State of Art of Gear Contact Fatigue Theories

doi:10.3901/JME.2022.03.095

Abstract

Abstract: The continuing improvement on the power density, loading capacity and fatigue life of gear transmissions used in industrial machineries such as in the aerospace, wind turbine and heavy-duty vehicle fields, inevitably places greater demands on the gear contact fatigue failure issues, which exist with various modes including micropitting, pitting and tooth flank fracture and become an important bottleneck limiting their performance. The state of the art of gear contact fatigue studies are reviewed, the fundamental gear contact fatigue modes and the existing fatigue theories including life prediction approaches are summarized. The roles of the continuous damage theory and the micro-structure mechanics on the gear contact fatigue study are introduced. Some improving treatments including superfinishing, coatings and shot peening are investigated. This review provides essential guidance for the further understanding of gear contact fatigue and the realization of gear anti-fatigue design and manufacturing.

Key words: gear contact fatigue, surface integrity, gear mesh interface, damage evolution, residual stress

CLC Number:

TH132

LIU Huaiju, ZHANG Boyu, ZHU Caichao, WEI Peitang. State of Art of Gear Contact Fatigue Theories[J]. Journal of Mechanical Engineering, 2022, 58(3): 95-120.

References

[1] LINK H,LACAVA W,VAN DAM J,et al. Gearbox reliability collaborative project report:Findings from phase 1 and phase 2 testing[R]. Golden:National Renewable Energy Lab,2011.
[2] NYGAARD J,RAWSON M,DANSON P,et al. Bearing steel microstructures after aircraft gas turbine engine service[J]. Materials Science and Technology,2014,30(15):1911-1918.
[3] KRANTZ T,ANDERSON C,SHAREEF I,et al. Testing aerospace gears for bending fatigue,pitting,and scuffing[C]//Proceedings of the ASME 2017 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference,Cleveland,USA:ASME,2017:1-2.
[4] KANG J-H,HOSSEINKHANI B,RIVERA-D AZ-DEL-CASTILLO P E. Rolling contact fatigue in bearings:Multiscale overview[J]. Materials Science and Technology,2012,28(1):44-49.
[5] 何春双,罗志强,郭军,等. Cr4Mo4V高温轴承钢滚动接触表面特征与疲劳损伤机制[J]. 金属热处理,2018,43(2):1-7. HE Chunshuang,LUO Zhiqiang,GUO Jun,et al. Characteristics of rolling contact surface and fatigue damage mechanism of Cr4Mo4V high temperature bearing steel[J]. Heat Treatment of Metals,2018,43(2):1-7.
[6] KHAN M A,COOPER D,STARR A. BS-ISO helical gear fatigue life estimation and wear quantitative feature analysis[J]. Strain,2009,45(4):358-363.
[7] ZHAO L,FRAZER R C,SHAW B. Comparative study of stress analysis of gears with different helix angle using the ISO 6336 standard and tooth contact analysis methods[J]. Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2016,230(7-8):1350-1358.
[8] KARPUSCHEWSKI B,BLEICHER O,BEUTNER M. Surface integrity inspection on gears using Barkhausen noise analysis[J]. Procedia Engineering,2011,19:162-171.
[9] JOUINI N,REVEL P,MAZERAN P-E,et al. The ability of precision hard turning to increase rolling contact fatigue life[J]. Tribology International,2013,59:141-146.
[10] RECH J,MOISAN A. Surface integrity in finish hard turning of case-hardened steels[J]. International Journal of Machine Tools and Manufacture,2003,43(5):543-550.
[11] ASLANTAS K,TASGETIREN S. A study of spur gear pitting formation and life prediction[J]. Wear,2004,257(11):1167-1175.
[12] GLODEŽ S,ABERŠEK B,FLAŠKER J,et al. Evaluation of the service life of gears in regard to surface pitting[J]. Engineering fracture mechanics,2004,71(4-6):429-438.
