橡胶隔振器单轴疲劳特性试验与预测方法的研究
|
摘要
橡胶隔振器因其优良的隔振、隔水、隔气、缓冲、抗拉及耐磨等性能已广泛应用于汽车隔振系统中。一直以来，工程界和学术界对橡胶隔振器减振性能的研究颇为关注，而对其疲劳耐久性能的研究则相对缺乏。我国在橡胶隔振件的疲劳研究尚处起步阶段，要想充分发挥橡胶隔振器在汽车行业的应用价值，还需对橡胶隔振器的疲劳性能展开更为系统、深入的研究。为提高橡胶隔振器的疲劳耐久性能，本文依据橡胶隔振器疲劳预测的基础理论，研究了橡胶隔振器疲劳特性试验方法及其疲劳寿命预测的问题。文中对橡胶隔振器疲劳耐久性能的研究成果在学术界及工程领域都具有重要的指导意义和应用价值。本文主要工作如下：
1）建立了橡胶疲劳寿命预测模型。在介绍目前常用评价橡胶疲劳寿命的损伤参量和橡胶元件疲劳寿命的预测模型基础上，通过对橡胶元件承载变形结果的分析，创建了橡胶元件张量形式的疲劳寿命预测公式、新的组合疲劳寿命评价损伤参量以及橡胶疲劳寿命可靠性分布概率的线性函数。
2）提出了橡胶隔振器力-位移计算精度的研究方法。通过对材料应变组合对五种本构模型参数拟合精度影响的分析以及橡胶隔振器力学计算方法探讨的基础上，采用有限元计算与模拟测试的方法得出不同本构模型和不同材料应变组合对其计算结果的影响。此部分的试验方法和结论不仅对橡胶隔振器的设计具有一定的参考价值，而且能为橡胶隔振器的理论分析和模拟计算提供试验支持。
3）设计了橡胶疲劳的试验方法。对橡胶疲劳试验中的激励载荷进行参数评价及载荷性质进行分类转化，设计了橡胶材料疲劳试验对象（如橡胶试片、橡胶试柱、环形橡胶试柱）并对其试验方法、试验原理、部分评价参数实测计算进行一系列的分析研究，对橡胶悬置疲劳试验方法及原理提出了相应结论。此部分的试验方法、试验原理对橡胶元件的疲劳试验设计具有典型借鉴意义。
4）提出了橡胶疲劳寿命的预测方法。利用有限元方法计算橡胶疲劳损伤等效参量、分析了橡胶元件应力、应变，进而运用新的疲劳预测模型预测了在不同承载应变形式下橡胶材料、橡胶元件的疲劳寿命趋势，得出了较为精确的填充型炭黑天然橡胶元件的疲劳寿命预测公式。随后采用统计方法对橡胶疲劳寿命的分布概率进行了统计学上的可靠性分析。
Rubber isolators are widely used in the vibration isolation system of automobile. This isprimarily due to their excellent vibration isolation properties, good water and air resistance,good cushion performance, high tensile strength and high wear resistance. However, theresearch undertaken so far was mainly focused on the damping properties of the rubbercomponents, and only a few investigations were on their fatigue durability. It is accepted thatbefore the full benefit of the rubber isolators can be realised in the automobile industry, afurther study on the fatigue properties of the rubber isolators has yet to be seen especially inChina. In this research project, to improve the fatigue and endurance performance of therubber isolators, the fatigue properties test and fatigue-life prediction method of rubberisolators have been studied based on the basic fatigue-life prediction theory of the rubberisolators. It is with reason to believe that the achievement of this research would have asignificant value in both academic and engineering fields. The following summarises the maincontents of this research:
1) Fatigue-life prediction model of rubber materials has been established. Thefrequently-used damage parameters for evaluating rubber materials fatigue-life have beenintroduced. And then bearing and deformation results of rubber elements have been analysed.Thus, tensor form fatigue-life prediction formula, new combined damage parameters forevaluating rubber materials fatigue-life and the reliability distribution probability linearfunction of the rubber materials fatigue-life has been obtained.
2) The methodology for studying the force-displacement calculation accuracy of rubberisolator has been developed. The influence of the materials strain combination on the fittingaccuracy of the five types of constitutive model parameters has been analysed. The mechanicscalculation method of the rubber isolators has been studied. Then, the influence of thedifference constitutive model and materials strain combination on the calculation results hasbeen obtained by finite element method and simulation test method. The experiment methodand results in this part can shed useful light on the design of the rubber isolator and provideexperimental support to theoretical analysis and simulation of the rubber isolator.
3) The fatigue test methodology of rubber materials has been designed. The incentive loadof rubber fatigue testing has been made parameter evaluation. And load nature has beenclassified and transformed. The experiment subject, such as the rubber material specimen,rubber test column and annular rubber test column, has been designed. The test methods, testprinciple and the actual measurement and calculation of part of the evaluation parameters have been studied. And then, the relevant conclusion of the fatigue test method and principleof rubber suspension has been obtained. The experimental method and principle in this partare very useful for fatigue test design of rubber materials.
4) The fatigue failure prediction method of rubber materials has been developed. Fatiguedamage equivalent parameters have been calculated by using the finite element method. Andthe stress and strain field has been analysed. The fatigue-life tendency of the rubber materialsparts has been predicted by employing the new fatigue prediction model. And a more accuratefatigue life prediction formula of carbon black filled natural rubber has been obtained. Then,the reliability analysis of the distribution probability of the rubber fatigue life has been carriedout by using the statistic method.
1）建立了橡胶疲劳寿命预测模型。在介绍目前常用评价橡胶疲劳寿命的损伤参量和橡胶元件疲劳寿命的预测模型基础上，通过对橡胶元件承载变形结果的分析，创建了橡胶元件张量形式的疲劳寿命预测公式、新的组合疲劳寿命评价损伤参量以及橡胶疲劳寿命可靠性分布概率的线性函数。
2）提出了橡胶隔振器力-位移计算精度的研究方法。通过对材料应变组合对五种本构模型参数拟合精度影响的分析以及橡胶隔振器力学计算方法探讨的基础上，采用有限元计算与模拟测试的方法得出不同本构模型和不同材料应变组合对其计算结果的影响。此部分的试验方法和结论不仅对橡胶隔振器的设计具有一定的参考价值，而且能为橡胶隔振器的理论分析和模拟计算提供试验支持。
3）设计了橡胶疲劳的试验方法。对橡胶疲劳试验中的激励载荷进行参数评价及载荷性质进行分类转化，设计了橡胶材料疲劳试验对象（如橡胶试片、橡胶试柱、环形橡胶试柱）并对其试验方法、试验原理、部分评价参数实测计算进行一系列的分析研究，对橡胶悬置疲劳试验方法及原理提出了相应结论。此部分的试验方法、试验原理对橡胶元件的疲劳试验设计具有典型借鉴意义。
4）提出了橡胶疲劳寿命的预测方法。利用有限元方法计算橡胶疲劳损伤等效参量、分析了橡胶元件应力、应变，进而运用新的疲劳预测模型预测了在不同承载应变形式下橡胶材料、橡胶元件的疲劳寿命趋势，得出了较为精确的填充型炭黑天然橡胶元件的疲劳寿命预测公式。随后采用统计方法对橡胶疲劳寿命的分布概率进行了统计学上的可靠性分析。
Rubber isolators are widely used in the vibration isolation system of automobile. This isprimarily due to their excellent vibration isolation properties, good water and air resistance,good cushion performance, high tensile strength and high wear resistance. However, theresearch undertaken so far was mainly focused on the damping properties of the rubbercomponents, and only a few investigations were on their fatigue durability. It is accepted thatbefore the full benefit of the rubber isolators can be realised in the automobile industry, afurther study on the fatigue properties of the rubber isolators has yet to be seen especially inChina. In this research project, to improve the fatigue and endurance performance of therubber isolators, the fatigue properties test and fatigue-life prediction method of rubberisolators have been studied based on the basic fatigue-life prediction theory of the rubberisolators. It is with reason to believe that the achievement of this research would have asignificant value in both academic and engineering fields. The following summarises the maincontents of this research:
1) Fatigue-life prediction model of rubber materials has been established. Thefrequently-used damage parameters for evaluating rubber materials fatigue-life have beenintroduced. And then bearing and deformation results of rubber elements have been analysed.Thus, tensor form fatigue-life prediction formula, new combined damage parameters forevaluating rubber materials fatigue-life and the reliability distribution probability linearfunction of the rubber materials fatigue-life has been obtained.
