chinese Academy of Sciences
11.
FuHRydelJJGolaAM, et al. (2019)
The relationship between 100Cr6 steelmaking, inclusion microstructure and rolling contact fatigue performance. International Journal of Fatigue129: 104899.
12.
GabelliALaiJLundT, et al. (2012)
The fatigue limit of bearing steels – Part II: Characterization for life rating standards. International Journal of Fatigue38: 169–180.
13.
GarudYS (1981)
A new approach to the evaluation of fatigue under multiaxial loadings. Journal of Engineering Materials and Technology103(2): 118–125.
14.
GB/T 4340.1-1999. Metallic materials- Vickers hardness test Part 1: Test method.
GuoRLeiXZhangD, et al. (2018)
Case study: The effect of running distance on the microstructure and properties of railroad axle bearings. Wear394–395: 159–165.
17.
HashimotoKHiraokaKKidaK, et al. (2013)
Effect of sulphide inclusions on rolling contact fatigue life of bearing steels. Materials Science and Technology28(1): 39–43.
18.
IoannidesEHarrisTA (1985)
A new fatigue life model for rolling bearings. Journal of Tribology107(3): 367–377.
19.
JiangBDongZZhouL, et al. (2016a)
Microstructural characterization and hardening mechanism of steel for large size bearing ring under fast heating and short soaking time condition. Steel Research International87(9): 1127–1136.
20.
JiangBMeiZZhouL, et al. (2016b)
Microstructure evolution, fracture and hardening mechanisms of quenched and tempered steel for large sized bearing rings at elevated quenching temperatures. Metals and Materials International22(4): 572–578.
21.
LiZYangBWuH, et al. (2013) An accelerated test method of rolling contact fatigue with small slip rate in metal material. CN Patent 103424307 A.
22.
LiuYMahadevanS (2005)
Multiaxial high-cycle fatigue criterion and life prediction for metals. International Journal of Fatigue27(7): 790–800.
23.
LundbergGPalmgrenA (1947)
Dynamic capacity of rolling bearings. Acta Polytechnica Scandinavica1: 3–50.
24.
MarsWVFatemiA (2005a)
Multiaxial fatigue of rubber: Part I: Equivalence criteria and theoretical aspects. Fatigue & Fracture of Engineering Materials & Structures28(6): 515–522.
25.
MarsWVFatemiA (2005b)
Multiaxial fatigue of rubber: Part II: Experimental observations and life predictions. Fatigue & Fracture of Engineering Materials & Structures28(6): 523–538.
26.
MatakeT (1977)
An explanation on fatigue limit under combined stress. Bulletin of JSME20(141): 257–263.
27.
MobasherMSSadeghiFWeinzapfelN, et al. (2015)
A damage mechanics approach to simulate butterfly wing formation around nonmetallic inclusions. Journal of Tribology137(1): 011404.
28.
PavlinaEJVan TyneCJ (2008)
Correlation of yield strength and tensile strength with hardness for steels. Journal of Materials Engineering and Performance17(6): 888–893.
29.
RancelLGómezMMedinaSF, et al. (2011)
Measurement of bainite packet size and its influence on cleavage fracture in a medium carbon bainitic steel. Materials Science and Engineering: A530: 21–27.
30.
RichmanRHLandgrafRW (1975)
Some effects of retained austenife on the fatigue resistance of carburized steel. Metallurgical Transactions A6(4): 955–964.
31.
RolandTRetraintDLuK, et al. (2006)
Fatigue life improvement through surface nanostructuring of stainless steel by means of surface mechanical attrition treatment. Scripta Materialia54(11): 1949–1954.
32.
ShamsaeiNFatemiA (2009)
Effect of hardness on multiaxial fatigue behaviour and some simple approximations for steels. Fatigue & Fracture of Engineering Materials & Structures32(8): 631–646.
33.
ShimizuSTsuchiyaKToshaK (2009)
Probabilistic stress-life (P-S-N) study on bearing steel using alternating torsion life test. Tribology Transactions52(6): 807–816.
34.
SinesG (1959)
Behavior of metals under complex static and alternating stresses. Metal Fatigue1: 145–169.
35.
SlackTSadeghiF (2010)
Explicit finite element modeling of subsurface initiated spalling in rolling contacts. Tribology International43(9): 1693–1702.
36.
TaoNRWangZBTongWP, et al. (2002)
An investigation of surface nanocrystallization mechanism in Fe induced by surface mechanical attrition treatment. Acta Materialia50(18): 4603–4616.
37.
VaculkaMNohálLVosynekP (2018)
Case study of multiaxial criteria for rolling contact fatigue of bearing steels. MATEC Web of Conferences165: 22017.
38.
VoskampAP (1985)
Material response to rolling contact loading. Journal of Tribology107(3): 359–364.
39.
VoskampAPÖsterlundRBeckerPC, et al. (2013)
Gradual changes in residual stress and microstructure during contact fatigue in ball bearings. Metals Technology7(1): 14–21.
40.
WalvekarAASadeghiF (2017)
Rolling contact fatigue of case carburized steels. International Journal of Fatigue95: 264–281.
41.
WangYSunG-QLiuJ, et al. (2022)
Multiaxial high-cycle fatigue failure and life prediction based on critical plane method. International Journal of Damage Mechanics31(8): 1165–1186.
42.
WeibullW (1939) A statistical theory of the strength of materials. Ing Vet Ak Handl Ingeniors Vetenskaps Akademien Handlingar., Stockholm
43.
WeinzapfelNSadeghiF (2013)
Numerical modeling of Sub-surface initiated spalling in rolling contacts. Tribology International59: 210–221.
44.
XieLPalmerDOttoF, et al. (2014)
Effect of surface hardening technique and case depth on rolling contact fatigue behavior of alloy steels. Tribology Transactions58(2): 215–224.
45.
XieLCZhouQHWenY, et al. (2016)
Microstructure variation and local plastic response of chrome molybdenum alloy steel after quasi rolling contact fatigue testing. Materials Science and Engineering: A659: 37–46.
46.
ZaretskyEVPoplawskiJVPetersSM (1996)
Comparison of life theories for rolling-element bearings. Tribology Transactions39(2): 237–248.
47.
ZaretskyEV (1987)
Fatigue criterion to system design, life, and reliability. Journal of Propulsion and Power3(1): 76–83.