[13] PEDRERO J I,PLEGUEZUELOS M,MU OZ M. Critical stress and load conditions for pitting calculations of involute spur and helical gear teeth[J]. Mechanism and Machine Theory,2011,46(4):425-437.
[14] SEABRA J,HÖHN B R,MICHAELIS K,et al. Pitting load carrying capacity under increased thermal conditions[J]. Industrial lubrication and tribology,2011, 16(1):11-16..
[15] UZUN M,MÜNIS M M,DÜZCÜKOĞLU H. Pitting formation in concave-convex gears manufactured from AISI 8620 steel[J]. Journal of Testing and Evaluation,2017,46(4):1708-1714.
[16] WEBER C,TOBIE T,STAHL K. Investigation on the flank surface durability of gears with increased pressure angle[J]. Forschung im Ingenieurwesen,2017,81(2-3):207-213.
[17] WINTER H,WEISS T. Some factors influencing the pitting,micro-pitting (frosted areas) and slow speed wear of surface hardened gears[J]. Journal of Mechanical Design,1981,103(2):499-505.
[18] HÖHN B R,OSTER P,EMMERT S. Micropitting in case-carburized gears-FZG micro-pitting test[J]. VDI Berichte,1996,1230:331-344.
[19] 王晓鹏,刘世军. 微点蚀齿轮法向接触刚度分形预估模型[J]. 机械工程学报,2021,57(1):68-76. WANG Xiaopeng,LIU Shijun. Fractal prediction model of normal contact stiffness of micro-pitting gear[J]. Journal of Mechanical Engineering,2021,57(1):68-76.
[20] TANAKA S,EZOE S,IDE K. Appreciable improvements in oil film formation and surface durability of gears with tooth profile modification[J]. JSME International Journal Ser 3,Vibration,Control Engineering,Engineering for Industry,1988,31(2):431-435.
[21] NAKANISHI T,ARIURA Y,UENO T. Load-carrying capacity of surface-hardened gears:Influence of surface roughness on surface durability:Vibration,Control Engineering,Engineering for Industry[J]. JSME International Journal,1987,30(259):161-167.
[22] FERNANDES P,MCDULING C. Surface contact fatigue failures in gears[J]. Engineering Failure Analysis,1997,4(2):99-107.
[23] LITTMANN W,KELLEY B,ANDERSON W,et al. Chemical effects of lubrication in contact fatigue-Part III:Load-life exponent,life scatter,and overall analysis[J]. Journal of Lubrication Technology,1976,98(2):308-315.
[24] MOORTHY V,SHAW B. An observation on the initiation of micro-pitting damage in as-ground and coated gears during contact fatigue[J]. Wear,2013,297(1-2):878-884.
[25] AL-MAYALI M,HUTT S,SHARIF K,et al. Experimental and numerical study of micropitting initiation in real rough surfaces in a micro-elastohydrodynamic lubrication regime[J]. Tribology Letters,2018,66(4):1-14.
[26] ERRICHELLO R. Critique of the ISO 15144-1 method to predict the risk of micropitting[J]. Gear Technology,2016,2:10-16.
[27] BOIADJIEV I,WITZIG J,TOBIE T,et al. Tooth flank fracture-basic principles and calculation model for a sub-surface-initiated fatigue failure mode of case-hardened gears[C]//International Gear Conference,Lyon,France:Chandos Publishing,2014:26-28.
[28] AL B,LANGLOIS P. Analysis of tooth interior fatigue fracture using boundary conditions form an efficient and accurate loaded tooth contact analysis[C]//British Gears Association Gears 2015 Technical Awareness Seminar,Newcastle,England:British Gear Association 2015:1-12.
[29] BEERMANN S,KISSLING U. Tooth flank fracture-A critical failure mode influence of macro and mciro geometry[C]//KISSsoft User Conference,Pune,India:KISSsoft,2015:1-14.
