参考文献
[1] Edwards D C. Polymer-filler interactions in rubber reinforcement[J]. J Mater Sci, 1990, 25 (10): 4175-4185.
[2] Zhang L Q, Jia D M. The nano-reinforcing technique and Science of rubber[C]. Symposium of International Rubber Conference, Beijing, China, 2004, A: 21.
[3] Kraus G. Reinforcement of elastomers by carbon-black[J]. Rubber Chem Technol, 1978, 51 (2): 297-321.
[4] Hamed G R. Reinforcement of rubber[J]. Rubber Chem Technol, 2000, 73 (3): 524-533.
[5] Heinrich G, Kluppel M, Vilgis T A. Reinforcement of elastomers[J]. Curr Opin Solid St M, 2002, 6 (3): 195-203.
[6] Wang M J. Effect of polymer-filler and filler-filler interactions on dynamic properties of filled vulcanizates[J]. Rubber Chem Technol, 1998, 71 (3): 520-589.
[7] Bokobza L. New Developments in rubber reinforcement[J]. Kautschuk Gummi Kunststoffe, 2009, 62 (1-2): 23-27.
[8] Bokobza L. The Reinforcement of elastomeric networks by fillers[J]. Macromol Mater Eng, 2004, 289 (7): 607-621.
[9] 张立群, 吴友平, 王益庆, 等. 橡胶的纳米增强及纳米复合技术[J]. 合成橡胶工业, 2000, (02): 71-77.
[10] 冯予星, 刘力, 张立群, 等. PP/POE共混合金的研究[J]. 工程塑料应用, 1999, (12): 6-9.
[11] Wu S H. Phase-structure and adhesion in polymer blends - a criterion for rubber toughening[J]. Polym, 1985, 26 (12): 1855-1863.
[12] Margolina A, Wu S H. Percolation model for brittle-tough transition in nylon rubber blends[J]. Polymer, 1988, 29 (12): 2170-2173.
[13] Wu S H. A generalized criterion for rubber toughening—the critical matrix ligament thickness[J]. J Appl Polym Sci, 1988, 35 (2): 549-561.
[14] Naunton W J S. The applied science of rubber[M]. London: Edward Arnold Ltd, 1961: 207-253.
[15] Kraus G. Reinforcement of elastomers[M]. New York: Interscience Publishers, 1965: 125-152.
[16] Smith T L, Rinde J A. Ultimate tensile properties of elastomers .Ⅴ. Rupture in constrained biaxial tensions[J]. Journal of Polymer Science Part A-2: Polymer Physics, 1969, 7 (4): 675-685.
[17] Dickie R A, Smith T L. Ultimate tensile properties of elastomers.Ⅵ. strength and extensibility of a styrene-butadiene rubber vulcanizate in equal biaxial tension[J]. Journal of Polymer Science Part A-2: Polymer Physics, 1969, 7 (4): 687-707.
[18] Boonstra B B. Mixing of carbon black and polymer—interaction and reinforcement[J]. J Appl Polym Sci, 1967, 11 (3): 389-406.
[19] Obrien J, Cashell E, Wardell G E, Mcbrierty V J. NMR investigation of interaction between carbon-black and cis-polybutadiene[J]. Rubber Chem Technol, 1977, 50 (4): 747-764.
[20] Wang M J, Wolff S, Donnet J B. Filler elastomer interactions.Ⅲ. carbon-black-surface energies and interactions with elastomer analogs[J]. Rubber Chem Technol, 1991, 64 (5): 714-736.
[21] van de Walle A, Tricot C, Gerspacher M. Modeling carbon black reinforcement in rubber compounds[J]. Kaut Gummi Kunstst, 1996, 49 (3): 172-179.
[22] Kilian H G, Strauss M, Hamm W. Universal properties in filler-loaded rubbers[J]. Rubber Chem Technol, 1994, 67 (1): 1-16.
[23] Strauss M, Pieper T, Peng W G, Kilian H G. Structure of filled rubbers and mechanism of reinforcement[J]. Makromolekulare Chemie-Macromolecular Symposia, 1993, 76: 131-136.
[24] Kilian H G. Reinforced vanderwaals-networks-a new concept of characterization[J]. Kaut Gummi Kunstst, 1986, 39 (8): 689-694.
[25] Reichert W F, Goritz D, Duschl E J. The double network, a model describing filled elastomers[J]. Polymer, 1993, 34 (6): 1216-1221.
[26] