SSBR屈挠疲劳破坏的微观机理研究及轮胎胎面基部胶的耐疲劳性能优化
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摘要
本文首先以微观结构不同的六种溶聚丁苯橡胶SSBR-T2003、T2530、T2000R、T1534、C2564A和VSL5025-1为研究对象,采用橡胶加工分析仪(RPA2000)、动态力学分析(DMA)、扫描电子显微镜(SEM)等手段分别考察了这些SSBR的微观结构、配方因素、炭黑填充橡胶网络、硫化交联网络以及防老剂对硫化胶耐屈挠疲劳性能的影响,根据RPA检测结果比较了炭黑填充网络和硫化交联网络对硫化胶屈挠疲劳破坏的影响,并对硫化胶的屈挠疲劳性能与粘弹特性及复合力学性能参数-强/粘比(T2/M*G”)的相关性进行了考察。本研究工作将橡胶试样的SEM疲劳破坏形貌分析与力学性能的相关性分析相结合,建立了炭黑填充橡胶的网络结构模型,并据此对SSBR屈挠疲劳破坏的微观机理进行了初步探讨。
研究表明：硫化胶的耐屈挠疲劳性能随着SSBR玻璃化温度(Tg)的升高而增强,同时随着应变损耗模量的增大而降低。高1,2-结构充油SSBR具有优良的屈挠疲劳性能,而防老剂种类及炭黑填充量对硫化胶的耐屈挠疲劳性能具有重要贡献。实验结果显示,硫化橡胶的耐屈挠疲劳性能随着炭黑填充橡胶网络密度的增大先升后降,随着化学交联密度的增加而单调降低。SSBR的微观结构不同,其屈挠疲劳性能对应的最佳炭黑填充量也不同,但此时各硫化胶试样的粘弹特性参数相差不大。实验表明,SSBR的屈挠疲劳破坏机理与T2/M*G”有关,T2/M*G"较低时硫化胶的屈挠疲劳破坏以机械强度破坏机理为主,T2/M*G”较高时则以力-化学破坏机理为主,防老剂对以力-化学机理进行的疲劳破坏防护效果明显。T2/M*G”的物理意义为炭黑对填充橡胶的补强与损耗特性的贡献之比,单因素变量硫化胶的屈挠疲劳性能随着T2/M*G”的增大而提高。SEM观测分析结果表明胶料内部存在有潜在缺陷,潜在缺陷对硫化胶的屈挠疲劳破坏效应低于填充炭黑产生的T2/M*G”的作用。
本研究工作针对疲劳历史不同的早期损坏轮胎样品进行了解剖分析,工作中采用傅里叶红外光谱仪(FTIR)、热重分析仪(TGA)、扫描电子显微镜(SEM)以及磁共振交联密度仪(NMR-CDS)等实验方法考察了胎面基部胶的疲劳破坏现象,分析归纳了疲劳破坏的本质及其规律,并根据上述SSBR试样疲劳破坏机理的研究结果对工业实用配方进行了耐疲劳破坏性能优化。结果表明：轮胎行驶过程中基部胶的疲劳破坏以高温降解及机械疲劳破坏为主,炭黑粒子分散的均匀程度对疲劳破坏性能有明显影响,在基部胶中并用低滞后炭黑在降低胶料压缩疲劳生热的同时,可显著提高硫化胶的耐屈挠龟裂寿命,但对耐裂纹扩展能力不利。实验还表明,在基部胶配方中并用高1,2-结构充油SSBR并对补强体系作相应调整,硫化胶的耐屈挠疲劳性能显著提高,其疲劳破坏界面的微观形貌呈现经受长时间屈挠变形取向后断裂的层层剥裂的沟壑状。
Firstly, influence of factors such as micro-structure of SSBR, compounding ingredients, filler-filler and filler-rubber rubber network, chemical network, processing additive TT100, antioxidant 4020 on flex fatigue life of 6 types of SSBR, SSBR-T2003, T2530, T2000R, T1534, C2564A and VSL5025-1, with different micro-sructures were investigated. Influence of filler-filler, filler -rubber network and chemical network on flex fatigue life of SSBR vulcanizates was compared with the application of Rubber Processing Analyzer (RPA2000). Visco-elasticity, along with a new proposed parameter, strength/viscosity ratio (T2M*G"), was related with the flex fatigue life of SSBR vulcanizates. A network model of carbon black filled rubber was established based on the SEM morphology analysis of fatigue fracture interface combined with the analysis of mechanical properties and correlated with the failure mechanism of SSBR vulcanizates'flex fatigue.
The results showed that:the flex fatigue life increased with the increasing of glass transition temperature and decreased with the increasing of loss modulus. Oil-extended SSBR with high 1,2-content had high flex fatigue life. The type of antioxidants and CB loads contributes more to the flex fatigue life than other factors. The flex fatigue life increased to the maximum value, then decreased with filler-filler and filler-rubber network density, while decreased with the increasing of chemical cross-linking density. Although the optimum CB loads for flex fatigue life of SSBR with different microstructure was different, the viscoelastic parameter of these samples fell in a very close range. The failure mechanism of SSBR was related to T2M*G". Rubber failed in mechanical strength failure mechanism when the value of T2/M*G" was lower, but failed in force-chemical failure mechanism when the value of T2/M*G" was higher. The protective effect of antioxidant 4020 was prominent when rubber failed in force-chemical mechanism. The physical meaning of T2/M*G" was the ratio of reinforcement of CB to hysteresis. The flex fatigue life increased with the increasing of T2/M*G" when only one factor was changed. Observation of SEM showed that there were potential defects in the compounds, and its influence on flex fatigue failure was less evident than that of T2/M*G" of CB filled rubber.
Specimen of tread-based rubber from damaged tire with different fatigue history was analyzed with Fourier Transform Infrared Spectropy (FTIR), Thermal Gravimetric Analysis (TGA), Scanning Electron Microscopy (SEM), Nuclear Magnetic Resonance Crosslink-density spectrometer (NMR-CDS). The essence and rule of fatigue failure was summarized and the failure mechanism concluded above was used to optimize the flex fatigue resistance for industrial practical application. The results showed that:high temperature degradation and mechanical fatigue were the main reasons for the fatigue failure of tread base. The uniform dispersion of CB particles played an important role on the fatigue failure performance of tires. The application of CB-DZ 13, special for low hysteresis of rubber, not only reduced the heat build-up, but also increased the resistance of flex cracking life significantly, but was negative to the resistance of crack growing properties. Application of oil-extended SSBR with high 1,2- content, combined with an adjustment on reinforcing system, improved the flex fatigue life of SSBR vulcanizates significantly. The SEM of fatigue failed interface presented a ravine-like morphology of exfoliated layers after long-term flex deformation and orientation.