[30] 肖伟中. 齿轮硬化层疲劳剥落强度研究与应用[D]. 北京:机械科学研究总院,2016. XIAO Weizhong. Study and application of fatigue peeling strength of gear hardened layer[D]. Beijing:General Research Institute of Mechanical Science,2016
[31] 刘怀举,刘鹤立,朱才朝,等. 轮齿齿面断裂失效研究综述[J]. 北京工业大学学报,2018,44(7):961-968. LIU Huaiju,LIU heli,ZHU Caichao,et al. Review of gear tooth surface fracture failure research[J]. Journal of Beijing University of Technology,2018,44(7):961-968.
[32] LIU H,LIU H,ZHU C,et al. A review on micropitting studies of steel gears[J]. Coatings,2019,9(1):42.
[33] ZHANG B,LIU H,ZHU C,et al. Simulation of the fatigue-wear coupling mechanism of an aviation gear[J]. Friction,2020,1:s40544-020-0447-3.
[34] SHEN F,HU W,MENG Q. A damage mechanics approach to fretting fatigue life prediction with consideration of elastic-plastic damage model and wear[J]. Tribology International,2015,82:176-190.
[35] MORALES-ESPEJEL G E,GABELLI A. Rolling bearing seizure and sliding effects on fatigue life[J]. Proceedings of the Institution of Mechanical Engineers,Part J:Journal of Engineering Tribology,2019,233(2):339-354.
[36] ZIMMER M,BARTEL D. Efficient running-in of gears and improved prediction of the tooth flank load carrying capacity[J]. Industrial Lubrication and Tribology,2019,71(3):366-373.
[37] SADEGHI F,JALALAHMADI B,SLACK T S,et al. A review of rolling contact fatigue[J]. Journal of Tribology,2009,131(4):041403.
[38] NI G,ZHU C,SONG C,et al. Tooth contact analysis of crossed beveloid gear transmission with parabolic modification[J]. Mechanism and Machine Theory,2017,113:40-52.
[39] LIANG C,SONG C,ZHU C,et al. Investigation of the effects with linear,circular and polynomial blades on contact characteristics for face-hobbed hypoid gears[J]. Mechanism and Machine Theory,2020,146:103739.
[40] LI S,ANISETTI A. A tribo-dynamic contact fatigue model for spur gear pairs[J]. International Journal of Fatigue,2017,98:81-91.
[41] ZHU C,CHEN S,LIU H,et al. Dynamic analysis of the drive train of a wind turbine based upon the measured load spectrum[J]. Journal of Mechanical Science and Technology,2014,28(6):2033-2040.
[42] LIU G,LIU H,ZHU C,et al. Design optimization of a wind turbine gear transmission based on fatigue reliability sensitivity[J]. Frontiers of Mechanical Engineering,2021,16(1):61-79.
[43] ZHOU Y,ZHU C,LIU H,et al. A numerical study on the contact fatigue life of a coated gear pair under EHL[J]. Industrial Lubrication and Tribology,2018,70(1):23-32.
[44] HE H,LIU H,ZHU C,et al. Study on the gear fatigue behavior considering the effect of residual stress based on the continuum damage approach[J]. Engineering Failure Analysis,2019,104:531-544.
[45] WARHADPANDE A,SADEGHI F,KOTZALAS M N,et al. Effects of plasticity on subsurface initiated spalling in rolling contact fatigue[J]. International Journal of Fatigue,2012,36(1):80-95.
[46] NEJAD R M,SHARIATI M,FARHANGDOOST K. Effect of wear on rolling contact fatigue crack growth in rails[J]. Tribology International,2016,94:118-125.
[47] WANG W,LIU H,ZHU C,et al. Effects of microstructure on rolling contact fatigue of a wind turbine gear based on crystal plasticity modeling[J]. International Journal of Fatigue,2019,120:73-86.
[48] WANG W,LIU H,ZHU C,et al. Micromechanical analysis of gear fatigue-ratcheting damage considering the phase state and inclusion[J]. Tribology International,2019,136:182-195.