2) The methodology for studying the force-displacement calculation accuracy of rubberisolator has been developed. The influence of the materials strain combination on the fittingaccuracy of the five types of constitutive model parameters has been analysed. The mechanicscalculation method of the rubber isolators has been studied. Then, the influence of thedifference constitutive model and materials strain combination on the calculation results hasbeen obtained by finite element method and simulation test method. The experiment methodand results in this part can shed useful light on the design of the rubber isolator and provideexperimental support to theoretical analysis and simulation of the rubber isolator.
3) The fatigue test methodology of rubber materials has been designed. The incentive loadof rubber fatigue testing has been made parameter evaluation. And load nature has beenclassified and transformed. The experiment subject, such as the rubber material specimen,rubber test column and annular rubber test column, has been designed. The test methods, testprinciple and the actual measurement and calculation of part of the evaluation parameters have been studied. And then, the relevant conclusion of the fatigue test method and principleof rubber suspension has been obtained. The experimental method and principle in this partare very useful for fatigue test design of rubber materials.
4) The fatigue failure prediction method of rubber materials has been developed. Fatiguedamage equivalent parameters have been calculated by using the finite element method. Andthe stress and strain field has been analysed. The fatigue-life tendency of the rubber materialsparts has been predicted by employing the new fatigue prediction model. And a more accuratefatigue life prediction formula of carbon black filled natural rubber has been obtained. Then,the reliability analysis of the distribution probability of the rubber fatigue life has been carriedout by using the statistic method.
引文
[1] Lewitzke C., Lee P. Application of Elastomeric Components for Noise and VibrationIsolation in the Automotive Industry [C]. SAE Technical Paper,2001-01-1447
[2] Shangguan Wen-Bin. Engine mounts and powertrain mounting systems: a review[J].International Journal of Vehicle Design,2009,49(4):22
[3]姜莞.商用车动力总成悬置性能模拟与疲劳寿命预测研究[D]:吉林大学,2011
[4] Degrange J. M., Thomine M., Kapsa Ph, et al. Influence of viscoelasticity on thetribological behaviour of carbon black filled nitrile rubber (NBR) for lip sealapplication[J]. Wear,2005,259(1-6):684-692
[5] J. Charlton D., J. Yang. A review of methods to characterize rubber elastic behaviour foruse in finite element analysis[J]. Rubber chemistry and technology,1994,67(481-503)
[6] Mars W.V., Fatemi A. A literature survey on fatigue analysis approaches for rubber[J].International Journal of Fatigue,2002,24(2002)(12)
[7] Andre N Cailletaud G, Piques R. Haigh diagram for fatigue crack initiation prediction ofnatural rubber components[J]. Kautschuk Und Gummi Kunstoffe,1999,52(120-123)
[8] MARS W. V. Factors That Affect the Fatigue Life of Rubber:A Literature Survey[J].Rubber chemistry and technology,2004,76(391-412)
[9] Hudson C. Michael, Seward Sue K. A literature review and inventory of the effects ofenvironment on the fatigue behavior of metals[J]. Engineering FractureMechanics,1976,8(2):315-329
[10] Saintier N., Cailletaud G., Piques R. Cyclic loadings and crystallization of natural rubber:An explanation of fatigue crack propagation reinforcement under a positive loadingratio[J]. Materials Science and Engineering: A,2011,528(3):1078-1086
[11] Merckel Yannick, Diani Julie, Brieu Mathias, et al. Experimental characterization andmodelling of the cyclic softening of carbon-black filled rubbers[J]. Materials Scienceand Engineering: A,2011,528(29–30):8651-8659
[12] Andriyana A., Saintier N., Verron E. Configurational Mechanics and Critical PlaneApproach: Concept and application to fatigue failure analysis of rubberlike materials[J].International Journal of Fatigue,2010,32(10):1627-1638
[13] Harbour Ryan J., Fatemi Ali, Mars Will V. Fatigue life analysis and predictions for NRand SBR under variable amplitude and multiaxial loading conditions[J]. InternationalJournal of Fatigue,2008,30(7):1231-1247
[14] Harbour Ryan J., Fatemi A. L. I., Mars Will V. Fatigue crack growth of filled rubberunder constant and variable amplitude loading conditions[J]. Fatigue&Fracture ofEngineering Materials&Structures,2007,30(7):640-652
[15] Andriyana A., Verron E. Prediction of fatigue life improvement in natural rubber usingconfigurational stress[J]. International Journal of Solids and Structures,2007,44(7-8):2079-2092
[16] Troshchenko V. Nonlocalized Fatigue Damage of Metals and Alloys. Part1. Inelasticity,Investigation Methods, and Results[J]. Strength of Materials,2005,37(4):337-356
[17] Mars W. V., Fatemi A. Multiaxial fatigue of rubber: Part II: experimental observationsand life predictions[J]. Fatigue&Fracture of Engineering Materials&Structures,2005,28(6):523-538
[18] Verron Erwan, Le Cam Jean-Beno t, Gornet Laurent. A multiaxial criterion for cracknucleation in rubber[J]. Mechanics Research Communications,2005,33(4):493-498
[19] Saintier N., Cailletaud G., Piques R. Multiaxial fatigue life prediction for a naturalrubber[J]. International Journal of Fatigue,2006,28(5-6):530-539
[20] Kazakeviciute-Makovska Rasa. Experimentally determined properties of softeningfunctions in pseudo-elastic models of the Mullins effect[J]. International Journal ofSolids and Structures,2007,44(11-12):4145-4157
[21] You Bong-Ryul, Lee Soon-Bok. A critical review on multiaxial fatigue assessments ofmetals[J]. International Journal of Fatigue,1996,18(4):235-244
[22] Hudson C. Michael, Seward Sue K. A literature review and inventory of the effects ofenvironment on the fatigue behavior of metals[J]. Engineering FractureMechanics,1976,8(2):315-329
