高速列车车轴旋转弯曲作用下微动疲劳损伤研究
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摘要
轨道车辆车轴轮座部位是微动疲劳损伤的典型实例,也是影响铁路运输安全的关键问题之一。本文以高速列车轮轴过盈配合部位的微动损伤为研究对象,采用小试样模拟微动疲劳试验与有限元仿真计算相结合的方法,研究旋转弯曲载荷导致轮轴过盈配合产生微动疲劳损伤的机理。主要内容如下：
(1)根据车辆轮座部的微动疲劳损伤特点,从高速列车车轴上切取试样,加工成模拟微动疲劳损伤的试样和标准光滑圆柱形试样,在四点旋转弯曲疲劳试验机上进行加载试验；通过单点疲劳试验和疲劳中断试验,研究旋转弯曲载荷下过盈配合的微动疲劳损伤规律。
(2)通过改变试样套管的几何尺寸实现轴套配合参数的变化,试验研究了过盈量、套管直径和套管长度对微动疲劳寿命的影响；在ABAQUS有限元软件中,建立套管试样的有限元模型,分析配合参数对微动疲劳寿命影响规律。
(3)在试样轴表面的不同位置制作同样的缺口,测试缺口试样的微动疲劳寿命；同时在ABAQUS有限元软件中建立含不同位置及深度裂纹的模型,利用能量法间接求解各裂纹前沿的应力强度因子,进而拟合出裂纹前沿应力强度因子与裂纹深度的关系式,通过Paris裂纹扩展模型计算裂纹扩展寿命。
(4)采用裂纹模拟技术、里兹(Ruiz)准则和Findley多轴疲劳准则三种方法,计算预测了轴套试样的微动疲劳强度,分析了它们对研究旋转弯曲载荷下过盈配合微动疲劳的适用性。
(5)依据欧洲高速列车标准EN13103,以非动力轴为对象,采用ABAQUS有限元软件,计算研究了过盈量、过渡圆弧半径、轮毂悬伸量、轮座和轴身直径比、空心度以及温度对空心车轴微动疲劳的影响规律,并采用Findley多轴疲劳准则评价了车轴轮座及邻近区域的微动疲劳强度。
In the railway transportation, the interference fit between wheel and axle is a typical example of fretting damage, and the wheel seat of axle is the weak zone for fatigue with the impact of fretting. In this paper, aimed at fretting damage of interference fit parts between wheel and axle used in high-speed train, the fretting damage of interference fit connection under rotating bending load is investigated, through the method of small specimen test simulating fretting fatigue and finite element simulation. The main work involves:
(1) According to the fretting form of railway hub and axle, rough part are cut from specific part of high-speed train axle, and machined in specimen that simulates fretting damage between wheel and axle and standard smooth cylindrical specimen. Then four points rotating bending fatigue machine is used, and the law of fretting fatigue damage of interference fit connection under rotating bending load is studied, through single point fatigue test method and fatigue interrupted test.
(2) By changing the geometry of casing, so the parameters of interference fit between axle and casing is changed. Base on this, the influence of interference value, casing diameter and casing length on fretting fatigue life was investigated. In the finite element code ABAQUS, the model of different specimens was established, and the variations of parameters that effect fretting fatigue were understood, according to the test condition.
(3) Notch is produced on different positions of surface of the specimens, and then four points rotating bending fatigue test was employed to test the fretting fatigue life of notch specimens. In the same time, the finite element model containing cracks with different position and depth were building, and energy method was applied to indirectly calculate the stress intensity factor of crack front. Furthermore, the relation between the stress intensity factor of the deepest point and the depth of crack was fitted, so the crack propagation life could be calculated with the help of Paris formulation.
(4) The Crack Analogy Method, Ruiz criterion and Findley multi-axial fatigue criterion were analyzed to predict the fretting fatigue life in detail, and the applicability of those methods to study fretting fatigue of interference fit connection under rotating bending load was researched. (5) According the European Standard EN 13103, and aimed at non-powered axle, the ABAQUS code was used to study the influence of interference value, axle fillet radius, hub extension, diameter ratio, hollowness and temperature on contact pressure and fretting fatigue of hollow axle in detail. Findley multi-axial criterion was employed to evaluate the fretting fatigue of wheel seat and its neighboring region.
(1)根据车辆轮座部的微动疲劳损伤特点,从高速列车车轴上切取试样,加工成模拟微动疲劳损伤的试样和标准光滑圆柱形试样,在四点旋转弯曲疲劳试验机上进行加载试验；通过单点疲劳试验和疲劳中断试验,研究旋转弯曲载荷下过盈配合的微动疲劳损伤规律。
(2)通过改变试样套管的几何尺寸实现轴套配合参数的变化,试验研究了过盈量、套管直径和套管长度对微动疲劳寿命的影响；在ABAQUS有限元软件中,建立套管试样的有限元模型,分析配合参数对微动疲劳寿命影响规律。
(3)在试样轴表面的不同位置制作同样的缺口,测试缺口试样的微动疲劳寿命；同时在ABAQUS有限元软件中建立含不同位置及深度裂纹的模型,利用能量法间接求解各裂纹前沿的应力强度因子,进而拟合出裂纹前沿应力强度因子与裂纹深度的关系式,通过Paris裂纹扩展模型计算裂纹扩展寿命。
(4)采用裂纹模拟技术、里兹(Ruiz)准则和Findley多轴疲劳准则三种方法,计算预测了轴套试样的微动疲劳强度,分析了它们对研究旋转弯曲载荷下过盈配合微动疲劳的适用性。
(5)依据欧洲高速列车标准EN13103,以非动力轴为对象,采用ABAQUS有限元软件,计算研究了过盈量、过渡圆弧半径、轮毂悬伸量、轮座和轴身直径比、空心度以及温度对空心车轴微动疲劳的影响规律,并采用Findley多轴疲劳准则评价了车轴轮座及邻近区域的微动疲劳强度。
In the railway transportation, the interference fit between wheel and axle is a typical example of fretting damage, and the wheel seat of axle is the weak zone for fatigue with the impact of fretting. In this paper, aimed at fretting damage of interference fit parts between wheel and axle used in high-speed train, the fretting damage of interference fit connection under rotating bending load is investigated, through the method of small specimen test simulating fretting fatigue and finite element simulation. The main work involves:
(1) According to the fretting form of railway hub and axle, rough part are cut from specific part of high-speed train axle, and machined in specimen that simulates fretting damage between wheel and axle and standard smooth cylindrical specimen. Then four points rotating bending fatigue machine is used, and the law of fretting fatigue damage of interference fit connection under rotating bending load is studied, through single point fatigue test method and fatigue interrupted test.
(2) By changing the geometry of casing, so the parameters of interference fit between axle and casing is changed. Base on this, the influence of interference value, casing diameter and casing length on fretting fatigue life was investigated. In the finite element code ABAQUS, the model of different specimens was established, and the variations of parameters that effect fretting fatigue were understood, according to the test condition.
(3) Notch is produced on different positions of surface of the specimens, and then four points rotating bending fatigue test was employed to test the fretting fatigue life of notch specimens. In the same time, the finite element model containing cracks with different position and depth were building, and energy method was applied to indirectly calculate the stress intensity factor of crack front. Furthermore, the relation between the stress intensity factor of the deepest point and the depth of crack was fitted, so the crack propagation life could be calculated with the help of Paris formulation.
(4) The Crack Analogy Method, Ruiz criterion and Findley multi-axial fatigue criterion were analyzed to predict the fretting fatigue life in detail, and the applicability of those methods to study fretting fatigue of interference fit connection under rotating bending load was researched. (5) According the European Standard EN 13103, and aimed at non-powered axle, the ABAQUS code was used to study the influence of interference value, axle fillet radius, hub extension, diameter ratio, hollowness and temperature on contact pressure and fretting fatigue of hollow axle in detail. Findley multi-axial criterion was employed to evaluate the fretting fatigue of wheel seat and its neighboring region.