[49] PLETZ M,DAVES W,YAO W,et al. Multi-scale finite element modeling to describe rolling contact fatigue in a wheel-rail test rig[J]. Tribology International,2014,80:147-155.
[50] DING J,LEEN S,WILLIAMS E,et al. A multi-scale model for fretting wear with oxidation-debris effects[J]. Proceedings of the Institution of Mechanical Engineers,Part J:Journal of Engineering Tribology,2009,223(7):1019-1031.
[51] LIU H. Lubricated contact analysis of a spur gear pair with dynamic loads[D]. Warwick:University of Warwick,2013.
[52] LUNDBERG G,PALMGREN A. Dynamic capacity of roller bearings[J]. Acta Polytech Mechanical Engineering Series,1952,2(4):96-127.
[53] IOANNIDES E,HARRIS T A. A new fatigue life model for rolling bearings[J]. Journal of Tribology,1985,107:367-377.
[54] HARRIS T,BARNSBY R. Life ratings for ball and roller bearings[J]. Proceedings of the Institution of Mechanical Engineers,Part J:Journal of Engineering Tribology,2001,215(6):577-595.
[55] STANDARDIZATION I O f. ISO 281-2007 Rolling bearings-dynamic load ratings and rating life[S]. Switzerland:International Organization for Standardization,2007.
[56] TALLIAN T. A data-fitted rolling bearing life prediction model-Part I:Mathematical model[J]. Tribology Transactions,1996,39(2):249-258.
[57] ZARETSKY E V. Fatigue criterion to system design,life,and reliability[J]. Journal of Propulsion and Power,1987,3(1):76-83.
[58] EPSTEIN D,YU T,WANG Q,et al. An efficient method of analyzing the effect of roughness on fatigue life in mixed-EHL contact[J]. Tribology Transactions,2003,46(2):273-281.
[59] KUDISH I I. A new statistical model of contact fatigue[J]. Tribology transactions,2000,43(4):711-721.
[60] ZARETSKY E V. Design of oil-lubricated machine components for life and reliability[C]//Seventh International Symposia on Tribology,Cracow:NASA Technical Memorandum,2007,214362.
[61] COY J J,TOWNSEND D P,ZARETSKY E V. Dynamic capacity and surface fatigue life for spur and helical gears[J]. Journal of Lubrication Technology,1976,98:267-276.
[62] COY J J,TOWNSEND D P,ZARETSKY E V. An update on the life analysis of spur gears[J]. Advanced Power Transmission Technology,1983:421-434.
[63] ZARETSKY E,PARKER R,ANDERSON W. A study of residual stress induced during rolling[J]. Journal of Lubrication Technology,1969,91:314-319.
[64] ZHOU R S. Surface topography and fatigue life of rolling contact bearing[J]. Tribology Transactions,1993,36(3):329-340.
[65] YOU B R,LEE S B. A critical review on multiaxial fatigue assessments of metals[J]. International Journal of Fatigue,1996,18(4):235-244.
[66] WANG Y,YAO W. Evaluation and comparison of several multiaxial fatigue criteria[J]. International Journal of Fatigue,2004,26(1):17-25.
[67] CONRADO E,GORLA C. Contact fatigue limits of gears,railway wheels and rails determined by means of multiaxial fatigue criteria[J]. Procedia Engineering,2011,10(0):965-970.
[68] BERETTA S,FOLETTI S. Propagation of small cracks under RCF:A challenge to Multiaxial Fatigue Criteria[C]//Proceedings of the 4th International Conference on Crack Paths,Gruppo Italiano Frattura,2012:15-28.
[69] REIS T,DE ABREU LIMA E,BERTELLI F,et al. Progression of plastic strain on heavy-haul railway rail under random pure rolling and its influence on crack initiation[J]. Advances in Engineering Software,2018,124:10-21.
[70] BROWN M W,MILLER K J. A theory for fatigue failure under multiaxial ctress-ctrain conditions[J]. Proceedings of the Institution of Mechanical Engineers,1972,187:745-755.