研究表明：硫化胶的耐屈挠疲劳性能随着SSBR玻璃化温度(Tg)的升高而增强,同时随着应变损耗模量的增大而降低。高1,2-结构充油SSBR具有优良的屈挠疲劳性能,而防老剂种类及炭黑填充量对硫化胶的耐屈挠疲劳性能具有重要贡献。实验结果显示,硫化橡胶的耐屈挠疲劳性能随着炭黑填充橡胶网络密度的增大先升后降,随着化学交联密度的增加而单调降低。SSBR的微观结构不同,其屈挠疲劳性能对应的最佳炭黑填充量也不同,但此时各硫化胶试样的粘弹特性参数相差不大。实验表明,SSBR的屈挠疲劳破坏机理与T2/M*G”有关,T2/M*G"较低时硫化胶的屈挠疲劳破坏以机械强度破坏机理为主,T2/M*G”较高时则以力-化学破坏机理为主,防老剂对以力-化学机理进行的疲劳破坏防护效果明显。T2/M*G”的物理意义为炭黑对填充橡胶的补强与损耗特性的贡献之比,单因素变量硫化胶的屈挠疲劳性能随着T2/M*G”的增大而提高。SEM观测分析结果表明胶料内部存在有潜在缺陷,潜在缺陷对硫化胶的屈挠疲劳破坏效应低于填充炭黑产生的T2/M*G”的作用。
本研究工作针对疲劳历史不同的早期损坏轮胎样品进行了解剖分析,工作中采用傅里叶红外光谱仪(FTIR)、热重分析仪(TGA)、扫描电子显微镜(SEM)以及磁共振交联密度仪(NMR-CDS)等实验方法考察了胎面基部胶的疲劳破坏现象,分析归纳了疲劳破坏的本质及其规律,并根据上述SSBR试样疲劳破坏机理的研究结果对工业实用配方进行了耐疲劳破坏性能优化。结果表明：轮胎行驶过程中基部胶的疲劳破坏以高温降解及机械疲劳破坏为主,炭黑粒子分散的均匀程度对疲劳破坏性能有明显影响,在基部胶中并用低滞后炭黑在降低胶料压缩疲劳生热的同时,可显著提高硫化胶的耐屈挠龟裂寿命,但对耐裂纹扩展能力不利。实验还表明,在基部胶配方中并用高1,2-结构充油SSBR并对补强体系作相应调整,硫化胶的耐屈挠疲劳性能显著提高,其疲劳破坏界面的微观形貌呈现经受长时间屈挠变形取向后断裂的层层剥裂的沟壑状。
Firstly, influence of factors such as micro-structure of SSBR, compounding ingredients, filler-filler and filler-rubber rubber network, chemical network, processing additive TT100, antioxidant 4020 on flex fatigue life of 6 types of SSBR, SSBR-T2003, T2530, T2000R, T1534, C2564A and VSL5025-1, with different micro-sructures were investigated. Influence of filler-filler, filler -rubber network and chemical network on flex fatigue life of SSBR vulcanizates was compared with the application of Rubber Processing Analyzer (RPA2000). Visco-elasticity, along with a new proposed parameter, strength/viscosity ratio (T2M*G"), was related with the flex fatigue life of SSBR vulcanizates. A network model of carbon black filled rubber was established based on the SEM morphology analysis of fatigue fracture interface combined with the analysis of mechanical properties and correlated with the failure mechanism of SSBR vulcanizates'flex fatigue.
The results showed that:the flex fatigue life increased with the increasing of glass transition temperature and decreased with the increasing of loss modulus. Oil-extended SSBR with high 1,2-content had high flex fatigue life. The type of antioxidants and CB loads contributes more to the flex fatigue life than other factors. The flex fatigue life increased to the maximum value, then decreased with filler-filler and filler-rubber network density, while decreased with the increasing of chemical cross-linking density. Although the optimum CB loads for flex fatigue life of SSBR with different microstructure was different, the viscoelastic parameter of these samples fell in a very close range. The failure mechanism of SSBR was related to T2M*G". Rubber failed in mechanical strength failure mechanism when the value of T2/M*G" was lower, but failed in force-chemical failure mechanism when the value of T2/M*G" was higher. The protective effect of antioxidant 4020 was prominent when rubber failed in force-chemical mechanism. The physical meaning of T2/M*G" was the ratio of reinforcement of CB to hysteresis. The flex fatigue life increased with the increasing of T2/M*G" when only one factor was changed. Observation of SEM showed that there were potential defects in the compounds, and its influence on flex fatigue failure was less evident than that of T2/M*G" of CB filled rubber.
Specimen of tread-based rubber from damaged tire with different fatigue history was analyzed with Fourier Transform Infrared Spectropy (FTIR), Thermal Gravimetric Analysis (TGA), Scanning Electron Microscopy (SEM), Nuclear Magnetic Resonance Crosslink-density spectrometer (NMR-CDS). The essence and rule of fatigue failure was summarized and the failure mechanism concluded above was used to optimize the flex fatigue resistance for industrial practical application. The results showed that:high temperature degradation and mechanical fatigue were the main reasons for the fatigue failure of tread base. The uniform dispersion of CB particles played an important role on the fatigue failure performance of tires. The application of CB-DZ 13, special for low hysteresis of rubber, not only reduced the heat build-up, but also increased the resistance of flex cracking life significantly, but was negative to the resistance of crack growing properties. Application of oil-extended SSBR with high 1,2- content, combined with an adjustment on reinforcing system, improved the flex fatigue life of SSBR vulcanizates significantly. The SEM of fatigue failed interface presented a ravine-like morphology of exfoliated layers after long-term flex deformation and orientation.
引文
[1]陈士朝.溶聚丁苯橡胶的性能研究[J].合成橡胶工业,1997,20(1)：6-9
[2]罗志河.关于发展溶聚丁苯橡胶的探讨[J].合成橡胶工业,1988,11(3)：191-195
[3]Phillips Petroleum Company. Process for countering efects of fastpoisons in continuous olefin polymerization[P]. U S,US4 239 870,1980Firestone Tire & Rubber
[4]Firestone Tire&Rubber Company. Polymerization process[P]. BritUK Pat Appl, GB 1 197 382,1970
[5]PhiHips Petroleum Company. Suppressing gel in the continuous solution polymerization of a conjugated diene with a monovinyl aromaticcompound [P].U S,US 4 091 198,1978
[6]Company. Continuous process of copoly-merizing butadiene and styrene[P].U S, US 3 787 377,1974
[7]李花婷SSBR在轮胎中的应用技术进展[J].轮胎工业,2005,25(5)：259-263.
[8]Bond R, Morton G. A tailor-made polymer for tire applications[J]. Polymer 84,25(1):132-140
[9]梁爱民.溶聚丁苯橡胶生产技术现状及发展趋势[A].中日橡胶技术交流会论文集[c].青岛：中国化工学会橡胶专业委员会,2003.5-25.
[10]Bond R, Morton G F.A tailor-made polymer for tyre applieations[J]. Polymer, 1984,25(1):132
[11]Tsutsumi F, Sakakibara M, Oshima N. Structure and dynamic properties of solution SBR coupled with tin compounds[J]. Rubber Chemistry and Technology, 1990,63(11):8-13.
[12]Cadwell S.M., Merrill R. A., Sloman C.M., Yost F. L., Dynamic fatigue life of rubber Industrial and Engineering Chemistry, Anal. Ed.,1940,12:19-23.
[13]Ellul M. D., Mechanical fatigue. In:A. Gent, Editor, Engineering with rubber, How to design rubber components, Carl Hanser Verlag, Munich,1992 (chapter6).
[14]Sun C., Gent A., Marteny P., Effect of Fatigue Step Loading Sequence on Residual Strength, Tire Science and Technology,1996,28:196-208.
[15]Lee B. L., Ku B. H., Liu D. S., Fatigue of cord-rubber composites(II):Strain-based fatigue failure criteria, Rubber Chemistry and Technology,1998, 71:866-888
[16]Mars W. V. and Fatemi A., Factors that affect the fatigue life of rubber:a literature survey, Rubber Chem Technol,2004,77:391-412.