引文
[1]张曙光.铁路高速列车应用基础理论与工程技术[M].北京,科学出版社,2007.
[2]Smith R A, Hillmansen S. A brief historical overview of the fatigue of railway axles[J].
Proceedings of the Institution of Mechanical Engineers, Part F:Journal of Rail and Rapid Transit,2004,218:267-277.
[3]侯卫星.车轴疲劳可靠性研究初探[J].铁道车辆,1989,1：7-11.
[4]石塚弘道.车轴轻量化途径[J].国外铁道车辆,1992,1：35-39.
[5]孙蕾,陈雷.铁路货车RD2型车轴轴颈卸荷槽质量问题研究与对策[J].铁道车辆,2006,44：11-17.
[6]何庆复.列车车轴抗微动损伤热喷涂层组织结构研究[J].铁道学报,2001,23：102-104.
[7]石塚弘道.车轴微振磨损的对策[J].国外内燃机车,1993,12：48-52.
[8]杨广雪,谢基龙.车轴设计参数对轴毂配合接触压力影响的研究[J].铁道学报,2009,31：31-35.
[9]张永生.东风4、7型机车车轴使用寿命的探讨[J].内燃机车,2002,12：24-26.
[10]郭志仁.车轴寿命谈[J].机车车辆工艺,1992,6：1-9.
[11]王树青.车轴感应淬火技术研究[J].金属热处理,2001,26：31-34.
[12]平川贤尔.高速动车用车轴的疲劳设计[J].国外内燃机车,1997,5：31-33.
[131 Hiromichi I改善新干线车辆车轴常规检测[J].国外铁道车辆,2001,38：42-45.
[14]李述松,唐东平,徐建生,宋春如.对DF4、8型机车车轴不良状态的研究[J].内燃机车,2003,8：32-34.
[15]李炳华,杜欣.高速机车车辆车轴的疲劳设计[J].内燃机车,2000,1：14-20.
[16]本松启美.日本新干线电动车用车轴的疲劳试验结果[J].国外铁道车辆,1992,6：31-39.
[17]刘伟,何庆复,张云.微动损伤对车轴疲劳寿命的影响[J].铁道学报,1998,20：115-118.
[18]王弘.40Cr、50车轴钢超高周疲劳性能研究及疲劳断裂机理探讨[D].成都,西南交通大学,2004.
[19]赵永翔, 杨冰, 孙亚芳,高庆.LZ50车轴钢的概率循环本构模型[J].机械工程学报,2004,40：48-53.
[20]杨广里,杜彦良.车轴钢疲劳小裂纹扩展特性[J].北方交通大学学报,1990,14：64-71.
[21]商跃进.车轴疲劳裂纹扩展寿命可靠性分析方法[J].兰州铁道学院学报,2003,22：44-46.
[22]Hirakawa K, Kubota M高速铁路车辆车轴的疲劳设计方法[J].电力机车与城轨车辆,2004,27：44-46.
[23]Akama M, Ishizuka H. Reliability analysis of Shinkansen vehicle axle using probabilistic fracture mechanics[J]. JSME International Journal, Series A:Mechanics and Material Engineering,1995,38:378-383.
[24]Akama M, Susuki I. Fatigue crack growth simulation and estimation for rolling contact[J]. Key Engineering Materials,2000,183.
[25]Akama M; Mori T. Boundary element analysis of surface initiated rolling contact fatigue[J]. Wear,2002,253:35-41
[26]Eden F M, Rose W N, Cunningham F L. The endurance of metals[J]. Institute of Mechanical Engineers,1911,
[27]Tomlinson G A. The rusting of steel surfaces in contact[J]. Royal Society-Proceedings,1927, 115:472-483.
[28]Mindlin R D. Compliance of elastic bodies in contact[J]. ASME Journal of Applied Mechanics, 1949,16:259-268.
[29]Feng I M, Rightmire B G. The mechanism of fretting. Mass.Inst.Of Tech, Cambridge, Mass., Ad4463:
[30]Nishioka K, Hirakawa K. Fundamental investigations of fretting fatigue[J]. Bull. Jap. Soc. Mech. Engrs,1969,12:692-697.
[31]Hurrick P L. The mechanism of fretting-a review[J]. Wear,1970,15:389-409.
[32]Waterhouse R B. Fretting corrosion[M]. Oxford, Pergamon Press,1972.
[33]Hoeppner D W, Goss G L. Research on the mechanism of fretting fatigue,corrosion fatigue:chemistry,mechanics,and microstructure. Nation Association of Corrosion Engineers,USA,1972:617-626.
[34]Endo K, Goto H. Initiation and propagation of fretting fatigue cracks[J].Wear 1976,38. 311-324.
[35]Berthier Y, Vincent L, Godet M. Velocity accommodation in fretting[J]. Wear,1988,125: 25-38.
[36]Zhou Z R, Fayeulle S, Vincent L. Cracking behavior of various aluminium alloys dnring fretting wear[J]. Wear,1992,155:317-330.
[37]Hills D A, Nowell D. Crack initiation criteria in fretting fatigue[J]. Wear.1989.136:329-343.
[38]Hills D A, Nowell D. The effect of wear on nucleation of cracks at the edge of an almost complete contact[J]. Wear.2010.268:900-904.
[39]周仲荣.微动磨损[M].北京,科学出版社,2002.
[40]Godfrey D, Bisson E E. Bonding of molybdenum disulfide to various materials to form solid lubricating film.2--Friction and endurance characteristics of films bonded by practical methods. National Advisory Committee for Aeronautics--Technical Notes,1952:
[41]Fenner A J, Field J E. Study of onset of fatigue damage due to fretting. North East Coast Institution of Engineers and Shipbuilders--Transactions,1960:
[42]Bethune B, Waterhouse R B. Adhesion of metal surfaces under fretting conditions [J]. Wear, 1968,12:289-296,369-374.
[43]Gaul D J, Duquette D J. Effect of fretting and environment on fatigue crack initiation and early propagation in a quenched and tempered 4130 steel[J]. Metallurgical transactions. A, Physical metallurgy and materials science,1980,11:1555-1561.
[44]Spink G M. Fretting fatigue of a 2.5%NiCrMoV low pressure turbine shaft shtee-The effect of different contact pad materials and of variable slip amplitude[J]. Wear,1990,136:281-297.
[45]Ruiz C, Boddington P, Chen K C. An investigation of fatigue and fretting in a dovetail joint[J]. Experimental Mechanics,1984,24:208-217.
[46]Ruiz C, Chen K C. Life assessment of dovetail joints between blades and disks in aeroengines London. Mech. E. Conference Publications,1986:187-194.
[47]Nowell D H, D.A. Crack initiation criteria in fretting fatigue[J]. Wear,1990,136:329-343.
[48]Fouvry S, Kapsa P, Vincent L. Quantification of fretting fatigue[J]. Wear,1996,200:186-205.
[49]Ruiz C, Wang Z P, Webb P H. Techniques for the characterization of fretting fatigue damage. Philadelphia. Standardization of fretting fatigue test methods and equipment, ASTM STP 1159, 1992:170-177.
[50]Elkholy A H. Fretting fatigue in elastic contacts due to tangential micro-motion[J]. Tribology International,1996,29:265-273.
[51]Lykins C, Mall S. High cycle fatigue fretting behavior of Ti-6Al-4V[C]//Proceedings of the 7th International Fatigue Conference, Beijing China,1999.
[52]Lykins C D, Mall S, Jain V. Evaluation of parameters for predicting fretting fatigue crack initiation[J]. International Journal of Fatigue,2000,22:703-716.
[53]Iyer I. Peak contact pressure, cyclic stress amplitude, contact semi-width and slip amplitude: relative effects on fretting fatigue life[J]. International Journal of fatigue,2001,23:193-206.