[23] MacDonald Douglas E. Ultrasonic frequency metal fatigue: A review of theinvestigations of the institute for the study of fatigue (fracture) and (structural)reliability[J]. Engineering Fracture Mechanics,1976,8(1):17-29
[24] Cadwell S. M., Merrill R. A., Sloman C. M., et al. Dynamic Fatigue Life of Rubber[J].Industrial&Engineering Chemistry Analytical Edition,1940,12(1):19-23
[25] Fielding J.H. Flex life and crystallization of synthetic rubber[J]. Ind EngChem,1943,(35):1259-1261
[26] Roberts B J Benzies J B. Relationship between uniaxial and equibiaxial fatigue fatigue ingum and carbon-black-filled vulcanizates[J]. Plastics and Rnbber:Materials andApplications,1978,3(49-54)
[27] Jankovich E., Leblanc F., Durand M., et al. A finite element method for the analysis ofrubber parts, experimental and analytical assessment[J]. Computers&Structures,1981,14(5–6):385-391
[28] Ro HS. Modeling and interpretation of fatigue failure initiation in rubber related topneumatic tires[D]: Purdue University,1989
[29] Kim W. D., a H. J. Lee, a J. Y. Kim, et al. Fatigue life estimation of an engine rubbermount[J]. International Journal of Fatigue,2004,26(553-560)
[30] Chang-Su Woo Wan-Doo Kim, Jae-Do Kwon. A study on the material properties andfatigue life prediction of natural rubber component[J]. Materials Science andEngineering:A,2006,483–484(376-381)
[31] Li Qian, Zhao Jian-cai, Zhao Bo. Fatigue life prediction of a rubber mount based on testof material properties and finite element analysis[J]. Engineering FailureAnalysis,2009,16(7):2304-2310
[32] Mars William Vernon. Multiaxial Fatigue of Rubber[D]: The University of Toledo,2001
[33] An application of a new electromagnetic sensor to real-time monitoring of fatigue crackgrowth in thin metal plates: Namkung, M.; Fulton, J.P.; Wincheski, B.; Clendenin, C.G.Review of Progress in Quantitative Nondestructive Evaluation, Brunswick, Maine(United States),1–6Aug.1993. Vol.13B, pp.1633–1640. Edited by D.O. Thompsonand D.E. Chimenti. Plenum Press (1994) ISBN0-306-44731-2[J]. NDT& EInternational,1995,28(4):246
[34] Abraham F., Alshuth T., Hannover, et al. The Dependence on Mean Stress and StressAmplitude of the Fatigue Life of Elastomers [M]. DIK-Publikation134, IRC2001.2001
[35] F. Abraham T. Alshuth and S. Jerrams. The effect of minimum stress and stressamplitude on the fatigue life of non strain crystallising elastomers[J]. Materials&Design,2005,26(3):239-245
[36] Luo R. K., Wu W. X. Fatigue failure analysis of anti-vibration rubber spring[J].Engineering Failure Analysis,2006,13(1):110-116
[37] Luo R.K., Morte W.J., Wu X.P. Fatigue failure investigation on anti-vibration springs[J].Engineering Failure Analysis,2009,16(5):1366-1378
[38] TRELOAR L. R. G. The Physics of Rubber Elasticity[M]. Oxford University Press,1975
[39]陈鹏,曾建谋,王文涛等.基于Pro/Toolkit二次开发的参数化程序设计[J].机电工程技术,2005,(06):78-81
[40]彭美春,赵锌泽,许志刚等.大型城市客车加速模拟工况排放特性的实验研究[J].环境污染与防治,2005,(03):175-177
[41]刘宇艳,万志敏.橡胶疲劳性能研究进展[J].合成橡胶工业,2000,(02):128-131
[42]汪艳萍.橡胶材料多轴疲劳寿命及微观结构研究[D]:天津大学,2007
[43] Harbour Ryan J., Fatemi Ali, Mars Will V. Constitutive Behavior and TemperatureEffects in NR and SBR Under Variable Amplitude and Multiaxial Loading Conditions[J].Journal of Engineering Materials and Technology,2008,130(1):011005-011011
[44] Zine A., Benseddiq N., Abdelaziz M. Na T, et al. Prediction of rubber fatigue life undermultiaxial loading[J]. Fatigue&Fracture of Engineering Materials&Structures,2006,29(3):267-278
[45] Zine A., Benseddiq N., Na t Abdelaziz M. Rubber fatigue life under multiaxial loading:Numerical and experimental investigations[J]. International Journal ofFatigue,2011,33(10):1360-1368
[46]汪艳萍.橡胶材料多轴疲劳寿命及微观结构研究[D].天津市:天津大学,2007
[47]王文涛,上官文斌,段小成等.基于线性疲劳累计损伤橡胶悬置疲劳寿命预测研究[J].机械工程学报,2012,(10):56-65
[48] Eshelby J. D. The Continuum Theory of Lattice Defects [M]//S. Frederick and T. David.Solid State Physics. Academic Press.1956:79-144
[49] Eshelby J. D. The elastic field of a crack extending non-uniformly under generalanti-plane loading[J]. Journal of the Mechanics and Physics of Solids,1969,17(3):177-199
[50] Verron E., Andriyana A. Definition of a new predictor for multiaxial fatigue cracknucleation in rubber[J]. Journal of the Mechanics and Physics of Solids,2008,56(2):417-443
[51] Saintier.N. Multiaxial fatigue life of a natural rubber: crack initiation mechanisms andlocal fatigue life criterion, dissertation,;2001[D]. Paris Ecole des Mines de Paris,2001
[52] Saintier N., Cailletaud G., Piques R. Crack initiation and propagation under multiaxialfatigue in a natural rubber[J]. International Journal of Fatigue,2006,28(1):61-72
[53] Bayraktar E., Bessri K., Bathias C. Deformation behaviour of elastomeric matrixcomposites under static loading conditions[J]. Engineering FractureMechanics,2008,75(9):2695-2706
[54] Mars W. V., Fatemi A. Fatigue crack nucleation and growth in filled natural rubber[J].Fatigue&Fracture of Engineering Materials&Structures,2003,26(9):779-789
[55] Rivlin.R.S. Large elastic deformations of isotropic materials IV, Further developmentsof the general theory[J]. Philosophical Transactions of the Royal Society of London1948b,A241(379-397)
[56] W.V. Mars. Experimental Investigation of Multiaxial Fatigue in Rubber [M].6thInternational Conference on Biaxial/Multiaxial Fatigue and Fracture. Lisbon, Portugal;Elsevier Science.2001
[57] Mars.W. V. Analysis of Fatigue Life under Complex Loading: Revisiting Cadwell MerillSloman and Yost [M]. a meeting of the Rubber Division, American Chemical SocietyGrand Rapids. Michigan.2004
[58] Mars W. V., Fatemi A. Observations of the Constitutive Response and Characterizationof Filled Natural Rubber Under Monotonic and Cyclic Multiracial Stress States[J].Journal of Engineering Materials and Technology,2004,126/19(19-28)
[59] W.V. Mars A. Fatemi Multiaxial stress effects on fatigue behavior of filled naturalrubber[J]. International Journal of Fatigue,2006,28(521–529)
[60] Mars W., Fatemi A. Nucleation and growth of small fatigue cracks in filled naturalrubber under multiaxial loading[J]. Journal of Materials Science,2006,41(22):7324-7332