[17]Mars W. V. and Fatemi A., Observations of the constitutive response and characterization of filled natural rubber under monotonic and cyclic multiaxial stress states, ASME J. Eng. Mater. Technol.,2004,126:19-28.
[18]Mars W. V. and Fatemi A., Multiaxial stress effects on fatigue behavior of filled natural rubber, International Journal of Fatigue,2006 28:521-529.
[19]Saintier N., Cailletaud G., Piques R., Multiaxial fatigue life prediction for a natural rubber, International journal of fatigue,2006,28:530-539.
[20]P. B. Lindley. Relation between hysteresis and the dynamic crack growth resistance of natural rubber [J]. International Journal of Fracture,1973,9(4): 449-462.
[21]G. J. Lake. Aspects of fatigue and fracture of rubber[J]. Prog. Rubber Technol. 1983,45:89-143.
[22]Beatty J. R., Fatigue of rubber, Rubber Chemistry and Technology,1964,37: 1341-1364.
[23]Fielding J. H., Flex life and crystallization if synthetic rubber, Industrial and Engineering Chemistry,1943,35:1259-1261.
[24]Abraham F., Alshuth T., Jerrams S., The effect of minimum stress and stress amplitude on the fatigue life of non strain crystallising elastomers, Materials and Design 2005,26:239-245.
[25]Lee B. L., Ku B. H., Liu D. S., Fatigue of cord-rubber composites (Ⅱ):Strain-based fatigue failure criteria[J]. Rubber Chemistry and Technology,1998,71:866-888.
[26]Lindley P. B., Relation between hysteresis and the dynamic crack growth resistance of natural rubber[J]. International Journal of Fracture,1973, 9:449-462.
[27]Busfield J. J. C., Ratsimba C. H. H., and Thomas A. G., "Finite Element Analysis of Elastomers, " D. Boast and V. A. Coveny, Eds., IMech E, United Kingdom,1999: 235.
[28]Mars W. V., Fatemi A., Multiaxial fatigue of rubber—part Ⅱ:experimental observations and life predictions[J]. Fatigue Fract Eng Mater Struct.,2005, 28:523-538.
[29]刘宇艳,万志敏,杜星文,周期载荷下聚酯纤维／橡胶复合材料和人造丝／橡胶复合材 料的疲劳行为[J].材料工程,2000(10),29-32.
[30]刘宇艳,田振辉,万志敏等,橡胶复合材料在循环载荷下的疲劳损伤特性[J].橡胶工业,2003,5：713-716.
[31]D. G. Young. Dynamic property and fatigue propagation research on tire sidewall and model compounds[J]. RUBBER CHEM. TECHNOL.,1985,58:785-805.
[32]D. G. Young. Fatigue crack propagation in elastomer compounds:effects of strain rate, temperature[J]. RUBBER CHEM. TECHNOL.,1986,59:809-825.
[33]A. J. M. Sumner, S. A. Kelbch, U. G. Eisele, Rubber World,212 (2),38 (1995).
[34]D. Hardy, H. Moneypenny, M. Holderied, J. Harris, R. Campion, G. Morgan, Paper No.2 presented at RubberChem'99, Belgium,(1999).
[35]C. Sun, A. N. Gent, P. Marteny. Effect of Fatigue Step Loading Sequence on Residual Strength[J]. Tire Sci. Technol.,2000,28:196.
[36]C. M. Roland, J. W. Sobiesky. Network recovery from uniaxial extension. Ⅱ. The origin of the Mullins effect[J]. RUBBER CHEM. TECHNOL.1989,62:683.
[37]Mars W. V., Fatemi A., Multiaxial fatigue of rubber—part Ⅰ:equivalence criteria and theoretical aspects. Fatigue Fract Eng Mater Struct 2005,28:515-522.
[38]孟宪德.橡胶的疲劳老化与防护[J].合成材料老化与应用,1992,(4)：10-21
[39]G. J. Lake, P. B. Lindley. Cut growth and fatigue of rubbers. II. Experiments on a noncrystallizing rubber[J].J Appl. Polym. Sci.1964,8:707-721.
[40]D. G. Young. Fatigue crack propagation in elastomer compounds:effects of strain rate, temperature,strain level, and oxidation[J]. RUBBER CHEM. TECHNOL.1986, 59:809.
[41]D. G. Young, J. A. Danik, RUBBER CHEM. TECHNOL.67,137 (1994).
[42]M. Braden, A. N. Gent. The attack of ozone on stretched rubber vulcanizates.Ⅱ. Conditions for cut growth[J]. J. of Appl. Polym. Sci.,1960,3(7):90-100.
[43]G. J. Lake, A. G. Thomas. Engineering with Rubber, How to Design Rubber Components. A. Gent, Ed., Carl Hanser Verlag, Munich (1992),ch.5.
[44]杨清芝主编.现代橡胶工艺学[M].北京：中国石化出版社,1997,315
[45]A. N. Gent, H. Hirakawa. Effect of temperature on the ozone cracking of butyl rubbers[J].J. Polym. Sci. Part A-2,1968,6:1481.
[46]A. N. Gent, J. E. McGrath, J. Polym. Sci., Part A 3,1473 (1965).
[47]Gent A. N., Hindi M., Effect of oxygen on the tear strength of elastomers, Rubber Chemistry and Technology 1990,63:123-34.
[48]Blackman E. J., McCall E. B., Relationship between the structures of natural rubber-vulcanizates and their thermal and oxidative aging, Rubber Chemistry and Technology,1970,43:651-663.
[49]C.M.Roland. Network recovery from uniaxial extension. I. Elastic equilibrium[J]. RUBBER CHEM. TECHNOL.,1989,62,863.
[50]D. G. Young.Dynamic property and fatigue propagation research on tire sidewall and model compounds[J]. RUBBER CHEM. TECHNOL.1985,58:785.
[51]王进文编译.改性炭黑对SBR拉伸性能和屈挠性能的影响[J].世界橡胶工业,2000,27(4)：4-6.
[52]裘怿明,肖建斌等.普通、半有效和有效硫化体系的NR/BR共混胶料的疲劳寿命曲线方程[J].橡胶工业,1999,46(2)：71-74.
[53]裘怿明,傅政等.不同硫化体系橡胶的疲劳断裂性能[J].合成橡胶工业,2000,23(2)：111-114.
[54]黄良平,杨军等.白炭黑原位接枝改性对橡胶屈挠性能的影响[A].2004年国际橡胶会议论文集[c].北京：中国化工学会橡胶专业委员会,2004.135-138.
[55]贾红兵等.填充剂表面改性剂对硫化胶疲劳性能的影响[J].高分子材料科学与工程,2002,18(1)：119-122.
[56]张士齐等.硫化橡胶疲劳和磨耗时的力化学后活化学效应研究[J].橡胶工业,1990,37(6)：354-359.
[57]Hamed, Gary R. Molecular aspects of the fatigue and fracture of rubber [J]. Rubber Chemistry and Technology,1994,67(3):529-536.
[58]张士齐,周翠微,邓知庆.研究炭黑补强硫化胶疲劳的分子历程[J].橡胶工业,1988,35(10)：616.
[59]张殿荣等.现代橡胶配方设计[M].北京：化学工业出版社,2001.87.