[54]Dang Van K, Maitournam M H. On a new methodology for quantitative modeling of fretting fatigue[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[55]Fouvry S, Kapsa P, Vincent L. Fretting-wear and fretting-fatigue:Relation through a mapping concept[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[56]Araujo J A, Nowell D. The effect of rapidly varying contact stress fields on fretting fatigue[J]. International Journal of Fatigue,2002,24:763-775.
[57]Troshchenko V T, Tsybanev G V, Khotsyanovsky A O. Two-parameter model of fretting fatigue crack growth[J]. Fatigue and Fracture of Engng Mater. Structs,1994,17:15-23.
[58]Giannakopoulos A E, Lindley T C, Suresh S. Application of fracture mechanics in fretting fatigue life assessment[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[59]Giannakopoulos A E, Lindley T C, Suresh S. Aspects of equivalence between contact mechanics and fracture mechanics:Theoretical connections and life-8i methodology for fretting fatigue[J]. Acta Mater,1998,46:2955-2968.
[60]Makino T, Yamamoto M, Hirakawa K. Fracture mechanics approach to the fretting fatigue strength of axle assemblies[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[61]Beretta S, Carboni M. Experiments and stochastic model for propagation lifetime of railway axles[J]. Eng. Fract. Mech.,2006,73:2627-2641.
[62]Beretta S, Ghidini A, Lombardo F. Fracture mechanics and scale effects in the fatigue of railway axles[J]. Engineering Fracture Mechanics,2005,72:195-208.
[63]Gutkin R, Alfredsson B. Growth of fretting fatigue cracks in a shrink-fitted joint subjected to rotating bending[J]. Engineering Failure Analysis,2008,15:582-596.
[64]Lee D H, Byeong C G. Fatigue life evaluation of press-fitted specimens by using multiaxial fatigue theory at contact edge[J]. Key Engineering Materials,2005,297-300:108-114.
[65]Lee D H, Kwon S J. The evolution of contact stress and surface profile in press-fitted shaft under partial slip conditions[J]. Key Engineering Materials,2006,321-323:1495-1498.
[66]Lee D H, kwon S J. The evolution of surface damage in press-fitted shaft according to the bending stress[J]. Advanced Materials Research,2007,24-25:1353-1356.
[67]Lee D H, Kwon S J. Observations of fatigue damage in the press-fitted shaft under bending loads[J]. Key Engineering Materials,2006,326-328:1071-1074.
[68]Alfredsson B. Fretting fatigue of a shrink-fit pin subjected to rotating bending:Experiments and simulations[J]. International Journal of Fatigue,2009,31:1559-1570.
[69]陈传尧.疲劳与断裂[M].武汉,华中科技大学出版社,2002.
[70]曾攀,俞新陆,颜永年,郑楚鸿.疲劳绝对尺寸效应[J].航空学报,1988,9：144-147.
[71]张明.微动疲劳损伤机理及其防护对策的研究[D].南京,南京航空航天大学,2002.
[72]Uhlig H H. Mechanism of fretting corrosion[J]. J.Appl.Mech,1954,21:401-407.
[73]Suh N P. An overview of the delamination theory of wear[J]. Wear,1977,44:1-16.
[74]Waterhouse R B. Fretting Wear. ASM Handbook. Friction, Lubrication, and Wear Technology, ASM International. USA,1992:
[75]Hoeppner D W. Mechanisms of Fretting Fatigue and their impact on test methods development. Standardization of Fretting Fatigue Test Methods and Equipment, ASTM STP 1159,1992:
[76]Murakami Y. stress intensity factors handbook[M]. New York, Pergamon,1987.
[77]赵华,周仲荣.数值方法在微动疲劳研究中的应用进展[J].摩擦学学报,2000,20：317-320.
[78]Zhou Z R, Vincent L. Mixed fretting regime[J]. Wear,1995,181:531-536.
[79]张大鹏, 陈光雄,田合强.车轴轮座微动损伤对车轴疲劳寿命的影响[J].机械设计与制造,2009,1：113-115.
[80]符杰.过盈配合的摩擦系数研究[D].辽宁,大连理工大学,2007.
[81]Kubota M, Odanaka H, Sakae C, Ohkomori Y, Kondo Y. The analysis of fretting fatigue failure in backup roll and its prevention[C]//Fretting Fatigue:Advances in Basic Understanding and Applications, Nagaoka, Japan,2002.
[82]Sosa G U, Hills D A, Sackfield A. Shrink-fit peg subject to bending and shearing forces[J]. Journal of Strain Analysis for Engineering Design,1999,34:23-29.
[83]Juuma T. Torsional fretting fatigue strength of a shrink-fitted shaft[J]. Wear,1999,231: 310-318.
[84]徐楠42CrMo钢疲劳可靠性分析与裂纹萌生微观机理研究[D].山东,山东大学,2006.
[85]Budinsi K G. Materials evaluation under fretting conditions[C]//American Society for Testing and Materials, Special Technical Publications 780, Warminster, PA, USA,1982.
[86]米彩盈.高速动力车承载结构疲劳强度工程方法研究[D].成都,西南交通大学,2006.
[87]王潍42CrMo钢疲劳短裂纹演化行为及疲劳寿命预测的研究[D].山东,山东大学,2008.
[88]Truman C E, Booker J D. Analysis of a shrink-fit failure on a gear hub/shaft assembly[J]. Engineering Failure Analysis,2007,14:557-572.
[89]李舜酩.机械疲劳与可靠性设计[M].北京,科学出版社,2006.
[90]Hirakawa K, Toyama K, Kubota M. Analysis and prevention of failure in railway axles[J]. International Journal of Fatigue,1998,20:135-144.
[91]Mutoh Y, Tanaka K. Fretting fatigue in several steels and a cast iron[J]. Wear,1988,125: 175-191.
[92]李诗卓,董祥林.材料的冲蚀磨损与微动磨损[M].北京,机械工业出版社,1987.
[93]Dobromirski J M. Variables of fretting process:are there 50 of them?[C]//Standardization of Fretting Fatigue Test Methods and Equipment, ASTM STP 1159, Philadelphia, PA, USA,1992.
[94]杨茂胜, 陈跃良, 郁大照,胡家林.微动疲劳研究的现状与展望[J].强度与环境,2008, 35：45-54.
[95]周仲荣,朱旻昊.复合微动磨损[M].上海,上海交通大学出版社.2004.
[96]Vingsbo O, Soderberg S. On fretting maps[J]. Wear,1988,126:131-147.
[97]Endo K, Goto H, Fukunaga T. Behaviors of frictional force in fretting fatigue[J]. Bulletin of the JSME,1974,17:647-654.
[98]Naboulsi S, Nicholas T. Limitations of the Coulomb friction assumption in fretting fatigue analysis[J]. International Journal of Solids and Structures,2003,40:6497-6512.
[99]Alfredsson B, Cadario A. A study on fretting friction evolution and fretting fatigue crack initiation for a spherical contact[J]. International Journal of Fatigue,2004,26:1037-1052.
[100]Swalla D R, Neu R W. Influence of coefficient of friction on fretting fatigue crack nucleation prediction[J]. Tribology International,2001,34:493-503.
[101]Lee S K, Nakazawa K, MSumita. Effects of contact load and contact curvature radius of cylinder pad on fretting fatigue in high strength steel[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[102]Leiva O. Effect of shear load on fretting fatigue behavior of Ti-6A1-4V[D]. Dayton, University of Dayton,2003.
[103]Wallace J M, Neu R W. Fretting fatigue crack nucleation in Ti-6Al-4V[J]. Fatigue and Fracture of Engineering Materials and Structures,2003,26:199-214.
[104]Bramhall R. Studies in fretting fatigue[D]. Oxford Oxford University,1973.
[105]Hills D A, Nowell D. On the mechanics of fretting fatigue[J]. Wear,1988,125:129-146.
[106]Sato K, Fujii H, Kodama S. Effects of stress ratio and fretting fatigue cycles on the accumulation of fretting fatigue damage to carbon steel S45C[J]. Bulletin of the JSME,1986, 29:2759-2764.