[61] Mars W. V., Fatemi A. Multiaxial stress effects on fatigue behavior of filled naturalrubber[J]. International Journal of Fatigue,2006,28(5-6):521-529
[62]谢新星.橡胶隔振器单轴疲劳寿命评价方法及预测研究[D]:华南理工大学,2011
[63]丁智平,陈吉平,宋传江等.橡胶弹性减振元件疲劳裂纹扩展寿命分析[J].机械工程学报,2010,(22)
[64]刘建勋,黄友剑,刘柏兵等.一种橡胶弹性元件疲劳寿命预测方法的研究[J].电力机车与城轨车辆,2011,(03):12-14+27
[65]张友南,杨军,陈忠海.天然橡胶制品抗疲劳性能的因素简析[J].世界橡胶工业,2002,(06):35-39
[66]黄友剑王明星,张友南.有限元分析中超弹材料模型采用的弹性体试验[J].特种橡胶制品,2001,(05)
[67]左国兵,王进,林达文等.金属-橡胶复合锥形弹簧的试验研究[J].铁道车辆,2005,(03):12-15+34
[68]王进,左国兵.疲劳试验在橡胶减振制品寿命预测中的应用[J].铁道车辆,2005,(07):7-10+45
[69]左国兵,王进,林达文等.金属-橡胶复合锥形弹簧的试验研究[J].铁道车辆,2005,(02):9-12+13
[70]王尤颜,白鸿柏,侯军芳.金属橡胶材料疲劳损伤性能研究[J].机械工程学报,2011,(02):65-71
[71]侯军芳,白鸿柏,李冬伟等.环境温度对金属橡胶材料力学特性和阻尼性能的影响研究[A].2006
[72]丁家松,张欢,童宗鹏等.船用橡胶隔振器寿命评估方法研究[J].振动与冲击,2010,(12):230-233+250
[73]王文涛,上官文斌,段小成.超弹性本构模型对橡胶隔振器静态特性预测影响的研究[J].汽车工程,2012,(06):544-550+539
[74] Treloar.L.R.G. The elasticity of a network of long-chain molecules[J]. Transactions ofFaraday Society,1946,42(83-94)
[75] S. M. Cadwell R. A. Merrill, C. M. Sloman, F. L. Yost. Dynamic Fatigue Life ofRubber[J]. Indutrial and Engineering Chemistry,1940,12(1):19-23
[76] Woo Chang-Su, Kim Wan-Doo, Kwon Jae-Do. A study on the material properties andfatigue life prediction of natural rubber component[J]. Materials Science andEngineering: A,2008,(483-484):376-381
[77] Moon Seong-In, Cho Il-Je, Woo Chang-Su, et al. Study on determination of durabilityanalysis process and fatigue damage parameter for rubber component[J]. Journal ofMechanical Science and Technology,2011,25(5):1159-1165
[78] Park C., Shim H., Choi D., et al. Shape optimization of rubber isolators in automotivecooling modules for the maximization of vibration isolation and fatigue life[J].International Journal of Automotive Technology,2012,13(1):61-75
[79]赵永翔.低周疲劳短裂纹行为和可靠性分析[D],1998
[80]黄卓,李苏军,郭波.基于混合Gamma分布的通用可靠性寿命数据拟合方法[J].航空学报,2008,(02):379-386
[81]王翼. Gamma分布函数的研究[D]:大连理工大学,2010
[82] Minguez M. G., Royo J. Evaluation of results of tension fatigue resistance tests onvulcanized rubber[J]. Polymer Testing,1980,1(4):287-302
[83]董聪.疲劳寿命分布模型的统一描述[J].强度与环境,1996,(03)
[84]吕箴,姚卫星.小样本下估计疲劳寿命分布的历史数据融合方法[J].应用力学学报,2008,(02):
[85] Abernethy Robert B., Engineers Society of Automotive. The new Weibull handbook[M].R.B. Abernethy,1998
[86]鄢君辉魏建锋,赵康等.拉-拉变幅载荷下45钢缺口件疲劳寿命分布的预测及其验证[J].机械工程材料,2001,(07)
[87] Yew M. C., Chou C. Y., Huang C. S., et al. The solder on rubber (SOR) interconnectiondesign and its reliability assessment based on shear strength test and finite elementanalysis[J]. Microelectronics Reliability,2006,46(9–11):1874-1879
[88] Wang Chung-Ho, Hsu Yi. Enhancing rubber component reliability by response model[J].Computers& Industrial Engineering,2009,57(3):806-812
[89] Govindjee Sanjay, Simo Juan. A micro-mechanically based continuum damage modelfor carbon black-filled rubbers incorporating Mullins' effect[J]. Journal of the Mechanicsand Physics of Solids,1991,39(1):87-112
[90] Royo J. Fatigue testing of rubber materials and articles[J]. Polymer Testing,1992,11(5):325-344
[91] Yeoh.O.H., Fleming P.D. A new attempt to reconcile the statistical andphenomenological theories of rubber elasticity[J]. J Polymer Sci,1997,(Part.B):1919-1931
[92] Meissner Bohumil, Matejka Libor. A structure-based constitutive equation forfiller-reinforced rubber-like networks and for the description of the Mullins effect[J].Polymer,2006,47(23):7997-8012
[93] Yew Ming-Chih, Chou Chan-Yen, Chiang Kuo-Ning. Reliability assessment for solderswith a stress buffer layer using ball shear strength test and board-level finite elementanalysis[J]. Microelectronics Reliability,2007,47(9–11):1658-1662
[94] Ayoub G., Na t-Abdelaziz M., Za ri F., et al. A continuum damage model for thehigh-cycle fatigue life prediction of styrene-butadiene rubber under multiaxial loading[J].International Journal of Solids and Structures,2011,48(18):2458-2466
[95] Mars W. V., Fatemi A. Multiaxial fatigue of rubber: Part I: equivalence criteria andtheoretical aspects[J]. Fatigue&Fracture of Engineering Materials&Structures,2005,28(6):515-522
[96] ABAQUS Inc.The Theory Manual[M]. Hibbit, Karlsson&Sorensen (HKS),2009
[97] J. Marin. Interpretation of fatigue strengths for combined stresses [M]. Proceedings ofthe international conference on fatigue of metals. London; Institution of MechanicalEngineers.1956:184-194
[98] B Crossland. Effect of large hydrostatic pressure on the torsional fatigue strengh of analloy steel [M]. International conference on fatigue of metals London. London.1959:138-149
[99] V.MARS W., A.FATEMI. A phenomenological model for the effect of R ratio onfatigue of strain crystallizing rubbers[M]. Akron, OH, ETATS-UNIS:AmericanChemical Society,2003
[100]姚斌辉.基于载荷谱的橡胶悬置疲劳寿命预测与试验研究[D].广州:华南理工大学,2012
[101]尚德广,王德俊.多轴疲劳强度[M].北京:科学出版社,2007
[102]吉林工业大学,武汉工学院.汽车可靠性设计[M].北京:机械工业出版社,1991:
[103] Yang Guangbin. Life Cycle Reliability Engineering[M]. USA:JOHN WI-LEY&SONS,2007
[104]董聪戎海武,夏人伟.疲劳寿命分布模型及其拟合优度检验[J].航空学报,1995,(02)
[105]蔡全才,徐勤丰,姜庆五等.含区间数据Gamma分布的参数估计[J].中国卫生统计,2005,(02):71-73+79
[106]靳慧.工程机械金属结构系统疲劳可靠性分析研究[D],2003
[107]钱文学.某型航空发动机低压压气机轮盘疲劳可靠性分析[D],2006
[108]徐明.橡胶类超弹性材料非线性本构关系研究和有限元分析[D].北京:北京航天航空大学
[109] Gillibert Jean, Brieu Mathias, Diani Julie. Anisotropy of direction-based constitutivemodels for rubber-like materials[J]. International Journal of Solids andStructures,2010,47(5):640-646
[110]郭巍,郑振忠,吴行等.实心橡胶轮胎非线性有限元分析[J].机械设计与制造,2011,(06)
[111]王寿梅赵国兴.橡胶变形响应的非线性有限元分析[J].北京航空航天大学学报,1996,(03)
[112]张汝清,詹先义.非线性有限元分析[M].重庆:重庆出版社,1991
[113] Ha Y. S., Cho J. R., Kim T. H., et al. Finite element analysis of rubber extrusion formingprocess for automobile weather strip[J]. Journal of Materials ProcessingTechnology,2008,201(1–3):168-173
[114] Shangguan Wen-Bin, lu Zhen-Hua, J Shi J. Finite element analysis of static elasticcharacteristics of the rubber isolators in automotive dynamic systems[D],2003
[115] C. Boyce M., M Arruda E. Constitutive models of rubber elasticity: a review[J]. RubberChemistry Technology,2000,73,(504-523)