[60]Woo Chang-Su, Kim Wan-Doo. A study on the fatigue life prediction and evaluation of rubber components. Symposium of international rubber conference,2004: 342-348.
[61]R. S. Rivlin, A. G. Thomas. Rupture of rubber:I. Characteristic energy for tearing [J]. J. Polym. Sci.,1953,10:291.
[62]C. M. Roland. Network recovery from uniaxial extension. Ⅱ. The origin of the Mullins effect[J]. RUBBER CHEM. TECHNOL.,1989,62:863.
[63]A. I. Medalia. Effect of carbon black on ultimate properties of rubber vulcanizates[J]. RUBBER CHEM. TECHNOL.,1987,60:45.
[64]W.V.Mars., A. FATEMI. Fatigue crack nucleation and growth in filled natural rubber[J]. Fatigue & Fracture of Engineering Materials & Structures,2003,26 (9):779-789.
[65]W D Kim, H J Lee, J Y Kim. Fatigue life estimation of an engine rubber mount [J]. International journal of fatigue,2004,26(5):553-560.
[66]Guido Raos, Margherita Moreno, Stefano Elli. Computational Experiments on Filled Rubber Viscoelasticity:What Is the Role of Particle-Particle Interactions?[J]. Macromolecules,2006,39(19):6744-6751.
[67]P. G. Santangelo, C. M. Roland. Role of Strain Crystallization in the Fatigue Resistance of Double Network Elastomers[j]. Rubber Chemistry And Technology,2003,76:892-898.
[68]I. S. Choi,C.M. Roland. Strain-crystallization of guayule and hevea rubber [J]. RUBBER CHEM. TECHNOL.,1997,70:202.
[69]S Wiese, S Jakschik, F Feustel. Fracture behaviour of flip chip solder joints. Electronic Components and Technology Conference,2001.51st:1299-1306.
[70]G. J. Lake, A. G. Thomas. The strength of highly elastic materials[J]. Proc. Royal Society of London, Series A.1961,300(1460):108-119.
[71]A A Griffith. The phenomena of rupture and flow in sol ids[J]. Philosophical Transactions of the Royal Society of London. Series A.1921,221:153-197.
[72]C Feichter, Z Major. Experimental determination of fatigue crack growth behavior and surface strain distribution of faint-waist pure shear specimens with different crack tip radii[J]. Rubber chemistry and technology,2006,79(4): 712-733.
[73]Ryan J. Harbour, Ali Fatemi.Will V. Mars. Fatigue crack orientation in NR and SBR under variable amplitude and multiaxial loading conditions[J]. J. Mater. Sci.,2008,43:1783-1794.
[74]M. F. Tse. Ozone Cracking and Flex Cracking of Crosslinked Polymer Blend Compounds[J]. Journal of Applied Polymer Science,2007,103:2183-2196.
[75]Verron E,Le Cam JB, Gornet J. A multiaxial criterion for crack nucleation in Rubber[J]. Mech. Res. Commun.,2006,33:493-498.
[76]王进,杨军等.橡胶疲劳破坏性能的研究[A].2004年国际橡胶会议中文论坛论文集[C].北京：中国化工学会橡胶专业委员会,2004.123-126.
[77]藤本邦彦Study on Three-Dimentionality Stressed Fatigue of NR/SBR Blended Rubber日本A协会志,1992,65(1),42
[78]藤本邦彦Study on Dynamic Creep of SBR/NR Blend Rubber日本A协会志,1991,64(5)：632.
[79]J.-B. Le Cam, B. Huneau, E. VerronJ.-B. Le Cam, B. Huneau, E. Verron etal. Mechanism of Fatigue Crack Growth in Carbon Black Filled Natural Rubber[J]. Macromolecules,2004,37 (13):5011-5017
[80]Takeshi Karino, Yuko Ikeda, Yoritaka Yasuda etal. Nonuniformity in Natural Rubber As Revealed by Small-Angle Neutron Scattering, Small-Angle X-ray Scattering, and Atomic Force Microscopy[J]. Biomacromolecules,2007,8(2): 693-699
[81]J.-B. Le Cam and E. Toussaint.Volume Variation in Stretched Natural Rubber: Competition between Cavitation and Stress-Induced Crystallization[J]. Macromolecules,2008,41(20):7579-7583.
[82]K. Legorju-jago and C. Bathias. Fatigue initiation and propagation in natural and synthetic rubbers[J]. International Journal of Fatigue,2002,24(2-4): 85-92.
[83]卢红斌,杨玉良.填充聚合物的熔体流变学[J].高分子通报,2001,12(1)：18-26
[84]32Kosinski L.E., Caruthers. J. M. [J] Rheol Acta,1986,25:153-160
[85]33 G. Kraus, Interactions of elastomers and reinforcing fillers [J] Rubber Chem. Technol.1965:38(5):1070-1115
[86]36 E. M. Dannenberg, Bound rubber and carbon black reinforcement [J]. Rubber Chem. Technol.1986,59(3):512-520
[87]3 Payne A R. The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I [J]. J Appl Polym Sci 1962,6(19):57-63
[88]4 Payne A. R., Watson W. F. Carbon black structure in rubber [J]. Rubber Chem Technol 1963,36(1):147-156
[89]Payne AR, Wittaker RE. Low strain dynamic properties of filled rubbers [J]. Rubber Chem Technol 1971,44(3):440-470
[90]Payne A R Dynamic properties of heat-treated butyl vulcanizates [J]. J Appl Polym Sci 1963,7(3):873-885
[91]Payne A R. Strainwork dependence of filler-loaded vulcanizates [J]. J Appl Polym Sci 1964,8(6):2661-2686
[92]Payne A R. In:Kraus G (ed) Reinforcement of elastomers. Interscience Publisher, NewYork, Chaper 3.1972
[93]Payne A R Effect of vulcanization on the low-strain dynamic properties of filled rubbers [J]. J Appl Polym Sci 1972,16(5):1191-1212
[94]Payne A R. The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I [J]. Rubber Chem Technol 1963,36(2):432-444
[95]Medalia A I Elastic modulus of vulcanizatioes as related to carbon black [J]. Rubber Chem Technol 1973,46(3):877-897
[96]Medalia A I Filler aggregates and their effect on reinforcement [J]. Rubber Chem Technol 1974,47(2):411-434
[97]Medalia AI Effect of carbon black on the dynamic properties of rubber vulcanizates [J]. Rubber Chem Technol.1978,51(3):437-524
[98]Voet A, Cook FR Mild stress softening and dynamic properties of rubber vulcanizates [J]. Rubber Chem Technol 1967,40(5):1364-1373
[99]Voet A, Cook FR. Analysis of contributions to dynamic mechanical properties of carbon filled vulcanized [J]. Rubber Chem Technol 1968,41 (5):1215-1219
[100]Sircar AK, Lamond TG Strain-dependent dynamic properties of carbon black reinforced vulcanizates, I. Individual elastomers, II. Elastomer blends [J]. Rubber Chem Technol 1975,48(1):79-97
[101]王梦蛟,填充聚合物-填料和填料-填料相互作用对填充硫化胶动态力学性能的影响[J].轮胎工业,2000,20(11)：670-677
[102]D. Stauffer and A. Aharony "Introduction to Percolation Theory",2nd Ed. Taylor & Francis, London,1994.