[107]Uhlig H H, Feng I M. Fretting corrosion of mild steel in air and nitrogen[J]. Journal of Applied Mechanics,1954,21:395-400.
[108]Waterhouse R B. Fretting, treatise on materials science and technolog[M]. Soctt, Academic Press,1978.
[109]Soderberg S, Bryggman U, McCullough T. Frequency effects in fretting wear[J]. Wear,1986, 110:19-34.
[110]Hurricks P L. Fretting wear of mild steel from 200 degree to 500 degree C[J]. Wear,1974,30: 189-212.
[111]阮孟光.光测力学[M].北京,北京航空航天大学出版社,1995.
[112]云大真.结构分析光测力学[M].辽宁,大连理工大学出版社,1996.
[113]何蕴增,杨丽红.非线性固体力学及其有限元法[M].黑龙江,哈尔滨工程大学,2007.
[114]殷有泉.非线性有限元基础[M].北京,北京大学出版社,2007.
[115]Rajasekaran R, Nowell D. On the finite element analysis of contacting bodies using submodelling[J]. Journal of Strain Analysis for Engineering Design,2005,40:95-106.
[116]柳溪.接触压力对微动疲劳行为的影响及寿命预测[D].杭州,浙江工业大学,2007.
[117]Ekberg A. Fretting fatigue of railway axles-A review of predictive methods and an outline of a finite element model[J]. Journal of Rail and Rapid Transit,2004,218:299-316.
[118]Giner E, Sukumar N, Fuenmayor F J, Vercher A. Singularity enrichment for complete sliding contact using the partition of unity finite element method[J]. International Journal for Numerical Methods in Engineering,2008,76:1402-1418.
[119]Li L, Shi Z F. Asymptotic analysis and finite element calculation of a rubber cone contacting with a rigid socket[J]. European Journal of Mechanics,2004,23:447-453.
[120]Tur M, Fuenmayor J, Mugadu A, Hills D A. On the analysis of singular stress fields. Part 2: Application to complete slipping contacts[J]. Journal of Strain Analysis for Engineering Design,2003,38:207-217.
[121]范钦珊,殷雅俊.材料力学[M].北京,清华大学出版社,2004.
[122]Juuma T. Torsional fretting fatigue strength of a shrink-fitted shaft with a grooved hub[J]. Tribology International,2000,33:537-543.
[123]Hassan A F. An investigation of the propagation behavior of fretting fatigue cracks in titanium alloys[D]. Dayton, Ohio, University of Dayton,2005.
[124]John A P. Fretting fatigue damage accumulation and crack nucleation in high-strength steels[D]. Atlanta, USA, Georgia Institute of Technology,2002.
[125]Waterhouse R B. Fretting fatigue[J]. International Materials Reviews,1992,37:77-97.
[126]何明鉴.机械构件的微动疲劳[M].北京,国防工业出版社,1994.
[127]Faanes S. Inclined cracks in fretting fatigue[J]. Engineering Fracture Mechanics,1995,52: 71-82.
[128]Sato K. Damage formation during fretting fatigue[J]. Wear,1988,125:163-174.
[129]Hattori T, Nakamura M. Fretting fatigue analysis using fracture mechanics[J]. JSME Int J Ser 1,1988,31:100-107.
[130]Tanaka K, Mutoh Y. Fretting fatigue in 0.55C spring steel and 0.45C carbon steel[J]. Fatigue and Fracture of Engineering Materials and Structures,1985,8:129-142.
[131]王自强,陈少华.高等断裂力学[M].北京,科学出版社,2009.
[132]Yoshiharu M, Jin-Quan X. Fracture mechanics approach to fretting fatigue and problems to be solved[J]. Tribology International,2003,36:99-107.
[133]Edwards P R. Fracture mechanics application to fretting joints[C]//Proceedings of the 6th International Conference on Fracture, New Delhi, Ind,1984.
[134]Yang B, Mall S. On crack initiation mechanisms in fretting fatigue[J]. J Appl Mech,2001,68: 76-80.
[135]Xu J Q, Mutoh Y. Stress field near the contact edge in fretting fatigue tests[J]. Solid Mechanics and Material Engineering,2002,45:510-516.
[136]Nicholas T, Hutson A, John R, Olson S. A fracture mechanics methodology assessment for fretting fatigue[J]. International Journal of Fatigue,2003,25:1069-1077.
[137]Giummarra C, Brockenbrough J R. Fretting fatigue analysis using a fracture mechanics based small crack growth prediction method[J]. Tribology International,2006,39:1166-1171.
[138]Golden P J, Calcaterra J R. A fracture mechanics life prediction methodology applied to dovetail fretting[J]. Tribology International,2006,39:1172-1180.
[139]解德,钱勤,李长安.断裂力学中的数值计算方法及工程应用[M].北京,科学出版社,2009.
[140]Liu Y, Stratman B, Mahadevan S. Fatigue crack initiation life prediction of railroad wheels[J]. International Journal of Fatigue,2006,28:747-756.
[141]Narayana K B, Dattaguru B, Ramamurthy T S, Vijayakumar K. Modified crack closure integral using six-noded isoparametric quadrilateral singular elements[J]. Engineering Fracture Mechanics,1990,
[142]Raju I S. Calculation of strain-energy release rates with higher order and singular finite elements[J]. Engineering Fracture Mechanics,1987,
[143]Sethuraman R, Maiti S K. Finite element based computation of strain energy release rate by modified crack closure integral[J]. Engineering Fracture Mechanics,1988,30:227-231.
[144]陈银强.圆柱体表面椭圆裂纹应力强度因子的有限元分析和研究[D].武汉,武汉工程大学,2006.
[145]郑红霞.货车车轮辐板孔裂纹形成原因及疲劳扩展特性研究[D].北京,北京交通大学,2007.
[146]高庆.工程断裂力学[M].重庆,重庆大学出版社,1992.
[147]刘青峰.疲劳裂纹连续扩展技术研究及在车辆工程中的应用[D].北京,北京交通大学,2004.
[148]Newman J C, Raju I S. Stress-intensity factors for internal surface cracks in cylindrical pressure vessels[J]. Journal of Pressure Vessel Technology,1980,102:342-346.
[149]Raju I S, Newman J C. Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates[J]. Engineering Fracture Mechanics,1979,11:817-829.
[150]Carpinteri A. Surface cracks in notched round bars under cyclic tension and bending[J]. International Journal of Fatigue,2006,28:251-260.
[151]Madia M, Beretta S, Zerbst U. An investigation on the influence of rotary bending and press fitting on stress intensity factors and fatigue crack growth in railway axles[J]. Engineering Fracture Mechanics,2008,75:1906-1920.
[152]赵少汴,王忠保.抗疲劳设计：方法与数据[M].北京,机械工业出版社,1997.
[153]程育仁,侯炳麟,孙晓保,野方文雄.三点弯曲试样的应力双轴效应对疲劳裂纹扩展门槛值的影响[J].北京交通大学学报,1988,4：23-28.
[154]雷冬.疲劳寿命预测若干方法的研究[D].合肥,中国科学技术大学,2006.
[155]Suresh S.王中光译.材料的疲劳[M].北京,国防工业出版社,1993.
[156]Ambrico J M, Begley M R. Plasticity in fretting contact[J]. Journal of the Mechanics and Physics of Solids,2000,48:2391-2417.
[157]杨万均.热尾榫结构微动疲劳寿命预测方法研究[D].南京,南京航空航天大学,2007.
[158]Wharton M H, Waterhouse R B, Hirakawa K, Nishioka K. The effect of different contact materials on the fretting fatigue strength of an aluminium alloy[J]. Wear,1973,26:253-260.
[159]Fouvry S, Kapsa P, Vincent L. Multiaxial fatigue analysis of fretting contact taking into account the size effect[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[160]朱旻昊,周仲荣.径向与复合微动的运行和损伤机理研究[D].成都,西南交通大学,2001.
[161]Fash J W, Socie D F, McDowell D L. Fatigue life estimates for a simple notched component under biaxial loading[C]//Multiaxial Fatigue, San Francisco, CA, USA,1985.