[71] MORROW J D. Cyclic plastic strain energy and fatigue of metals[J]. Internal Friction,Damping,and Cyclic Plasticity,1965:45-87.
[72] ZHENG Z,SUN T,XU X,et al. Numerical simulation of steel wheel dynamic cornering fatigue test[J]. Engineering Failure Analysis,2014,39:124-134.
[73] TOMAZINCIC D,NECEMER B,VESENJAK M,et al. Low-cycle fatigue life of thin-plate auxetic cellular structures made from aluminium alloy 7075-T651[J]. Fatigue & Fracture of Engineering Materials & Structures,2019,42(5):1022-1036.
[74] ZHANG B,LIU H,ZHU C,et al. Numerical simulation of competing mechanism between pitting and micro-pitting of a wind turbine gear considering surface roughness[J]. Engineering Failure Analysis,2019,104:1-12.
[75] 宋恩鹏,陆华,何刚,等. 多轴疲劳寿命分析方法在飞机结构上的应用[J]. 北京航空航天大学学报,2016,42(5):906-911. SONG Enpeng,LU Hua,HE Gang,et al. Application of multiaxial fatigue life analysis method to aircraft structures[J]. Journal of Beijing University of Aeronautics and Astronautics,2016,42(5):906-911.
[76] FATEMI A,SOCIE D F. A critical plane approach to multiaxial fatigue damage including out-of-phase loading[J]. Fatigue & Fracture of Engineering Materials & Structures,1988,11(3):149-165.
[77] SAUVAGE P,JACOBS G,SOUS C,et al. On an extension of the Fatemi and Socie equation for rolling contact in rolling bearings[C]//Proceedings of the 7th International Conference on Fracture Fatigue and Wear,Singapore,2018:438-457.
[78] KIANI M,FRY G. Fatigue analysis of railway wheel using a multiaxial strain-based critical-plane index[J]. Fatigue & Fracture of Engineering Materials & Structures,2018,41(2):412-424.
[79] BASAN R,MAROHNIĆ T. Multiaxial fatigue life calculation model for components in rolling-sliding line contact with application to gears[J]. Fatigue & Fracture of Engineering Materials & Structures,2019,42(7):1478-1493.
[80] LIU H,WANG W,ZHU C,et al. A microstructure sensitive contact fatigue model of a carburized gear[J]. Wear,2019,436-437:203035.
[81] VIJAY A,SADEGHI F. A continuum damage mechanics framework for modeling the effect of crystalline anisotropy on rolling contact fatigue[J]. Tribology International,2019,140:105845.
[82] ALLEY E S,NEU R W. Microstructure-sensitive modeling of rolling contact fatigue[J]. International Journal of Fatigue,2010,32(5):841-850.
[83] JIANG Y,SEHITOGLU H. Modeling of cyclic ratchetting plasticity,part I:Development of constitutive relations[J]. Journal of Applied Mechanics,1996,63(3):720-725.
[84] JIANG Y,SEHITOGLU H. A model for rolling contact failure[J]. Wear,1999,224(1):38-49.
[85] RINGSBERG J W. Life prediction of rolling contact fatigue crack initiation[J]. International Journal of Fatigue,2001,23(7):575-586.
[86] ZHANG B,LIU H,BAI H,et al. Ratchetting-multiaxial fatigue damage analysis in gear rolling contact considering tooth surface roughness[J]. Wear,2019,428:137-146.
[87] BOWER A,JOHNSON K. The influence of strain hardening on cumulative plastic deformation in rolling and sliding line contact[J]. Journal of the Mechanics and Physics of Solids,1989,37(4):471-493.
[88] 梁喜仁,陶功权,陆文教,等. 地铁钢轨滚动接触疲劳损伤研究[J]. 机械工程学报,2019,55(2):147-155. LIANG Xiren,TAO Gongquan,LU Wenjiao,et al. Study on the rail rolling contact fatigue of subway[J]. Journal of Mechanical Engineering,2019,55(2):147-155.