[103]Choi Sung-seen. Improvement of properties of silica-filled natural rubber compounds using polychloroprene [J]. J Appl. Polym. Sci.2002,83(12):2609-2616,
[104]冯希金,轮胎疲劳寿命研究的进展,橡胶科技市场[J],(6)：8-12
[105]庄继德,现代汽车轮胎技术,北京：北京理工大学出版社[M],2001.3：21
[106]何志刚、周孔亢、应世洲等,轮胎疲劳失效研究综述,机械工程学报[J],2009,45(3)：76-83
[107]戴永谦,宋希庚,薛冬新.裂纹生长方法在橡胶疲劳分析中的应用研究[J].振动与冲击,2005,24(4)：115-119.
[108]SAINTER N, CAILLETAUD G. Crack initiation and propagation under multiaxial fatigue in a natural rubber [J]. Int. J. Fatigue,2006,28(1):61-72.
[109]MARS W V. A literature survey on fatigue analysis approaches for rubber [J]. Int. J. Fatigue,2002,24(9):949-961.
[110]KIM J H, JEONG H Y. A study on the material properties and fatigue life of natural rubber with different carbon blacks[J]. Int. J. Fatigue,2005,27(3): 263-272.
[111]GRIFFITH A A. The phenomena of rupture and flow in solids[J]. Philosophical Transaction of Royal Society of London, Series A,1920,221:163-198.
[112]INGLIS C E. Stresses in a plate due to the presence of cracks and sharp corners[J]. Transactions of the Institute of Naval Architects,1913,55:219-241.
[113]GREENSMITH H W. Rupture of rubber IV. Tearing properties of vulvanizates containing carbon black[J]. Journal of Polymer Science,1956,21:175-187.
[114]SCHUBEL P M, GDOUTOS E E. Fatigue characterization of tire rubber[J]. Theoretical and Applied Fracture Mechanics,2004,42(2):149-154.
[115]OZUPEK S, BECKER E B. Finite element method for the study of belt edge delaminations in truck tires[J]. Rubber Chemistry and Technology,2005,78(4): 557-571.
[116]SOUTHERN E, THOMAS A G. Studies of rubber abrasion [J]. Plastics and Rubber： Materials and Applications,1978,3(4):133-138.
[117]GROSCH K. Rolling resistance and fatigue life of tires [J]. Rubber Chemistry and Technology,1988,61(1):42-63.
[118]66 Huang Y S, Yoeh 0 H. Crack initiation and propagation in model COrd—rubber composites. Rubber Chemistry and Tec—hnology.1989.62:709-731
[119]EBBOTT T G. Application of finite element-base fracture mechanics analysis to cord-rubber structures [J]. Tire Science and Technol.,1996,24(3):220-235.
[120]WEI Y T, TIAN Z H, DU X W. Finite element model for the rolling loss prediction and fracture analysis of radial tires[J]. Tire Science and Technol.,1999,27(4): 250-276.
[121]危银涛.轮胎热力学分析及耐久性评价[D].哈尔滨：哈尔滨工业大学,1997.88-93.
[122]深崛美英.弹性体疲劳寿命的预测[J].橡胶译丛,1986(4)：67-76.
[123]肖建斌,江爱民,焦清锋,等NR/SBR共混物的动态疲劳与断裂特征[J].高分子材料科学与工程,1999,15(2)：136-139.
[124]肖建斌,国继红,邹志德,等.不同补强体系胶料疲劳断裂性能的研究[J].橡胶工业,2000,47(10)：584-587.
[125]裘怿明,傅政,刘旭阳,等.多项式回归拟合NR/BR共混胶料疲劳断裂曲线[J].橡胶工业,1998,45(3)：137-139.
[126]右田哲彦.橡胶的疲劳与破坏机理与配方设计[J].橡胶译丛,1981(2)：1-19.
[127]SOUTH J T. Mechanic properties and durability of natural rubber compounds and composites [D]. Virginia, USA:Virginia Polytechnic Institute and State University,2001.
[128]SONG J. Fatigue of cord-rubber composites for tires [D]. Washington D. C., USA:Pennsylvania University,2004.
[129]Hirakawa H. Urano F. Kida M. Analysis of fatigue process of rubber vulcanizetes, Rubber Chemistry and Technology,1978,51:201-214.
[130]Omira N., Takahashi M., The fatigue properties of silicone rubber[A] Presebted at the Meeting of the Rubber Division[J] Washington Hilton:Amertion Chemical Society,1990.
[131]倪玉山,徐军,张华兵.轮胎中橡胶材料断口形貌及破坏机理分析[J].高分子材料科学与工程,2004,20(6)：184-186.
[132]Xie Z M, Miao C Q, Wan Z M, etal. Investigation of t he carbon black network in natural rubber under cyclic deformation [J]. Journal of Macromolecular Science. Physics,2005,B44(3):3452351.
[133]谢志民,王友善,马娟娜.填充橡胶中的炭黑网络研究[J].橡胶工业,2008,55(7)：4404-407.
[134]Eldred R. J., Journal of polymer science, Polymer Letter(Ed.),1972,10,391.
[135]Mathew N. M., Bhowmick A. K., De S. K., Chemical and scanning electron microscopy studies on fatigue failure of natural rubber vulcanizates, Rubber Chemistry and Technology,1982,55(1):51-61.
[136]Hainsworth S. V., An environmental scanning electron microscopy investigation of fatigue crack initiation and propagation in elastomers, Polymer Testing, 2007,26 (1):60-70.
[137]Le Cam J. B., Huneau B., Verron E., Mechanism of Fatigue Crack Growth in Carbon Black Filled Natural Rubber, Macromolecules,2004,37 (13):5011-5017.
[138]J-B. Le Cam, E. Toussaint. The Mechanism of Fatigue Crack Growth in Rubbers under Severe Loading:the Effect of Stress-Induced Crystallization[J]. Macromolecules,2010,43(10):4708-4714
[139]Milber C, B lumichB,U nseldK etal. NMR Imaging of Thermal-oxidative Ageing in SBR. K autschukG ummiK unststoff,1995,4:254
[140]Takuya Suzuki, Noboru Osaka, Hitoshi Endo etal. Nonuniformity in Cross-Linked Natural Rubber as Revealed by Contrast-Variation Small-Angle Neutron Scattering[J]. Macromolecules,2010,43(3):1556-1563.
[2]罗志河.关于发展溶聚丁苯橡胶的探讨[J].合成橡胶工业,1988,11(3)：191-195
[3]Phillips Petroleum Company. Process for countering efects of fastpoisons in continuous olefin polymerization[P]. U S,US4 239 870,1980Firestone Tire & Rubber
[4]Firestone Tire&Rubber Company. Polymerization process[P]. BritUK Pat Appl, GB 1 197 382,1970
[5]PhiHips Petroleum Company. Suppressing gel in the continuous solution polymerization of a conjugated diene with a monovinyl aromaticcompound [P].U S,US 4 091 198,1978
[6]Company. Continuous process of copoly-merizing butadiene and styrene[P].U S, US 3 787 377,1974
[7]李花婷SSBR在轮胎中的应用技术进展[J].轮胎工业,2005,25(5)：259-263.
[8]Bond R, Morton G. A tailor-made polymer for tire applications[J]. Polymer 84,25(1):132-140
[9]梁爱民.溶聚丁苯橡胶生产技术现状及发展趋势[A].中日橡胶技术交流会论文集[c].青岛：中国化工学会橡胶专业委员会,2003.5-25.