[162]鲁丽君.桅杆结构纤绳连接拉耳风致疲劳裂纹萌生于扩展寿命预测[D].武汉,武汉理工大学,2008.
[163]Fatemi A, Socie D F. A critical plane approach to multiaxial fatigue damage including out-of-phase loading[J]. Fatigue and fracture of engineering materials and structures,1988,11: 149-165.
[164]Swalla D R. Fretting fatigue damage prediction using multiaxial fatigue criteria[D]. Atlanta, GA, USA, Georgia Institute of Technology,1999.
[165]Neu R W. Methodologies for linking nucleation and propagation approaches for predicting life under fretting fatigue[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[166]Findley W N. Theory for effect of mean stress on fatigue of metals under combined torsion and axial load or bending. [C]//ASME Meeting, New York, NY, United States,1958.
[167]王英玉,姚卫星.材料多轴疲劳破坏准则回顾[J].机械强度,2003,25：246-250.
[168]Fellows L J, Nowell D, Hills D A. Analysis of crack initiation and propagation in fretting fatigue:the effective initial flaw size methodology [J]. Fatigue and Fracture of Engineering Materials and Structures,1997,20:61-70.
[169]Sato K, Fuji H, Kodama S. Crack propagation behavior in fretting fatigue[J]. Wear,1986, 107:245-262.
[170]Faanes S, Fernando U S. Influence of contact loading on fretting fatigue behaviour[J]. Fatigue Fract Eng Mater Struct,1994,17:939-947.
[171]Chan K S, Lee Y, Davidson D L, Hudak S J. A fracture mechanics approach to high cycle fretting fatigue based on the worst case fret concept. I. Model development[J]. International Journal of Fracture,2001,112:299-330.
[172]Beretta S, Carboni M. Simulation of fatigue crack propagation in railway axles[C]//34th National Symposium on Fatigue and Fracture Mechanics, Tampa, FL, United states,2005.
[173]Beretta S, Carboni M, Conte A L, Palermo E. An investigation of the effects of corrosion on the fatigue strength of AlN axle steel[J]. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2008,222:129-143.
[174]GiannakopoulosAE A E, TC T C L, Suresh S. Aspects of equivalence between contact mechanics and fracture mechanics:Theoretical connections and life-8i methodology for fretting fatigue[J]. Acta Mater,1998,46:2955-2968.
[175]Nadai A I. Theory of Flow and Fracture of Solids. New York.1963:
[176]Williams M L. J. Appl. Mech,1957,24:109.
[177]Isida M. Tension of a half plane containing array cracks, branched cracks, and cracks emanating from sharp notches[J]. Transactions of the Japan Society of Mechanical Engineers, 1979,45:306-319.
[178]Conner B P, Lindley T C, Nicholas T, Suresh S. Application of a fracture mechanics based life prediction method for contact fatigue[J]. International Journal of Fatigue,2004,26: 511-520.
[179]Paris P C, Gomez M P, Anderson W P. A rational analytic theory of fatigue[J]. Trends in Engineering,1961,13:9-14.
[180]Grobe M, Fischer G. Development of an Innovative High Performance Railway Wheelset[C]//Structural Durability in Railway Engineering, Germany,2006.
[181]Grubisic V, Fischer G. Usage Related Design and Validation of Wheelset Axles[C]//Structural Durability in Railway Engineering, Germany,2006.
[182]杨继震,任尊松.CRH2动车组拖车轮对轴箱强度分析[D].北京,北京交通大学,2008.
[183]张云,赵锁宗.东风4型内燃机车车轴裂纹原因分析[J].机车车辆工艺,1995,12：38-41.
[184]陈晗.轮对加工、组装质量对预防车轴早期疲劳裂纹的探索[J].机车车辆工艺,2004,23 75-77.
[185]石塚弘道,彭惠民.车体、转向架构架和车轴的疲劳研究[J].国外机车车辆工艺,2009,11：38-41.
[2]Smith R A, Hillmansen S. A brief historical overview of the fatigue of railway axles[J].
Proceedings of the Institution of Mechanical Engineers, Part F:Journal of Rail and Rapid Transit,2004,218:267-277.
[3]侯卫星.车轴疲劳可靠性研究初探[J].铁道车辆,1989,1：7-11.
[4]石塚弘道.车轴轻量化途径[J].国外铁道车辆,1992,1：35-39.
[5]孙蕾,陈雷.铁路货车RD2型车轴轴颈卸荷槽质量问题研究与对策[J].铁道车辆,2006,44：11-17.
[6]何庆复.列车车轴抗微动损伤热喷涂层组织结构研究[J].铁道学报,2001,23：102-104.
[7]石塚弘道.车轴微振磨损的对策[J].国外内燃机车,1993,12：48-52.
[8]杨广雪,谢基龙.车轴设计参数对轴毂配合接触压力影响的研究[J].铁道学报,2009,31：31-35.
[9]张永生.东风4、7型机车车轴使用寿命的探讨[J].内燃机车,2002,12：24-26.
[10]郭志仁.车轴寿命谈[J].机车车辆工艺,1992,6：1-9.
[11]王树青.车轴感应淬火技术研究[J].金属热处理,2001,26：31-34.
[12]平川贤尔.高速动车用车轴的疲劳设计[J].国外内燃机车,1997,5：31-33.
[131 Hiromichi I改善新干线车辆车轴常规检测[J].国外铁道车辆,2001,38：42-45.
[14]李述松,唐东平,徐建生,宋春如.对DF4、8型机车车轴不良状态的研究[J].内燃机车,2003,8：32-34.
[15]李炳华,杜欣.高速机车车辆车轴的疲劳设计[J].内燃机车,2000,1：14-20.
[16]本松启美.日本新干线电动车用车轴的疲劳试验结果[J].国外铁道车辆,1992,6：31-39.
[17]刘伟,何庆复,张云.微动损伤对车轴疲劳寿命的影响[J].铁道学报,1998,20：115-118.
[18]王弘.40Cr、50车轴钢超高周疲劳性能研究及疲劳断裂机理探讨[D].成都,西南交通大学,2004.
[19]赵永翔, 杨冰, 孙亚芳,高庆.LZ50车轴钢的概率循环本构模型[J].机械工程学报,2004,40：48-53.
[20]杨广里,杜彦良.车轴钢疲劳小裂纹扩展特性[J].北方交通大学学报,1990,14：64-71.
[21]商跃进.车轴疲劳裂纹扩展寿命可靠性分析方法[J].兰州铁道学院学报,2003,22：44-46.
[22]Hirakawa K, Kubota M高速铁路车辆车轴的疲劳设计方法[J].电力机车与城轨车辆,2004,27：44-46.
[23]Akama M, Ishizuka H. Reliability analysis of Shinkansen vehicle axle using probabilistic fracture mechanics[J]. JSME International Journal, Series A:Mechanics and Material Engineering,1995,38:378-383.
[24]Akama M, Susuki I. Fatigue crack growth simulation and estimation for rolling contact[J]. Key Engineering Materials,2000,183.
[25]Akama M; Mori T. Boundary element analysis of surface initiated rolling contact fatigue[J]. Wear,2002,253:35-41
[26]Eden F M, Rose W N, Cunningham F L. The endurance of metals[J]. Institute of Mechanical Engineers,1911,
[27]Tomlinson G A. The rusting of steel surfaces in contact[J]. Royal Society-Proceedings,1927, 115:472-483.
[28]Mindlin R D. Compliance of elastic bodies in contact[J]. ASME Journal of Applied Mechanics, 1949,16:259-268.
[29]Feng I M, Rightmire B G. The mechanism of fretting. Mass.Inst.Of Tech, Cambridge, Mass., Ad4463:
[30]Nishioka K, Hirakawa K. Fundamental investigations of fretting fatigue[J]. Bull. Jap. Soc. Mech. Engrs,1969,12:692-697.