[116]郭仲衡.非线性弹性理论[M].北京:科学出版社,1980
[117] Guo Z., Sluys L.J. Constitutive modelling of hyperelastic rubber-like materials[J].2008
[118]特雷劳尔L.R.G,王梦姣,王培国等译.橡胶弹性物理学[M].北京:化学工业出版社,1982
[119] Ali Aidy, Hosseini M., Sahari B. B. A Review of Constitutive Models for Rubber-LikeMaterials[J]. American Journal of Engineering and Applied Sciences,2010,3(1):232-239
[120] Ling Yun. Constitutive models, load-deflection relations, and instabilities of elastomericmaterials and structures[D]: State University of New York at Binghamto,1992
[121]朱艳峰.橡胶材料的本构模型[J].橡胶工业,2006
[122]李晓芳.橡胶材料的超弹性本构模型[J].弹性体,2005,15(1)
[123] Arruda Ellen M., Boyce Mary C. A three-dimensional constitutive model for the largestretch behavior of rubber elastic materials[J]. Journal of the Mechanics and Physics ofSolids,1993,41(2):389-412
[124] Avril Stéphane, Bonnet Marc, Bretelle Anne-Sophie, et al. Overview of IdentificationMethods of Mechanical Parameters Based on Full-field Measurements[J]. ExperimentalMechanics,2008,48(4):381-402
[125] Bergstr m J. S., Boyce M. C. Large strain time-dependent behavior of filledelastomers[J]. Mechanics of Materials,2000,32(11):627-644
[126] Marckmann G., Verron E., Gornet L., et al. A theory of network alteration for theMullins effect[J]. Journal of the Mechanics and Physics of Solids,2002,50(9):2011-2028
[127] Zhong Allan."A constitutive model for the Mullins effect with permanent set in aparticle-reinforced rubber" by A. Dorfmann and R.W. Ogden[J]. International Journal ofSolids and Structures,2005,42(13):3967-3969
[128]孟祥宾,郑志峰.试验链节数不同时,国产12B滚子链条疲劳寿命的可靠性分析与计算[J].吉林大学学报(工学版),1984,(02)
[129]孙亮.农用拖车疲劳寿命的可靠性分析[J].农业机械学报,1987,(02)
[130]杨德滋车惠民.混凝土在重复荷载作用下疲劳寿命分布的概率方法研究[J].铁道学报,1990,(04)
[131]罗毅，高镇同.疲劳寿命可靠性分析模型[J].机械强度,1994,(03)
[132] Saintier N., Cailletaud G., Piques R. Multiaxial fatigue life prediction for a naturalrubber[J]. International Journal of Fatigue,2005,28(5-6):530-539
[133] Legorju-jago K., Bathias C. Fatigue initiation and propagation in natural and syntheticrubbers[J]. International Journal of Fatigue,2002,24(2-4):85-92
[134] Ryan J. Harbour Ali Fatemi b, Will V. Mars Fatigue life analysis and predictions forNR and SBR under variable amplitude and multiaxial loading conditions[J].International Journal of Fatigue,2007,30(7):1231-1247
[135] Flamm M., Spreckels J., Steinweger T., et al. Effects of very high loads on fatigue life ofNR elastomer materials[J]. International Journal of Fatigue,2011,33(9):1189-1198
[136]王文涛,上官文斌,段小成等.基于线性疲劳累计损伤橡胶悬置疲劳寿命预测研究[J].机械工程学报,2012,(10)
[137] Andrews Clinton J. An end-use approach to reliability investment analysis[J]. EnergyEconomics,1992,14(4):248-254
[138] Breitung K., Casciati F., Faravelli L. Reliability based stability analysis for activelycontrolled structures[J]. Engineering Structures,1998,20(3):211-215
[139]王飞,张方晓.机械热弱链设计及其安全性评估方法研究[J].兵工学报,2011,(05):632-635
[140] Rice John A. Mathematical Statistics and Data Analysis[M]. California:Duxbury,1995
[141] Mars W., Fatemi A. A novel specimen for investigating the mechanical behavior ofelastomers under multiaxial loading conditions[J]. Experimental Mechanics,2004,44(2):136-146
[142] Harbour R., Fatemi A., Mars W. V. Fatigue Crack Growth of Rubber under VariableAmplitude Loading [C]. the9th International Fatigue Congress. Atlanta, Georgia
[143] Lü Peiyin, Li Qingbin, Song Yupu. Damage constitutive of concrete under uniaxialalternate tension-compression fatigue loading based on double bounding surfaces[J].International Journal of Solids and Structures,2004,41(11-12):3151-3166
[144] Zhi Suo, Gun Wong Wing, Hui Luo Xiao, et al. Evaluation of fatigue crack behavior inasphalt concrete pavements with different polymer modifiers[J]. Construction andBuilding Materials,2012,27(1):117-125
[145] Jordon J. B., Bernard J. D., Newman Jr J. C. Quantifying microstructurally small fatiguecrack growth in an aluminum alloy using a silicon-rubber replica method[J].International Journal of Fatigue,2012,36(1):206-210
[146]何小静.橡胶隔振器静态特性计算与建模方法的研究[D]：华南理工大学,2012
[147]姚斌辉.基于载荷谱的橡胶悬置疲劳寿命预测与试验研究[D]：华南理工大学,2012
[2] Shangguan Wen-Bin. Engine mounts and powertrain mounting systems: a review[J].International Journal of Vehicle Design,2009,49(4):22
[3]姜莞.商用车动力总成悬置性能模拟与疲劳寿命预测研究[D]:吉林大学,2011
[4] Degrange J. M., Thomine M., Kapsa Ph, et al. Influence of viscoelasticity on thetribological behaviour of carbon black filled nitrile rubber (NBR) for lip sealapplication[J]. Wear,2005,259(1-6):684-692
[5] J. Charlton D., J. Yang. A review of methods to characterize rubber elastic behaviour foruse in finite element analysis[J]. Rubber chemistry and technology,1994,67(481-503)
[6] Mars W.V., Fatemi A. A literature survey on fatigue analysis approaches for rubber[J].International Journal of Fatigue,2002,24(2002)(12)
[7] Andre N Cailletaud G, Piques R. Haigh diagram for fatigue crack initiation prediction ofnatural rubber components[J]. Kautschuk Und Gummi Kunstoffe,1999,52(120-123)
[8] MARS W. V. Factors That Affect the Fatigue Life of Rubber:A Literature Survey[J].Rubber chemistry and technology,2004,76(391-412)
[9] Hudson C. Michael, Seward Sue K. A literature review and inventory of the effects ofenvironment on the fatigue behavior of metals[J]. Engineering FractureMechanics,1976,8(2):315-329
[10] Saintier N., Cailletaud G., Piques R. Cyclic loadings and crystallization of natural rubber:An explanation of fatigue crack propagation reinforcement under a positive loadingratio[J]. Materials Science and Engineering: A,2011,528(3):1078-1086
[11] Merckel Yannick, Diani Julie, Brieu Mathias, et al. Experimental characterization andmodelling of the cyclic softening of carbon-black filled rubbers[J]. Materials Scienceand Engineering: A,2011,528(29–30):8651-8659
[12] Andriyana A., Saintier N., Verron E. Configurational Mechanics and Critical PlaneApproach: Concept and application to fatigue failure analysis of rubberlike materials[J].International Journal of Fatigue,2010,32(10):1627-1638