[10]Bond R, Morton G F.A tailor-made polymer for tyre applieations[J]. Polymer, 1984,25(1):132
[11]Tsutsumi F, Sakakibara M, Oshima N. Structure and dynamic properties of solution SBR coupled with tin compounds[J]. Rubber Chemistry and Technology, 1990,63(11):8-13.
[12]Cadwell S.M., Merrill R. A., Sloman C.M., Yost F. L., Dynamic fatigue life of rubber Industrial and Engineering Chemistry, Anal. Ed.,1940,12:19-23.
[13]Ellul M. D., Mechanical fatigue. In:A. Gent, Editor, Engineering with rubber, How to design rubber components, Carl Hanser Verlag, Munich,1992 (chapter6).
[14]Sun C., Gent A., Marteny P., Effect of Fatigue Step Loading Sequence on Residual Strength, Tire Science and Technology,1996,28:196-208.
[15]Lee B. L., Ku B. H., Liu D. S., Fatigue of cord-rubber composites(II):Strain-based fatigue failure criteria, Rubber Chemistry and Technology,1998, 71:866-888
[16]Mars W. V. and Fatemi A., Factors that affect the fatigue life of rubber:a literature survey, Rubber Chem Technol,2004,77:391-412.
[17]Mars W. V. and Fatemi A., Observations of the constitutive response and characterization of filled natural rubber under monotonic and cyclic multiaxial stress states, ASME J. Eng. Mater. Technol.,2004,126:19-28.
[18]Mars W. V. and Fatemi A., Multiaxial stress effects on fatigue behavior of filled natural rubber, International Journal of Fatigue,2006 28:521-529.
[19]Saintier N., Cailletaud G., Piques R., Multiaxial fatigue life prediction for a natural rubber, International journal of fatigue,2006,28:530-539.
[20]P. B. Lindley. Relation between hysteresis and the dynamic crack growth resistance of natural rubber [J]. International Journal of Fracture,1973,9(4): 449-462.
[21]G. J. Lake. Aspects of fatigue and fracture of rubber[J]. Prog. Rubber Technol. 1983,45:89-143.
[22]Beatty J. R., Fatigue of rubber, Rubber Chemistry and Technology,1964,37: 1341-1364.
[23]Fielding J. H., Flex life and crystallization if synthetic rubber, Industrial and Engineering Chemistry,1943,35:1259-1261.
[24]Abraham F., Alshuth T., Jerrams S., The effect of minimum stress and stress amplitude on the fatigue life of non strain crystallising elastomers, Materials and Design 2005,26:239-245.
[25]Lee B. L., Ku B. H., Liu D. S., Fatigue of cord-rubber composites (Ⅱ):Strain-based fatigue failure criteria[J]. Rubber Chemistry and Technology,1998,71:866-888.
[26]Lindley P. B., Relation between hysteresis and the dynamic crack growth resistance of natural rubber[J]. International Journal of Fracture,1973, 9:449-462.
[27]Busfield J. J. C., Ratsimba C. H. H., and Thomas A. G., "Finite Element Analysis of Elastomers, " D. Boast and V. A. Coveny, Eds., IMech E, United Kingdom,1999: 235.
[28]Mars W. V., Fatemi A., Multiaxial fatigue of rubber—part Ⅱ:experimental observations and life predictions[J]. Fatigue Fract Eng Mater Struct.,2005, 28:523-538.
[29]刘宇艳,万志敏,杜星文,周期载荷下聚酯纤维／橡胶复合材料和人造丝／橡胶复合材 料的疲劳行为[J].材料工程,2000(10),29-32.
[30]刘宇艳,田振辉,万志敏等,橡胶复合材料在循环载荷下的疲劳损伤特性[J].橡胶工业,2003,5：713-716.
[31]D. G. Young. Dynamic property and fatigue propagation research on tire sidewall and model compounds[J]. RUBBER CHEM. TECHNOL.,1985,58:785-805.
[32]D. G. Young. Fatigue crack propagation in elastomer compounds:effects of strain rate, temperature[J]. RUBBER CHEM. TECHNOL.,1986,59:809-825.
[33]A. J. M. Sumner, S. A. Kelbch, U. G. Eisele, Rubber World,212 (2),38 (1995).
[34]D. Hardy, H. Moneypenny, M. Holderied, J. Harris, R. Campion, G. Morgan, Paper No.2 presented at RubberChem'99, Belgium,(1999).
[35]C. Sun, A. N. Gent, P. Marteny. Effect of Fatigue Step Loading Sequence on Residual Strength[J]. Tire Sci. Technol.,2000,28:196.
[36]C. M. Roland, J. W. Sobiesky. Network recovery from uniaxial extension. Ⅱ. The origin of the Mullins effect[J]. RUBBER CHEM. TECHNOL.1989,62:683.
[37]Mars W. V., Fatemi A., Multiaxial fatigue of rubber—part Ⅰ:equivalence criteria and theoretical aspects. Fatigue Fract Eng Mater Struct 2005,28:515-522.
[38]孟宪德.橡胶的疲劳老化与防护[J].合成材料老化与应用,1992,(4)：10-21
[39]G. J. Lake, P. B. Lindley. Cut growth and fatigue of rubbers. II. Experiments on a noncrystallizing rubber[J].J Appl. Polym. Sci.1964,8:707-721.
[40]D. G. Young. Fatigue crack propagation in elastomer compounds:effects of strain rate, temperature,strain level, and oxidation[J]. RUBBER CHEM. TECHNOL.1986, 59:809.
[41]D. G. Young, J. A. Danik, RUBBER CHEM. TECHNOL.67,137 (1994).
[42]M. Braden, A. N. Gent. The attack of ozone on stretched rubber vulcanizates.Ⅱ. Conditions for cut growth[J]. J. of Appl. Polym. Sci.,1960,3(7):90-100.
[43]G. J. Lake, A. G. Thomas. Engineering with Rubber, How to Design Rubber Components. A. Gent, Ed., Carl Hanser Verlag, Munich (1992),ch.5.
[44]杨清芝主编.现代橡胶工艺学[M].北京：中国石化出版社,1997,315
[45]A. N. Gent, H. Hirakawa. Effect of temperature on the ozone cracking of butyl rubbers[J].J. Polym. Sci. Part A-2,1968,6:1481.
[46]A. N. Gent, J. E. McGrath, J. Polym. Sci., Part A 3,1473 (1965).
[47]Gent A. N., Hindi M., Effect of oxygen on the tear strength of elastomers, Rubber Chemistry and Technology 1990,63:123-34.
[48]Blackman E. J., McCall E. B., Relationship between the structures of natural rubber-vulcanizates and their thermal and oxidative aging, Rubber Chemistry and Technology,1970,43:651-663.
[49]C.M.Roland. Network recovery from uniaxial extension. I. Elastic equilibrium[J]. RUBBER CHEM. TECHNOL.,1989,62,863.
[50]D. G. Young.Dynamic property and fatigue propagation research on tire sidewall and model compounds[J]. RUBBER CHEM. TECHNOL.1985,58:785.
[51]王进文编译.改性炭黑对SBR拉伸性能和屈挠性能的影响[J].世界橡胶工业,2000,27(4)：4-6.
[52]裘怿明,肖建斌等.普通、半有效和有效硫化体系的NR/BR共混胶料的疲劳寿命曲线方程[J].橡胶工业,1999,46(2)：71-74.