[31]Hurrick P L. The mechanism of fretting-a review[J]. Wear,1970,15:389-409.
[32]Waterhouse R B. Fretting corrosion[M]. Oxford, Pergamon Press,1972.
[33]Hoeppner D W, Goss G L. Research on the mechanism of fretting fatigue,corrosion fatigue:chemistry,mechanics,and microstructure. Nation Association of Corrosion Engineers,USA,1972:617-626.
[34]Endo K, Goto H. Initiation and propagation of fretting fatigue cracks[J].Wear 1976,38. 311-324.
[35]Berthier Y, Vincent L, Godet M. Velocity accommodation in fretting[J]. Wear,1988,125: 25-38.
[36]Zhou Z R, Fayeulle S, Vincent L. Cracking behavior of various aluminium alloys dnring fretting wear[J]. Wear,1992,155:317-330.
[37]Hills D A, Nowell D. Crack initiation criteria in fretting fatigue[J]. Wear.1989.136:329-343.
[38]Hills D A, Nowell D. The effect of wear on nucleation of cracks at the edge of an almost complete contact[J]. Wear.2010.268:900-904.
[39]周仲荣.微动磨损[M].北京,科学出版社,2002.
[40]Godfrey D, Bisson E E. Bonding of molybdenum disulfide to various materials to form solid lubricating film.2--Friction and endurance characteristics of films bonded by practical methods. National Advisory Committee for Aeronautics--Technical Notes,1952:
[41]Fenner A J, Field J E. Study of onset of fatigue damage due to fretting. North East Coast Institution of Engineers and Shipbuilders--Transactions,1960:
[42]Bethune B, Waterhouse R B. Adhesion of metal surfaces under fretting conditions [J]. Wear, 1968,12:289-296,369-374.
[43]Gaul D J, Duquette D J. Effect of fretting and environment on fatigue crack initiation and early propagation in a quenched and tempered 4130 steel[J]. Metallurgical transactions. A, Physical metallurgy and materials science,1980,11:1555-1561.
[44]Spink G M. Fretting fatigue of a 2.5%NiCrMoV low pressure turbine shaft shtee-The effect of different contact pad materials and of variable slip amplitude[J]. Wear,1990,136:281-297.
[45]Ruiz C, Boddington P, Chen K C. An investigation of fatigue and fretting in a dovetail joint[J]. Experimental Mechanics,1984,24:208-217.
[46]Ruiz C, Chen K C. Life assessment of dovetail joints between blades and disks in aeroengines London. Mech. E. Conference Publications,1986:187-194.
[47]Nowell D H, D.A. Crack initiation criteria in fretting fatigue[J]. Wear,1990,136:329-343.
[48]Fouvry S, Kapsa P, Vincent L. Quantification of fretting fatigue[J]. Wear,1996,200:186-205.
[49]Ruiz C, Wang Z P, Webb P H. Techniques for the characterization of fretting fatigue damage. Philadelphia. Standardization of fretting fatigue test methods and equipment, ASTM STP 1159, 1992:170-177.
[50]Elkholy A H. Fretting fatigue in elastic contacts due to tangential micro-motion[J]. Tribology International,1996,29:265-273.
[51]Lykins C, Mall S. High cycle fatigue fretting behavior of Ti-6Al-4V[C]//Proceedings of the 7th International Fatigue Conference, Beijing China,1999.
[52]Lykins C D, Mall S, Jain V. Evaluation of parameters for predicting fretting fatigue crack initiation[J]. International Journal of Fatigue,2000,22:703-716.
[53]Iyer I. Peak contact pressure, cyclic stress amplitude, contact semi-width and slip amplitude: relative effects on fretting fatigue life[J]. International Journal of fatigue,2001,23:193-206.
[54]Dang Van K, Maitournam M H. On a new methodology for quantitative modeling of fretting fatigue[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[55]Fouvry S, Kapsa P, Vincent L. Fretting-wear and fretting-fatigue:Relation through a mapping concept[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[56]Araujo J A, Nowell D. The effect of rapidly varying contact stress fields on fretting fatigue[J]. International Journal of Fatigue,2002,24:763-775.
[57]Troshchenko V T, Tsybanev G V, Khotsyanovsky A O. Two-parameter model of fretting fatigue crack growth[J]. Fatigue and Fracture of Engng Mater. Structs,1994,17:15-23.
[58]Giannakopoulos A E, Lindley T C, Suresh S. Application of fracture mechanics in fretting fatigue life assessment[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[59]Giannakopoulos A E, Lindley T C, Suresh S. Aspects of equivalence between contact mechanics and fracture mechanics:Theoretical connections and life-8i methodology for fretting fatigue[J]. Acta Mater,1998,46:2955-2968.
[60]Makino T, Yamamoto M, Hirakawa K. Fracture mechanics approach to the fretting fatigue strength of axle assemblies[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[61]Beretta S, Carboni M. Experiments and stochastic model for propagation lifetime of railway axles[J]. Eng. Fract. Mech.,2006,73:2627-2641.
[62]Beretta S, Ghidini A, Lombardo F. Fracture mechanics and scale effects in the fatigue of railway axles[J]. Engineering Fracture Mechanics,2005,72:195-208.
[63]Gutkin R, Alfredsson B. Growth of fretting fatigue cracks in a shrink-fitted joint subjected to rotating bending[J]. Engineering Failure Analysis,2008,15:582-596.
[64]Lee D H, Byeong C G. Fatigue life evaluation of press-fitted specimens by using multiaxial fatigue theory at contact edge[J]. Key Engineering Materials,2005,297-300:108-114.
[65]Lee D H, Kwon S J. The evolution of contact stress and surface profile in press-fitted shaft under partial slip conditions[J]. Key Engineering Materials,2006,321-323:1495-1498.
[66]Lee D H, kwon S J. The evolution of surface damage in press-fitted shaft according to the bending stress[J]. Advanced Materials Research,2007,24-25:1353-1356.
[67]Lee D H, Kwon S J. Observations of fatigue damage in the press-fitted shaft under bending loads[J]. Key Engineering Materials,2006,326-328:1071-1074.
[68]Alfredsson B. Fretting fatigue of a shrink-fit pin subjected to rotating bending:Experiments and simulations[J]. International Journal of Fatigue,2009,31:1559-1570.
[69]陈传尧.疲劳与断裂[M].武汉,华中科技大学出版社,2002.
[70]曾攀,俞新陆,颜永年,郑楚鸿.疲劳绝对尺寸效应[J].航空学报,1988,9：144-147.
[71]张明.微动疲劳损伤机理及其防护对策的研究[D].南京,南京航空航天大学,2002.
[72]Uhlig H H. Mechanism of fretting corrosion[J]. J.Appl.Mech,1954,21:401-407.
[73]Suh N P. An overview of the delamination theory of wear[J]. Wear,1977,44:1-16.
[74]Waterhouse R B. Fretting Wear. ASM Handbook. Friction, Lubrication, and Wear Technology, ASM International. USA,1992:
[75]Hoeppner D W. Mechanisms of Fretting Fatigue and their impact on test methods development. Standardization of Fretting Fatigue Test Methods and Equipment, ASTM STP 1159,1992:
[76]Murakami Y. stress intensity factors handbook[M]. New York, Pergamon,1987.
[77]赵华,周仲荣.数值方法在微动疲劳研究中的应用进展[J].摩擦学学报,2000,20：317-320.
[78]Zhou Z R, Vincent L. Mixed fretting regime[J]. Wear,1995,181:531-536.
[79]张大鹏, 陈光雄,田合强.车轴轮座微动损伤对车轴疲劳寿命的影响[J].机械设计与制造,2009,1：113-115.
[80]符杰.过盈配合的摩擦系数研究[D].辽宁,大连理工大学,2007.
[81]Kubota M, Odanaka H, Sakae C, Ohkomori Y, Kondo Y. The analysis of fretting fatigue failure in backup roll and its prevention[C]//Fretting Fatigue:Advances in Basic Understanding and Applications, Nagaoka, Japan,2002.