[13] Harbour Ryan J., Fatemi Ali, Mars Will V. Fatigue life analysis and predictions for NRand SBR under variable amplitude and multiaxial loading conditions[J]. InternationalJournal of Fatigue,2008,30(7):1231-1247
[14] Harbour Ryan J., Fatemi A. L. I., Mars Will V. Fatigue crack growth of filled rubberunder constant and variable amplitude loading conditions[J]. Fatigue&Fracture ofEngineering Materials&Structures,2007,30(7):640-652
[15] Andriyana A., Verron E. Prediction of fatigue life improvement in natural rubber usingconfigurational stress[J]. International Journal of Solids and Structures,2007,44(7-8):2079-2092
[16] Troshchenko V. Nonlocalized Fatigue Damage of Metals and Alloys. Part1. Inelasticity,Investigation Methods, and Results[J]. Strength of Materials,2005,37(4):337-356
[17] Mars W. V., Fatemi A. Multiaxial fatigue of rubber: Part II: experimental observationsand life predictions[J]. Fatigue&Fracture of Engineering Materials&Structures,2005,28(6):523-538
[18] Verron Erwan, Le Cam Jean-Beno t, Gornet Laurent. A multiaxial criterion for cracknucleation in rubber[J]. Mechanics Research Communications,2005,33(4):493-498
[19] Saintier N., Cailletaud G., Piques R. Multiaxial fatigue life prediction for a naturalrubber[J]. International Journal of Fatigue,2006,28(5-6):530-539
[20] Kazakeviciute-Makovska Rasa. Experimentally determined properties of softeningfunctions in pseudo-elastic models of the Mullins effect[J]. International Journal ofSolids and Structures,2007,44(11-12):4145-4157
[21] You Bong-Ryul, Lee Soon-Bok. A critical review on multiaxial fatigue assessments ofmetals[J]. International Journal of Fatigue,1996,18(4):235-244
[22] Hudson C. Michael, Seward Sue K. A literature review and inventory of the effects ofenvironment on the fatigue behavior of metals[J]. Engineering FractureMechanics,1976,8(2):315-329
[23] MacDonald Douglas E. Ultrasonic frequency metal fatigue: A review of theinvestigations of the institute for the study of fatigue (fracture) and (structural)reliability[J]. Engineering Fracture Mechanics,1976,8(1):17-29
[24] Cadwell S. M., Merrill R. A., Sloman C. M., et al. Dynamic Fatigue Life of Rubber[J].Industrial&Engineering Chemistry Analytical Edition,1940,12(1):19-23
[25] Fielding J.H. Flex life and crystallization of synthetic rubber[J]. Ind EngChem,1943,(35):1259-1261
[26] Roberts B J Benzies J B. Relationship between uniaxial and equibiaxial fatigue fatigue ingum and carbon-black-filled vulcanizates[J]. Plastics and Rnbber:Materials andApplications,1978,3(49-54)
[27] Jankovich E., Leblanc F., Durand M., et al. A finite element method for the analysis ofrubber parts, experimental and analytical assessment[J]. Computers&Structures,1981,14(5–6):385-391
[28] Ro HS. Modeling and interpretation of fatigue failure initiation in rubber related topneumatic tires[D]: Purdue University,1989
[29] Kim W. D., a H. J. Lee, a J. Y. Kim, et al. Fatigue life estimation of an engine rubbermount[J]. International Journal of Fatigue,2004,26(553-560)
[30] Chang-Su Woo Wan-Doo Kim, Jae-Do Kwon. A study on the material properties andfatigue life prediction of natural rubber component[J]. Materials Science andEngineering:A,2006,483–484(376-381)
[31] Li Qian, Zhao Jian-cai, Zhao Bo. Fatigue life prediction of a rubber mount based on testof material properties and finite element analysis[J]. Engineering FailureAnalysis,2009,16(7):2304-2310
[32] Mars William Vernon. Multiaxial Fatigue of Rubber[D]: The University of Toledo,2001
[33] An application of a new electromagnetic sensor to real-time monitoring of fatigue crackgrowth in thin metal plates: Namkung, M.; Fulton, J.P.; Wincheski, B.; Clendenin, C.G.Review of Progress in Quantitative Nondestructive Evaluation, Brunswick, Maine(United States),1–6Aug.1993. Vol.13B, pp.1633–1640. Edited by D.O. Thompsonand D.E. Chimenti. Plenum Press (1994) ISBN0-306-44731-2[J]. NDT& EInternational,1995,28(4):246
[34] Abraham F., Alshuth T., Hannover, et al. The Dependence on Mean Stress and StressAmplitude of the Fatigue Life of Elastomers [M]. DIK-Publikation134, IRC2001.2001
[35] F. Abraham T. Alshuth and S. Jerrams. The effect of minimum stress and stressamplitude on the fatigue life of non strain crystallising elastomers[J]. Materials&Design,2005,26(3):239-245
[36] Luo R. K., Wu W. X. Fatigue failure analysis of anti-vibration rubber spring[J].Engineering Failure Analysis,2006,13(1):110-116
[37] Luo R.K., Morte W.J., Wu X.P. Fatigue failure investigation on anti-vibration springs[J].Engineering Failure Analysis,2009,16(5):1366-1378
[38] TRELOAR L. R. G. The Physics of Rubber Elasticity[M]. Oxford University Press,1975
[39]陈鹏,曾建谋,王文涛等.基于Pro/Toolkit二次开发的参数化程序设计[J].机电工程技术,2005,(06):78-81
[40]彭美春,赵锌泽,许志刚等.大型城市客车加速模拟工况排放特性的实验研究[J].环境污染与防治,2005,(03):175-177
[41]刘宇艳,万志敏.橡胶疲劳性能研究进展[J].合成橡胶工业,2000,(02):128-131
[42]汪艳萍.橡胶材料多轴疲劳寿命及微观结构研究[D]:天津大学,2007
[43] Harbour Ryan J., Fatemi Ali, Mars Will V. Constitutive Behavior and TemperatureEffects in NR and SBR Under Variable Amplitude and Multiaxial Loading Conditions[J].Journal of Engineering Materials and Technology,2008,130(1):011005-011011
[44] Zine A., Benseddiq N., Abdelaziz M. Na T, et al. Prediction of rubber fatigue life undermultiaxial loading[J]. Fatigue&Fracture of Engineering Materials&Structures,2006,29(3):267-278
[45] Zine A., Benseddiq N., Na t Abdelaziz M. Rubber fatigue life under multiaxial loading:Numerical and experimental investigations[J]. International Journal ofFatigue,2011,33(10):1360-1368
[46]汪艳萍.橡胶材料多轴疲劳寿命及微观结构研究[D].天津市:天津大学,2007
[47]王文涛,上官文斌,段小成等.基于线性疲劳累计损伤橡胶悬置疲劳寿命预测研究[J].机械工程学报,2012,(10):56-65
[48] Eshelby J. D. The Continuum Theory of Lattice Defects [M]//S. Frederick and T. David.Solid State Physics. Academic Press.1956:79-144
[49] Eshelby J. D. The elastic field of a crack extending non-uniformly under generalanti-plane loading[J]. Journal of the Mechanics and Physics of Solids,1969,17(3):177-199