[53]裘怿明,傅政等.不同硫化体系橡胶的疲劳断裂性能[J].合成橡胶工业,2000,23(2)：111-114.
[54]黄良平,杨军等.白炭黑原位接枝改性对橡胶屈挠性能的影响[A].2004年国际橡胶会议论文集[c].北京：中国化工学会橡胶专业委员会,2004.135-138.
[55]贾红兵等.填充剂表面改性剂对硫化胶疲劳性能的影响[J].高分子材料科学与工程,2002,18(1)：119-122.
[56]张士齐等.硫化橡胶疲劳和磨耗时的力化学后活化学效应研究[J].橡胶工业,1990,37(6)：354-359.
[57]Hamed, Gary R. Molecular aspects of the fatigue and fracture of rubber [J]. Rubber Chemistry and Technology,1994,67(3):529-536.
[58]张士齐,周翠微,邓知庆.研究炭黑补强硫化胶疲劳的分子历程[J].橡胶工业,1988,35(10)：616.
[59]张殿荣等.现代橡胶配方设计[M].北京：化学工业出版社,2001.87.
[60]Woo Chang-Su, Kim Wan-Doo. A study on the fatigue life prediction and evaluation of rubber components. Symposium of international rubber conference,2004: 342-348.
[61]R. S. Rivlin, A. G. Thomas. Rupture of rubber:I. Characteristic energy for tearing [J]. J. Polym. Sci.,1953,10:291.
[62]C. M. Roland. Network recovery from uniaxial extension. Ⅱ. The origin of the Mullins effect[J]. RUBBER CHEM. TECHNOL.,1989,62:863.
[63]A. I. Medalia. Effect of carbon black on ultimate properties of rubber vulcanizates[J]. RUBBER CHEM. TECHNOL.,1987,60:45.
[64]W.V.Mars., A. FATEMI. Fatigue crack nucleation and growth in filled natural rubber[J]. Fatigue & Fracture of Engineering Materials & Structures,2003,26 (9):779-789.
[65]W D Kim, H J Lee, J Y Kim. Fatigue life estimation of an engine rubber mount [J]. International journal of fatigue,2004,26(5):553-560.
[66]Guido Raos, Margherita Moreno, Stefano Elli. Computational Experiments on Filled Rubber Viscoelasticity:What Is the Role of Particle-Particle Interactions?[J]. Macromolecules,2006,39(19):6744-6751.
[67]P. G. Santangelo, C. M. Roland. Role of Strain Crystallization in the Fatigue Resistance of Double Network Elastomers[j]. Rubber Chemistry And Technology,2003,76:892-898.
[68]I. S. Choi,C.M. Roland. Strain-crystallization of guayule and hevea rubber [J]. RUBBER CHEM. TECHNOL.,1997,70:202.
[69]S Wiese, S Jakschik, F Feustel. Fracture behaviour of flip chip solder joints. Electronic Components and Technology Conference,2001.51st:1299-1306.
[70]G. J. Lake, A. G. Thomas. The strength of highly elastic materials[J]. Proc. Royal Society of London, Series A.1961,300(1460):108-119.
[71]A A Griffith. The phenomena of rupture and flow in sol ids[J]. Philosophical Transactions of the Royal Society of London. Series A.1921,221:153-197.
[72]C Feichter, Z Major. Experimental determination of fatigue crack growth behavior and surface strain distribution of faint-waist pure shear specimens with different crack tip radii[J]. Rubber chemistry and technology,2006,79(4): 712-733.
[73]Ryan J. Harbour, Ali Fatemi.Will V. Mars. Fatigue crack orientation in NR and SBR under variable amplitude and multiaxial loading conditions[J]. J. Mater. Sci.,2008,43:1783-1794.
[74]M. F. Tse. Ozone Cracking and Flex Cracking of Crosslinked Polymer Blend Compounds[J]. Journal of Applied Polymer Science,2007,103:2183-2196.
[75]Verron E,Le Cam JB, Gornet J. A multiaxial criterion for crack nucleation in Rubber[J]. Mech. Res. Commun.,2006,33:493-498.
[76]王进,杨军等.橡胶疲劳破坏性能的研究[A].2004年国际橡胶会议中文论坛论文集[C].北京：中国化工学会橡胶专业委员会,2004.123-126.
[77]藤本邦彦Study on Three-Dimentionality Stressed Fatigue of NR/SBR Blended Rubber日本A协会志,1992,65(1),42
[78]藤本邦彦Study on Dynamic Creep of SBR/NR Blend Rubber日本A协会志,1991,64(5)：632.
[79]J.-B. Le Cam, B. Huneau, E. VerronJ.-B. Le Cam, B. Huneau, E. Verron etal. Mechanism of Fatigue Crack Growth in Carbon Black Filled Natural Rubber[J]. Macromolecules,2004,37 (13):5011-5017
[80]Takeshi Karino, Yuko Ikeda, Yoritaka Yasuda etal. Nonuniformity in Natural Rubber As Revealed by Small-Angle Neutron Scattering, Small-Angle X-ray Scattering, and Atomic Force Microscopy[J]. Biomacromolecules,2007,8(2): 693-699
[81]J.-B. Le Cam and E. Toussaint.Volume Variation in Stretched Natural Rubber: Competition between Cavitation and Stress-Induced Crystallization[J]. Macromolecules,2008,41(20):7579-7583.
[82]K. Legorju-jago and C. Bathias. Fatigue initiation and propagation in natural and synthetic rubbers[J]. International Journal of Fatigue,2002,24(2-4): 85-92.
[83]卢红斌,杨玉良.填充聚合物的熔体流变学[J].高分子通报,2001,12(1)：18-26
[84]32Kosinski L.E., Caruthers. J. M. [J] Rheol Acta,1986,25:153-160
[85]33 G. Kraus, Interactions of elastomers and reinforcing fillers [J] Rubber Chem. Technol.1965:38(5):1070-1115
[86]36 E. M. Dannenberg, Bound rubber and carbon black reinforcement [J]. Rubber Chem. Technol.1986,59(3):512-520
[87]3 Payne A R. The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I [J]. J Appl Polym Sci 1962,6(19):57-63
[88]4 Payne A. R., Watson W. F. Carbon black structure in rubber [J]. Rubber Chem Technol 1963,36(1):147-156
[89]Payne AR, Wittaker RE. Low strain dynamic properties of filled rubbers [J]. Rubber Chem Technol 1971,44(3):440-470
[90]Payne A R Dynamic properties of heat-treated butyl vulcanizates [J]. J Appl Polym Sci 1963,7(3):873-885
[91]Payne A R. Strainwork dependence of filler-loaded vulcanizates [J]. J Appl Polym Sci 1964,8(6):2661-2686
[92]Payne A R. In:Kraus G (ed) Reinforcement of elastomers. Interscience Publisher, NewYork, Chaper 3.1972
[93]Payne A R Effect of vulcanization on the low-strain dynamic properties of filled rubbers [J]. J Appl Polym Sci 1972,16(5):1191-1212
[94]Payne A R. The dynamic properties of carbon black-loaded natural rubber vulcanizates. Part I [J]. Rubber Chem Technol 1963,36(2):432-444
[95]Medalia A I Elastic modulus of vulcanizatioes as related to carbon black [J]. Rubber Chem Technol 1973,46(3):877-897
[96]Medalia A I Filler aggregates and their effect on reinforcement [J]. Rubber Chem Technol 1974,47(2):411-434
[97]Medalia AI Effect of carbon black on the dynamic properties of rubber vulcanizates [J]. Rubber Chem Technol.1978,51(3):437-524
[98]Voet A, Cook FR Mild stress softening and dynamic properties of rubber vulcanizates [J]. Rubber Chem Technol 1967,40(5):1364-1373
[99]Voet A, Cook FR. Analysis of contributions to dynamic mechanical properties of carbon filled vulcanized [J]. Rubber Chem Technol 1968,41 (5):1215-1219
[100]Sircar AK, Lamond TG Strain-dependent dynamic properties of carbon black reinforced vulcanizates, I. Individual elastomers, II. Elastomer blends [J]. Rubber Chem Technol 1975,48(1):79-97
[101]王梦蛟,填充聚合物-填料和填料-填料相互作用对填充硫化胶动态力学性能的影响[J].轮胎工业,2000,20(11)：670-677
[102]D. Stauffer and A. Aharony "Introduction to Percolation Theory",2nd Ed. Taylor & Francis, London,1994.