[82]Sosa G U, Hills D A, Sackfield A. Shrink-fit peg subject to bending and shearing forces[J]. Journal of Strain Analysis for Engineering Design,1999,34:23-29.
[83]Juuma T. Torsional fretting fatigue strength of a shrink-fitted shaft[J]. Wear,1999,231: 310-318.
[84]徐楠42CrMo钢疲劳可靠性分析与裂纹萌生微观机理研究[D].山东,山东大学,2006.
[85]Budinsi K G. Materials evaluation under fretting conditions[C]//American Society for Testing and Materials, Special Technical Publications 780, Warminster, PA, USA,1982.
[86]米彩盈.高速动力车承载结构疲劳强度工程方法研究[D].成都,西南交通大学,2006.
[87]王潍42CrMo钢疲劳短裂纹演化行为及疲劳寿命预测的研究[D].山东,山东大学,2008.
[88]Truman C E, Booker J D. Analysis of a shrink-fit failure on a gear hub/shaft assembly[J]. Engineering Failure Analysis,2007,14:557-572.
[89]李舜酩.机械疲劳与可靠性设计[M].北京,科学出版社,2006.
[90]Hirakawa K, Toyama K, Kubota M. Analysis and prevention of failure in railway axles[J]. International Journal of Fatigue,1998,20:135-144.
[91]Mutoh Y, Tanaka K. Fretting fatigue in several steels and a cast iron[J]. Wear,1988,125: 175-191.
[92]李诗卓,董祥林.材料的冲蚀磨损与微动磨损[M].北京,机械工业出版社,1987.
[93]Dobromirski J M. Variables of fretting process:are there 50 of them?[C]//Standardization of Fretting Fatigue Test Methods and Equipment, ASTM STP 1159, Philadelphia, PA, USA,1992.
[94]杨茂胜, 陈跃良, 郁大照,胡家林.微动疲劳研究的现状与展望[J].强度与环境,2008, 35：45-54.
[95]周仲荣,朱旻昊.复合微动磨损[M].上海,上海交通大学出版社.2004.
[96]Vingsbo O, Soderberg S. On fretting maps[J]. Wear,1988,126:131-147.
[97]Endo K, Goto H, Fukunaga T. Behaviors of frictional force in fretting fatigue[J]. Bulletin of the JSME,1974,17:647-654.
[98]Naboulsi S, Nicholas T. Limitations of the Coulomb friction assumption in fretting fatigue analysis[J]. International Journal of Solids and Structures,2003,40:6497-6512.
[99]Alfredsson B, Cadario A. A study on fretting friction evolution and fretting fatigue crack initiation for a spherical contact[J]. International Journal of Fatigue,2004,26:1037-1052.
[100]Swalla D R, Neu R W. Influence of coefficient of friction on fretting fatigue crack nucleation prediction[J]. Tribology International,2001,34:493-503.
[101]Lee S K, Nakazawa K, MSumita. Effects of contact load and contact curvature radius of cylinder pad on fretting fatigue in high strength steel[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[102]Leiva O. Effect of shear load on fretting fatigue behavior of Ti-6A1-4V[D]. Dayton, University of Dayton,2003.
[103]Wallace J M, Neu R W. Fretting fatigue crack nucleation in Ti-6Al-4V[J]. Fatigue and Fracture of Engineering Materials and Structures,2003,26:199-214.
[104]Bramhall R. Studies in fretting fatigue[D]. Oxford Oxford University,1973.
[105]Hills D A, Nowell D. On the mechanics of fretting fatigue[J]. Wear,1988,125:129-146.
[106]Sato K, Fujii H, Kodama S. Effects of stress ratio and fretting fatigue cycles on the accumulation of fretting fatigue damage to carbon steel S45C[J]. Bulletin of the JSME,1986, 29:2759-2764.
[107]Uhlig H H, Feng I M. Fretting corrosion of mild steel in air and nitrogen[J]. Journal of Applied Mechanics,1954,21:395-400.
[108]Waterhouse R B. Fretting, treatise on materials science and technolog[M]. Soctt, Academic Press,1978.
[109]Soderberg S, Bryggman U, McCullough T. Frequency effects in fretting wear[J]. Wear,1986, 110:19-34.
[110]Hurricks P L. Fretting wear of mild steel from 200 degree to 500 degree C[J]. Wear,1974,30: 189-212.
[111]阮孟光.光测力学[M].北京,北京航空航天大学出版社,1995.
[112]云大真.结构分析光测力学[M].辽宁,大连理工大学出版社,1996.
[113]何蕴增,杨丽红.非线性固体力学及其有限元法[M].黑龙江,哈尔滨工程大学,2007.
[114]殷有泉.非线性有限元基础[M].北京,北京大学出版社,2007.
[115]Rajasekaran R, Nowell D. On the finite element analysis of contacting bodies using submodelling[J]. Journal of Strain Analysis for Engineering Design,2005,40:95-106.
[116]柳溪.接触压力对微动疲劳行为的影响及寿命预测[D].杭州,浙江工业大学,2007.
[117]Ekberg A. Fretting fatigue of railway axles-A review of predictive methods and an outline of a finite element model[J]. Journal of Rail and Rapid Transit,2004,218:299-316.
[118]Giner E, Sukumar N, Fuenmayor F J, Vercher A. Singularity enrichment for complete sliding contact using the partition of unity finite element method[J]. International Journal for Numerical Methods in Engineering,2008,76:1402-1418.
[119]Li L, Shi Z F. Asymptotic analysis and finite element calculation of a rubber cone contacting with a rigid socket[J]. European Journal of Mechanics,2004,23:447-453.
[120]Tur M, Fuenmayor J, Mugadu A, Hills D A. On the analysis of singular stress fields. Part 2: Application to complete slipping contacts[J]. Journal of Strain Analysis for Engineering Design,2003,38:207-217.
[121]范钦珊,殷雅俊.材料力学[M].北京,清华大学出版社,2004.
[122]Juuma T. Torsional fretting fatigue strength of a shrink-fitted shaft with a grooved hub[J]. Tribology International,2000,33:537-543.
[123]Hassan A F. An investigation of the propagation behavior of fretting fatigue cracks in titanium alloys[D]. Dayton, Ohio, University of Dayton,2005.
[124]John A P. Fretting fatigue damage accumulation and crack nucleation in high-strength steels[D]. Atlanta, USA, Georgia Institute of Technology,2002.
[125]Waterhouse R B. Fretting fatigue[J]. International Materials Reviews,1992,37:77-97.
[126]何明鉴.机械构件的微动疲劳[M].北京,国防工业出版社,1994.
[127]Faanes S. Inclined cracks in fretting fatigue[J]. Engineering Fracture Mechanics,1995,52: 71-82.
[128]Sato K. Damage formation during fretting fatigue[J]. Wear,1988,125:163-174.
[129]Hattori T, Nakamura M. Fretting fatigue analysis using fracture mechanics[J]. JSME Int J Ser 1,1988,31:100-107.
[130]Tanaka K, Mutoh Y. Fretting fatigue in 0.55C spring steel and 0.45C carbon steel[J]. Fatigue and Fracture of Engineering Materials and Structures,1985,8:129-142.
[131]王自强,陈少华.高等断裂力学[M].北京,科学出版社,2009.
[132]Yoshiharu M, Jin-Quan X. Fracture mechanics approach to fretting fatigue and problems to be solved[J]. Tribology International,2003,36:99-107.
[133]Edwards P R. Fracture mechanics application to fretting joints[C]//Proceedings of the 6th International Conference on Fracture, New Delhi, Ind,1984.
[134]Yang B, Mall S. On crack initiation mechanisms in fretting fatigue[J]. J Appl Mech,2001,68: 76-80.
[135]Xu J Q, Mutoh Y. Stress field near the contact edge in fretting fatigue tests[J]. Solid Mechanics and Material Engineering,2002,45:510-516.