[50] Verron E., Andriyana A. Definition of a new predictor for multiaxial fatigue cracknucleation in rubber[J]. Journal of the Mechanics and Physics of Solids,2008,56(2):417-443
[51] Saintier.N. Multiaxial fatigue life of a natural rubber: crack initiation mechanisms andlocal fatigue life criterion, dissertation,;2001[D]. Paris Ecole des Mines de Paris,2001
[52] Saintier N., Cailletaud G., Piques R. Crack initiation and propagation under multiaxialfatigue in a natural rubber[J]. International Journal of Fatigue,2006,28(1):61-72
[53] Bayraktar E., Bessri K., Bathias C. Deformation behaviour of elastomeric matrixcomposites under static loading conditions[J]. Engineering FractureMechanics,2008,75(9):2695-2706
[54] Mars W. V., Fatemi A. Fatigue crack nucleation and growth in filled natural rubber[J].Fatigue&Fracture of Engineering Materials&Structures,2003,26(9):779-789
[55] Rivlin.R.S. Large elastic deformations of isotropic materials IV, Further developmentsof the general theory[J]. Philosophical Transactions of the Royal Society of London1948b,A241(379-397)
[56] W.V. Mars. Experimental Investigation of Multiaxial Fatigue in Rubber [M].6thInternational Conference on Biaxial/Multiaxial Fatigue and Fracture. Lisbon, Portugal;Elsevier Science.2001
[57] Mars.W. V. Analysis of Fatigue Life under Complex Loading: Revisiting Cadwell MerillSloman and Yost [M]. a meeting of the Rubber Division, American Chemical SocietyGrand Rapids. Michigan.2004
[58] Mars W. V., Fatemi A. Observations of the Constitutive Response and Characterizationof Filled Natural Rubber Under Monotonic and Cyclic Multiracial Stress States[J].Journal of Engineering Materials and Technology,2004,126/19(19-28)
[59] W.V. Mars A. Fatemi Multiaxial stress effects on fatigue behavior of filled naturalrubber[J]. International Journal of Fatigue,2006,28(521–529)
[60] Mars W., Fatemi A. Nucleation and growth of small fatigue cracks in filled naturalrubber under multiaxial loading[J]. Journal of Materials Science,2006,41(22):7324-7332
[61] Mars W. V., Fatemi A. Multiaxial stress effects on fatigue behavior of filled naturalrubber[J]. International Journal of Fatigue,2006,28(5-6):521-529
[62]谢新星.橡胶隔振器单轴疲劳寿命评价方法及预测研究[D]:华南理工大学,2011
[63]丁智平,陈吉平,宋传江等.橡胶弹性减振元件疲劳裂纹扩展寿命分析[J].机械工程学报,2010,(22)
[64]刘建勋,黄友剑,刘柏兵等.一种橡胶弹性元件疲劳寿命预测方法的研究[J].电力机车与城轨车辆,2011,(03):12-14+27
[65]张友南,杨军,陈忠海.天然橡胶制品抗疲劳性能的因素简析[J].世界橡胶工业,2002,(06):35-39
[66]黄友剑王明星,张友南.有限元分析中超弹材料模型采用的弹性体试验[J].特种橡胶制品,2001,(05)
[67]左国兵,王进,林达文等.金属-橡胶复合锥形弹簧的试验研究[J].铁道车辆,2005,(03):12-15+34
[68]王进,左国兵.疲劳试验在橡胶减振制品寿命预测中的应用[J].铁道车辆,2005,(07):7-10+45
[69]左国兵,王进,林达文等.金属-橡胶复合锥形弹簧的试验研究[J].铁道车辆,2005,(02):9-12+13
[70]王尤颜,白鸿柏,侯军芳.金属橡胶材料疲劳损伤性能研究[J].机械工程学报,2011,(02):65-71
[71]侯军芳,白鸿柏,李冬伟等.环境温度对金属橡胶材料力学特性和阻尼性能的影响研究[A].2006
[72]丁家松,张欢,童宗鹏等.船用橡胶隔振器寿命评估方法研究[J].振动与冲击,2010,(12):230-233+250
[73]王文涛,上官文斌,段小成.超弹性本构模型对橡胶隔振器静态特性预测影响的研究[J].汽车工程,2012,(06):544-550+539
[74] Treloar.L.R.G. The elasticity of a network of long-chain molecules[J]. Transactions ofFaraday Society,1946,42(83-94)
[75] S. M. Cadwell R. A. Merrill, C. M. Sloman, F. L. Yost. Dynamic Fatigue Life ofRubber[J]. Indutrial and Engineering Chemistry,1940,12(1):19-23
[76] Woo Chang-Su, Kim Wan-Doo, Kwon Jae-Do. A study on the material properties andfatigue life prediction of natural rubber component[J]. Materials Science andEngineering: A,2008,(483-484):376-381
[77] Moon Seong-In, Cho Il-Je, Woo Chang-Su, et al. Study on determination of durabilityanalysis process and fatigue damage parameter for rubber component[J]. Journal ofMechanical Science and Technology,2011,25(5):1159-1165
[78] Park C., Shim H., Choi D., et al. Shape optimization of rubber isolators in automotivecooling modules for the maximization of vibration isolation and fatigue life[J].International Journal of Automotive Technology,2012,13(1):61-75
[79]赵永翔.低周疲劳短裂纹行为和可靠性分析[D],1998
[80]黄卓,李苏军,郭波.基于混合Gamma分布的通用可靠性寿命数据拟合方法[J].航空学报,2008,(02):379-386
[81]王翼. Gamma分布函数的研究[D]:大连理工大学,2010
[82] Minguez M. G., Royo J. Evaluation of results of tension fatigue resistance tests onvulcanized rubber[J]. Polymer Testing,1980,1(4):287-302
[83]董聪.疲劳寿命分布模型的统一描述[J].强度与环境,1996,(03)
[84]吕箴,姚卫星.小样本下估计疲劳寿命分布的历史数据融合方法[J].应用力学学报,2008,(02):
[85] Abernethy Robert B., Engineers Society of Automotive. The new Weibull handbook[M].R.B. Abernethy,1998
[86]鄢君辉魏建锋,赵康等.拉-拉变幅载荷下45钢缺口件疲劳寿命分布的预测及其验证[J].机械工程材料,2001,(07)
[87] Yew M. C., Chou C. Y., Huang C. S., et al. The solder on rubber (SOR) interconnectiondesign and its reliability assessment based on shear strength test and finite elementanalysis[J]. Microelectronics Reliability,2006,46(9–11):1874-1879
[88] Wang Chung-Ho, Hsu Yi. Enhancing rubber component reliability by response model[J].Computers& Industrial Engineering,2009,57(3):806-812
[89] Govindjee Sanjay, Simo Juan. A micro-mechanically based continuum damage modelfor carbon black-filled rubbers incorporating Mullins' effect[J]. Journal of the Mechanicsand Physics of Solids,1991,39(1):87-112
[90] Royo J. Fatigue testing of rubber materials and articles[J]. Polymer Testing,1992,11(5):325-344
[91] Yeoh.O.H., Fleming P.D. A new attempt to reconcile the statistical andphenomenological theories of rubber elasticity[J]. J Polymer Sci,1997,(Part.B):1919-1931
[92] Meissner Bohumil, Matejka Libor. A structure-based constitutive equation forfiller-reinforced rubber-like networks and for the description of the Mullins effect[J].Polymer,2006,47(23):7997-8012
[93] Yew Ming-Chih, Chou Chan-Yen, Chiang Kuo-Ning. Reliability assessment for solderswith a stress buffer layer using ball shear strength test and board-level finite elementanalysis[J]. Microelectronics Reliability,2007,47(9–11):1658-1662
[94] Ayoub G., Na t-Abdelaziz M., Za ri F., et al. A continuum damage model for thehigh-cycle fatigue life prediction of styrene-butadiene rubber under multiaxial loading[J].International Journal of Solids and Structures,2011,48(18):2458-2466
[95] Mars W. V., Fatemi A. Multiaxial fatigue of rubber: Part I: equivalence criteria andtheoretical aspects[J]. Fatigue&Fracture of Engineering Materials&Structures,2005,28(6):515-522