[89] MINER M A. Cumulative damage in fatigue[J]. Journal of Applied Mechanics,1945,12(3):A159-A164.
[90] KRAJCINOVIC D. Continuum damage mechanics[J]. Applied Mechanics Reviews,1984,37(1):1-6.
[91] HE H,LIU H,ZHU C,et al. Study of rolling contact fatigue behavior of a wind turbine gear based on damage-coupled elastic-plastic model[J]. International Journal of Mechanical Sciences,2018,141:512-519.
[92] RAJE N,SADEGHI F,RATEICK R G. A statistical damage mechanics model for subsurface initiated spalling in rolling contacts[J]. Journal of Tribology,2008,130(4):042201.
[93] JALALAHMADI B,SADEGHI F. A voronoi FE fatigue damage model for life scatter in rolling contacts[J]. Journal of Tribology,2010,132(2):021404.
[94] MOGHADDAM S M,SADEGHI F,WEINZAPFEL N,et al. A damage mechanics approach to simulate butterfly wing formation around nonmetallic inclusions[J]. Journal of Tribology-Transactions of the ASME,2015,137(1):011400.
[95] SHEN Y,MOGHADAM S M,SADEGHI F,et al. Effect of retained austenite-Compressive residual stresses on rolling contact fatigue life of carburized AISI 8620 steel[J]. International Journal of Fatigue,2015,75:135-144.
[96] WALVEKAR A A,SADEGHI F. Rolling contact fatigue of case carburized steels[J]. International Journal of Fatigue,2017,95:264-281.
[97] MORRIS D,SADEGHI F,CHEN Y-C,et al. Predicting material performance in rolling contact fatigue via torsional fatigue[J]. Tribology Transactions,2019,62(4):614-625.
[98] GOLMOHAMMADI Z,SADEGHI F. A 3D finite element model for investigating effects of refurbishing on rolling contact fatigue[J]. Tribology Transactions,2020,63(2):1-14.
[99] HE H,LIU H,ZHU C,et al. Analysis of the fatigue crack initiation of a wind turbine gear considering load sequence effect[J]. International Journal of Damage Mechanics,2020,29(2):207-225.
[100] LE M,VILLE F,KLEBER X,et al. Rolling contact fatigue crack propagation in nitrided alloyed steels[J]. Proceedings of the Institution of Mechanical Engineers,Part J:Journal of Engineering Tribology,2017,231(9):1192-1208.
[101] RYCERZ P,OLVER A,KADIRIC A. Propagation of surface initiated rolling contact fatigue cracks in bearing steel[J]. International Journal of Fatigue,2017,97:29-38.
[102] MATSUNAGA H,SHOMURA N,MURAMOTO S,et al. Shear mode threshold for a small fatigue crack in a bearing steel[J]. Fatigue & Fracture of Engineering Materials & Structures,2011,34(1):72-82.
[103] ANCELLOTTI S,FONTANARI V,DALLAGO M,et al. A novel experimental procedure to reproduce the load history at the crack tip produced by lubricated rolling sliding contact fatigue[J]. Engineering fracture mechanics,2018,192:129-147.
[104] 周宇,邝迪峰,郑晓峰,等. 基于三维重构的钢轨滚动接触疲劳裂纹扩展预测[J]. 机械工程学报,2018,54(4):158-166. ZHOU Yu,KUANG Difeng,ZHENG Xiaofeng,et al. Prediction of the rail head checks propagation based on three dimensional reconstruction[J]. Journal of Mechanical Engineering,2018,54(4):158-166.
[105] PARIS P,ERDOGAN F. A critical analysis of crack propagation laws[J]. Journal of Basic Engineering,1963,85(4):528-533.
[106] KEER L M,BRYANT M D. A pitting model for rolling contact fatigue[J]. Journal of Lubrication Technology,1983,105:198-205.