[136]Nicholas T, Hutson A, John R, Olson S. A fracture mechanics methodology assessment for fretting fatigue[J]. International Journal of Fatigue,2003,25:1069-1077.
[137]Giummarra C, Brockenbrough J R. Fretting fatigue analysis using a fracture mechanics based small crack growth prediction method[J]. Tribology International,2006,39:1166-1171.
[138]Golden P J, Calcaterra J R. A fracture mechanics life prediction methodology applied to dovetail fretting[J]. Tribology International,2006,39:1172-1180.
[139]解德,钱勤,李长安.断裂力学中的数值计算方法及工程应用[M].北京,科学出版社,2009.
[140]Liu Y, Stratman B, Mahadevan S. Fatigue crack initiation life prediction of railroad wheels[J]. International Journal of Fatigue,2006,28:747-756.
[141]Narayana K B, Dattaguru B, Ramamurthy T S, Vijayakumar K. Modified crack closure integral using six-noded isoparametric quadrilateral singular elements[J]. Engineering Fracture Mechanics,1990,
[142]Raju I S. Calculation of strain-energy release rates with higher order and singular finite elements[J]. Engineering Fracture Mechanics,1987,
[143]Sethuraman R, Maiti S K. Finite element based computation of strain energy release rate by modified crack closure integral[J]. Engineering Fracture Mechanics,1988,30:227-231.
[144]陈银强.圆柱体表面椭圆裂纹应力强度因子的有限元分析和研究[D].武汉,武汉工程大学,2006.
[145]郑红霞.货车车轮辐板孔裂纹形成原因及疲劳扩展特性研究[D].北京,北京交通大学,2007.
[146]高庆.工程断裂力学[M].重庆,重庆大学出版社,1992.
[147]刘青峰.疲劳裂纹连续扩展技术研究及在车辆工程中的应用[D].北京,北京交通大学,2004.
[148]Newman J C, Raju I S. Stress-intensity factors for internal surface cracks in cylindrical pressure vessels[J]. Journal of Pressure Vessel Technology,1980,102:342-346.
[149]Raju I S, Newman J C. Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates[J]. Engineering Fracture Mechanics,1979,11:817-829.
[150]Carpinteri A. Surface cracks in notched round bars under cyclic tension and bending[J]. International Journal of Fatigue,2006,28:251-260.
[151]Madia M, Beretta S, Zerbst U. An investigation on the influence of rotary bending and press fitting on stress intensity factors and fatigue crack growth in railway axles[J]. Engineering Fracture Mechanics,2008,75:1906-1920.
[152]赵少汴,王忠保.抗疲劳设计：方法与数据[M].北京,机械工业出版社,1997.
[153]程育仁,侯炳麟,孙晓保,野方文雄.三点弯曲试样的应力双轴效应对疲劳裂纹扩展门槛值的影响[J].北京交通大学学报,1988,4：23-28.
[154]雷冬.疲劳寿命预测若干方法的研究[D].合肥,中国科学技术大学,2006.
[155]Suresh S.王中光译.材料的疲劳[M].北京,国防工业出版社,1993.
[156]Ambrico J M, Begley M R. Plasticity in fretting contact[J]. Journal of the Mechanics and Physics of Solids,2000,48:2391-2417.
[157]杨万均.热尾榫结构微动疲劳寿命预测方法研究[D].南京,南京航空航天大学,2007.
[158]Wharton M H, Waterhouse R B, Hirakawa K, Nishioka K. The effect of different contact materials on the fretting fatigue strength of an aluminium alloy[J]. Wear,1973,26:253-260.
[159]Fouvry S, Kapsa P, Vincent L. Multiaxial fatigue analysis of fretting contact taking into account the size effect[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[160]朱旻昊,周仲荣.径向与复合微动的运行和损伤机理研究[D].成都,西南交通大学,2001.
[161]Fash J W, Socie D F, McDowell D L. Fatigue life estimates for a simple notched component under biaxial loading[C]//Multiaxial Fatigue, San Francisco, CA, USA,1985.
[162]鲁丽君.桅杆结构纤绳连接拉耳风致疲劳裂纹萌生于扩展寿命预测[D].武汉,武汉理工大学,2008.
[163]Fatemi A, Socie D F. A critical plane approach to multiaxial fatigue damage including out-of-phase loading[J]. Fatigue and fracture of engineering materials and structures,1988,11: 149-165.
[164]Swalla D R. Fretting fatigue damage prediction using multiaxial fatigue criteria[D]. Atlanta, GA, USA, Georgia Institute of Technology,1999.
[165]Neu R W. Methodologies for linking nucleation and propagation approaches for predicting life under fretting fatigue[C]//The 2nd International Symposium on Fretting Fatigue:Current Technology and Practices, Salt Lake City, UT, USA,2000.
[166]Findley W N. Theory for effect of mean stress on fatigue of metals under combined torsion and axial load or bending. [C]//ASME Meeting, New York, NY, United States,1958.
[167]王英玉,姚卫星.材料多轴疲劳破坏准则回顾[J].机械强度,2003,25：246-250.
[168]Fellows L J, Nowell D, Hills D A. Analysis of crack initiation and propagation in fretting fatigue:the effective initial flaw size methodology [J]. Fatigue and Fracture of Engineering Materials and Structures,1997,20:61-70.
[169]Sato K, Fuji H, Kodama S. Crack propagation behavior in fretting fatigue[J]. Wear,1986, 107:245-262.
[170]Faanes S, Fernando U S. Influence of contact loading on fretting fatigue behaviour[J]. Fatigue Fract Eng Mater Struct,1994,17:939-947.
[171]Chan K S, Lee Y, Davidson D L, Hudak S J. A fracture mechanics approach to high cycle fretting fatigue based on the worst case fret concept. I. Model development[J]. International Journal of Fracture,2001,112:299-330.
[172]Beretta S, Carboni M. Simulation of fatigue crack propagation in railway axles[C]//34th National Symposium on Fatigue and Fracture Mechanics, Tampa, FL, United states,2005.
[173]Beretta S, Carboni M, Conte A L, Palermo E. An investigation of the effects of corrosion on the fatigue strength of AlN axle steel[J]. Proc Inst Mech Eng Part F J Rail Rapid Transit, 2008,222:129-143.
[174]GiannakopoulosAE A E, TC T C L, Suresh S. Aspects of equivalence between contact mechanics and fracture mechanics:Theoretical connections and life-8i methodology for fretting fatigue[J]. Acta Mater,1998,46:2955-2968.
[175]Nadai A I. Theory of Flow and Fracture of Solids. New York.1963:
[176]Williams M L. J. Appl. Mech,1957,24:109.
[177]Isida M. Tension of a half plane containing array cracks, branched cracks, and cracks emanating from sharp notches[J]. Transactions of the Japan Society of Mechanical Engineers, 1979,45:306-319.
[178]Conner B P, Lindley T C, Nicholas T, Suresh S. Application of a fracture mechanics based life prediction method for contact fatigue[J]. International Journal of Fatigue,2004,26: 511-520.
[179]Paris P C, Gomez M P, Anderson W P. A rational analytic theory of fatigue[J]. Trends in Engineering,1961,13:9-14.
[180]Grobe M, Fischer G. Development of an Innovative High Performance Railway Wheelset[C]//Structural Durability in Railway Engineering, Germany,2006.
[181]Grubisic V, Fischer G. Usage Related Design and Validation of Wheelset Axles[C]//Structural Durability in Railway Engineering, Germany,2006.
[182]杨继震,任尊松.CRH2动车组拖车轮对轴箱强度分析[D].北京,北京交通大学,2008.
[183]张云,赵锁宗.东风4型内燃机车车轴裂纹原因分析[J].机车车辆工艺,1995,12：38-41.
[184]陈晗.轮对加工、组装质量对预防车轴早期疲劳裂纹的探索[J].机车车辆工艺,2004,23 75-77.
[185]石塚弘道,彭惠民.车体、转向架构架和车轴的疲劳研究[J].国外机车车辆工艺,2009,11：38-41.