[103]Choi Sung-seen. Improvement of properties of silica-filled natural rubber compounds using polychloroprene [J]. J Appl. Polym. Sci.2002,83(12):2609-2616,
[104]冯希金,轮胎疲劳寿命研究的进展,橡胶科技市场[J],(6)：8-12
[105]庄继德,现代汽车轮胎技术,北京：北京理工大学出版社[M],2001.3：21
[106]何志刚、周孔亢、应世洲等,轮胎疲劳失效研究综述,机械工程学报[J],2009,45(3)：76-83
[107]戴永谦,宋希庚,薛冬新.裂纹生长方法在橡胶疲劳分析中的应用研究[J].振动与冲击,2005,24(4)：115-119.
[108]SAINTER N, CAILLETAUD G. Crack initiation and propagation under multiaxial fatigue in a natural rubber [J]. Int. J. Fatigue,2006,28(1):61-72.
[109]MARS W V. A literature survey on fatigue analysis approaches for rubber [J]. Int. J. Fatigue,2002,24(9):949-961.
[110]KIM J H, JEONG H Y. A study on the material properties and fatigue life of natural rubber with different carbon blacks[J]. Int. J. Fatigue,2005,27(3): 263-272.
[111]GRIFFITH A A. The phenomena of rupture and flow in solids[J]. Philosophical Transaction of Royal Society of London, Series A,1920,221:163-198.
[112]INGLIS C E. Stresses in a plate due to the presence of cracks and sharp corners[J]. Transactions of the Institute of Naval Architects,1913,55:219-241.
[113]GREENSMITH H W. Rupture of rubber IV. Tearing properties of vulvanizates containing carbon black[J]. Journal of Polymer Science,1956,21:175-187.
[114]SCHUBEL P M, GDOUTOS E E. Fatigue characterization of tire rubber[J]. Theoretical and Applied Fracture Mechanics,2004,42(2):149-154.
[115]OZUPEK S, BECKER E B. Finite element method for the study of belt edge delaminations in truck tires[J]. Rubber Chemistry and Technology,2005,78(4): 557-571.
[116]SOUTHERN E, THOMAS A G. Studies of rubber abrasion [J]. Plastics and Rubber： Materials and Applications,1978,3(4):133-138.
[117]GROSCH K. Rolling resistance and fatigue life of tires [J]. Rubber Chemistry and Technology,1988,61(1):42-63.
[118]66 Huang Y S, Yoeh 0 H. Crack initiation and propagation in model COrd—rubber composites. Rubber Chemistry and Tec—hnology.1989.62:709-731
[119]EBBOTT T G. Application of finite element-base fracture mechanics analysis to cord-rubber structures [J]. Tire Science and Technol.,1996,24(3):220-235.
[120]WEI Y T, TIAN Z H, DU X W. Finite element model for the rolling loss prediction and fracture analysis of radial tires[J]. Tire Science and Technol.,1999,27(4): 250-276.
[121]危银涛.轮胎热力学分析及耐久性评价[D].哈尔滨：哈尔滨工业大学,1997.88-93.
[122]深崛美英.弹性体疲劳寿命的预测[J].橡胶译丛,1986(4)：67-76.
[123]肖建斌,江爱民,焦清锋,等NR/SBR共混物的动态疲劳与断裂特征[J].高分子材料科学与工程,1999,15(2)：136-139.
[124]肖建斌,国继红,邹志德,等.不同补强体系胶料疲劳断裂性能的研究[J].橡胶工业,2000,47(10)：584-587.
[125]裘怿明,傅政,刘旭阳,等.多项式回归拟合NR/BR共混胶料疲劳断裂曲线[J].橡胶工业,1998,45(3)：137-139.
[126]右田哲彦.橡胶的疲劳与破坏机理与配方设计[J].橡胶译丛,1981(2)：1-19.
[127]SOUTH J T. Mechanic properties and durability of natural rubber compounds and composites [D]. Virginia, USA:Virginia Polytechnic Institute and State University,2001.
[128]SONG J. Fatigue of cord-rubber composites for tires [D]. Washington D. C., USA:Pennsylvania University,2004.
[129]Hirakawa H. Urano F. Kida M. Analysis of fatigue process of rubber vulcanizetes, Rubber Chemistry and Technology,1978,51:201-214.
[130]Omira N., Takahashi M., The fatigue properties of silicone rubber[A] Presebted at the Meeting of the Rubber Division[J] Washington Hilton:Amertion Chemical Society,1990.
[131]倪玉山,徐军,张华兵.轮胎中橡胶材料断口形貌及破坏机理分析[J].高分子材料科学与工程,2004,20(6)：184-186.
[132]Xie Z M, Miao C Q, Wan Z M, etal. Investigation of t he carbon black network in natural rubber under cyclic deformation [J]. Journal of Macromolecular Science. Physics,2005,B44(3):3452351.
[133]谢志民,王友善,马娟娜.填充橡胶中的炭黑网络研究[J].橡胶工业,2008,55(7)：4404-407.
[134]Eldred R. J., Journal of polymer science, Polymer Letter(Ed.),1972,10,391.
[135]Mathew N. M., Bhowmick A. K., De S. K., Chemical and scanning electron microscopy studies on fatigue failure of natural rubber vulcanizates, Rubber Chemistry and Technology,1982,55(1):51-61.
[136]Hainsworth S. V., An environmental scanning electron microscopy investigation of fatigue crack initiation and propagation in elastomers, Polymer Testing, 2007,26 (1):60-70.
[137]Le Cam J. B., Huneau B., Verron E., Mechanism of Fatigue Crack Growth in Carbon Black Filled Natural Rubber, Macromolecules,2004,37 (13):5011-5017.
[138]J-B. Le Cam, E. Toussaint. The Mechanism of Fatigue Crack Growth in Rubbers under Severe Loading:the Effect of Stress-Induced Crystallization[J]. Macromolecules,2010,43(10):4708-4714
[139]Milber C, B lumichB,U nseldK etal. NMR Imaging of Thermal-oxidative Ageing in SBR. K autschukG ummiK unststoff,1995,4:254
[140]Takuya Suzuki, Noboru Osaka, Hitoshi Endo etal. Nonuniformity in Cross-Linked Natural Rubber as Revealed by Contrast-Variation Small-Angle Neutron Scattering[J]. Macromolecules,2010,43(3):1556-1563.