[96] ABAQUS Inc.The Theory Manual[M]. Hibbit, Karlsson&Sorensen (HKS),2009
[97] J. Marin. Interpretation of fatigue strengths for combined stresses [M]. Proceedings ofthe international conference on fatigue of metals. London; Institution of MechanicalEngineers.1956:184-194
[98] B Crossland. Effect of large hydrostatic pressure on the torsional fatigue strengh of analloy steel [M]. International conference on fatigue of metals London. London.1959:138-149
[99] V.MARS W., A.FATEMI. A phenomenological model for the effect of R ratio onfatigue of strain crystallizing rubbers[M]. Akron, OH, ETATS-UNIS:AmericanChemical Society,2003
[100]姚斌辉.基于载荷谱的橡胶悬置疲劳寿命预测与试验研究[D].广州:华南理工大学,2012
[101]尚德广,王德俊.多轴疲劳强度[M].北京:科学出版社,2007
[102]吉林工业大学,武汉工学院.汽车可靠性设计[M].北京:机械工业出版社,1991:
[103] Yang Guangbin. Life Cycle Reliability Engineering[M]. USA:JOHN WI-LEY&SONS,2007
[104]董聪戎海武,夏人伟.疲劳寿命分布模型及其拟合优度检验[J].航空学报,1995,(02)
[105]蔡全才,徐勤丰,姜庆五等.含区间数据Gamma分布的参数估计[J].中国卫生统计,2005,(02):71-73+79
[106]靳慧.工程机械金属结构系统疲劳可靠性分析研究[D],2003
[107]钱文学.某型航空发动机低压压气机轮盘疲劳可靠性分析[D],2006
[108]徐明.橡胶类超弹性材料非线性本构关系研究和有限元分析[D].北京:北京航天航空大学
[109] Gillibert Jean, Brieu Mathias, Diani Julie. Anisotropy of direction-based constitutivemodels for rubber-like materials[J]. International Journal of Solids andStructures,2010,47(5):640-646
[110]郭巍,郑振忠,吴行等.实心橡胶轮胎非线性有限元分析[J].机械设计与制造,2011,(06)
[111]王寿梅赵国兴.橡胶变形响应的非线性有限元分析[J].北京航空航天大学学报,1996,(03)
[112]张汝清,詹先义.非线性有限元分析[M].重庆:重庆出版社,1991
[113] Ha Y. S., Cho J. R., Kim T. H., et al. Finite element analysis of rubber extrusion formingprocess for automobile weather strip[J]. Journal of Materials ProcessingTechnology,2008,201(1–3):168-173
[114] Shangguan Wen-Bin, lu Zhen-Hua, J Shi J. Finite element analysis of static elasticcharacteristics of the rubber isolators in automotive dynamic systems[D],2003
[115] C. Boyce M., M Arruda E. Constitutive models of rubber elasticity: a review[J]. RubberChemistry Technology,2000,73,(504-523)
[116]郭仲衡.非线性弹性理论[M].北京:科学出版社,1980
[117] Guo Z., Sluys L.J. Constitutive modelling of hyperelastic rubber-like materials[J].2008
[118]特雷劳尔L.R.G,王梦姣,王培国等译.橡胶弹性物理学[M].北京:化学工业出版社,1982
[119] Ali Aidy, Hosseini M., Sahari B. B. A Review of Constitutive Models for Rubber-LikeMaterials[J]. American Journal of Engineering and Applied Sciences,2010,3(1):232-239
[120] Ling Yun. Constitutive models, load-deflection relations, and instabilities of elastomericmaterials and structures[D]: State University of New York at Binghamto,1992
[121]朱艳峰.橡胶材料的本构模型[J].橡胶工业,2006
[122]李晓芳.橡胶材料的超弹性本构模型[J].弹性体,2005,15(1)
[123] Arruda Ellen M., Boyce Mary C. A three-dimensional constitutive model for the largestretch behavior of rubber elastic materials[J]. Journal of the Mechanics and Physics ofSolids,1993,41(2):389-412
[124] Avril Stéphane, Bonnet Marc, Bretelle Anne-Sophie, et al. Overview of IdentificationMethods of Mechanical Parameters Based on Full-field Measurements[J]. ExperimentalMechanics,2008,48(4):381-402
[125] Bergstr m J. S., Boyce M. C. Large strain time-dependent behavior of filledelastomers[J]. Mechanics of Materials,2000,32(11):627-644
[126] Marckmann G., Verron E., Gornet L., et al. A theory of network alteration for theMullins effect[J]. Journal of the Mechanics and Physics of Solids,2002,50(9):2011-2028
[127] Zhong Allan."A constitutive model for the Mullins effect with permanent set in aparticle-reinforced rubber" by A. Dorfmann and R.W. Ogden[J]. International Journal ofSolids and Structures,2005,42(13):3967-3969
[128]孟祥宾,郑志峰.试验链节数不同时,国产12B滚子链条疲劳寿命的可靠性分析与计算[J].吉林大学学报(工学版),1984,(02)
[129]孙亮.农用拖车疲劳寿命的可靠性分析[J].农业机械学报,1987,(02)
[130]杨德滋车惠民.混凝土在重复荷载作用下疲劳寿命分布的概率方法研究[J].铁道学报,1990,(04)
[131]罗毅，高镇同.疲劳寿命可靠性分析模型[J].机械强度,1994,(03)
[132] Saintier N., Cailletaud G., Piques R. Multiaxial fatigue life prediction for a naturalrubber[J]. International Journal of Fatigue,2005,28(5-6):530-539
[133] Legorju-jago K., Bathias C. Fatigue initiation and propagation in natural and syntheticrubbers[J]. International Journal of Fatigue,2002,24(2-4):85-92
[134] Ryan J. Harbour Ali Fatemi b, Will V. Mars Fatigue life analysis and predictions forNR and SBR under variable amplitude and multiaxial loading conditions[J].International Journal of Fatigue,2007,30(7):1231-1247
[135] Flamm M., Spreckels J., Steinweger T., et al. Effects of very high loads on fatigue life ofNR elastomer materials[J]. International Journal of Fatigue,2011,33(9):1189-1198
[136]王文涛,上官文斌,段小成等.基于线性疲劳累计损伤橡胶悬置疲劳寿命预测研究[J].机械工程学报,2012,(10)
[137] Andrews Clinton J. An end-use approach to reliability investment analysis[J]. EnergyEconomics,1992,14(4):248-254
[138] Breitung K., Casciati F., Faravelli L. Reliability based stability analysis for activelycontrolled structures[J]. Engineering Structures,1998,20(3):211-215
[139]王飞,张方晓.机械热弱链设计及其安全性评估方法研究[J].兵工学报,2011,(05):632-635
[140] Rice John A. Mathematical Statistics and Data Analysis[M]. California:Duxbury,1995
[141] Mars W., Fatemi A. A novel specimen for investigating the mechanical behavior ofelastomers under multiaxial loading conditions[J]. Experimental Mechanics,2004,44(2):136-146
[142] Harbour R., Fatemi A., Mars W. V. Fatigue Crack Growth of Rubber under VariableAmplitude Loading [C]. the9th International Fatigue Congress. Atlanta, Georgia
[143] Lü Peiyin, Li Qingbin, Song Yupu. Damage constitutive of concrete under uniaxialalternate tension-compression fatigue loading based on double bounding surfaces[J].International Journal of Solids and Structures,2004,41(11-12):3151-3166
[144] Zhi Suo, Gun Wong Wing, Hui Luo Xiao, et al. Evaluation of fatigue crack behavior inasphalt concrete pavements with different polymer modifiers[J]. Construction andBuilding Materials,2012,27(1):117-125
[145] Jordon J. B., Bernard J. D., Newman Jr J. C. Quantifying microstructurally small fatiguecrack growth in an aluminum alloy using a silicon-rubber replica method[J].International Journal of Fatigue,2012,36(1):206-210
[146]何小静.橡胶隔振器静态特性计算与建模方法的研究[D]：华南理工大学,2012
[147]姚斌辉.基于载荷谱的橡胶悬置疲劳寿命预测与试验研究[D]：华南理工大学,2012