[107] BLAKE J,CHENG H. A surface pitting life model for spur gears:Part I-Life prediction[J]. Journal of Tribology,1991,113:712-718.
[108] GHAFFARI M A,PAHL E,XIAO S. Three dimensional fatigue crack initiation and propagation analysis of a gear tooth under various load conditions and fatigue life extension with boron/epoxy patches[J]. Engineering Fracture Mechanics,2015,135:126-146.
[109] FAJDIGA G,SRAML M. Fatigue crack initiation and propagation under cyclic contact loading[J]. Engineering fracture mechanics,2009,76(9):1320-1335.
[110] GUAN J,WANG L,ZHANG C,et al. Effects of non-metallic inclusions on the crack propagation in bearing steel[J]. Tribology International,2017,106:123-131.
[111] HE H,LIU H,ZHU C. Andrea Mura Numerical study on the fatigue crack propagation behaviors in lubricated rolling contact[J]. Chinese Journal of Aeronautics,2020. https://doi.org/10.1016/j.cja.2021.03.012.
[112] GHOSH S,MOORTHY S. Three dimensional Voronoi cell finite element model for microstructures with ellipsoidal heterogeneties[J]. Computational Mechanics,2004,34(6):510-531.
[113] LEWIS A,JORDAN K,GELTMACHER A. Determination of critical microstructural features in an austenitic stainless steel using image-based finite element modeling[J]. Metallurgical and Materials Transactions A,2008,39(5):1109-1117.
[114] VAJRAGUPTA N,WECHSUWANMANEE P,LIAN J,et al. The modeling scheme to evaluate the influence of microstructure features on microcrack formation of DP-steel:The artificial microstructure model and its application to predict the strain hardening behavior[J]. Computational Materials Science,2014,94:198-213.
[115] TAYLOR G I,ELAM C F. The distortion of an aluminium crystal during a tensile test[J]. Proceedings of the Royal Society of London A,1923,102(719):643-667.
[116] CHAI G C. Micro mechanical behaviors and damage in nickel base alloy and steels during very high cycle fatigue[J]. Solid State Phenomena,2017,258:506-513.
[117] CASTELLUCCIO G M,MUSINSKI W D,MCDOWELL D L. Computational micromechanics of fatigue of microstructures in the HCF-VHCF regimes[J]. International Journal of Fatigue,2016,93:387-396.
[118] JALALAHMADI B,SADEGHI F. A Voronoi FE fatigue damage model for life scatter in rolling contacts[J]. Journal of Tribology,2010,132(2):021404.
[119] BOMIDI J A,WEINZAPFEL N,SADEGHI F,et al. An improved approach for 3D rolling contact fatigue simulations with microstructure topology[J]. Tribology Transactions,2013,56(3):385-399.
[120] WARHADPANDE A,SADEGHI F,EVANS R D. Microstructural alterations in bearing steels under rolling contact fatigue:Part 2-Diffusion-based modeling approach[J]. Tribology Transactions,2014,57(1):66-76.
[121] MORRIS D,SADEGHI F,CHEN Y C,et al. A novel approach for modeling retained austenite transformations during rolling contact fatigue[J]. Fatigue & Fracture of Engineering Materials & Structures,2018,41(4):831-843.
[122] MORRIS D,SADEGHI F,CHEN Y-C,et al. Effect of residual stresses on microstructural evolution due to rolling contact fatigue[J]. Journal of Tribology,2018,140(6):061402.
[123] WEI P,ZHOU H,LIU H,et al. Modeling of contact fatigue damage behavior of a wind turbine carburized gear considering its mechanical properties and microstructure gradients[J]. International Journal of Mechanical Sciences,2019,156:283-296.
[124] ZHOU H,WEI P,LIU H,et al. Roles of microstructure,inclusion,and surface roughness on rolling contact fatigue of a wind turbine gear[J]. Fatigue & Fracture of Engineering Materials & Structures,2020,43(7):1368-1383.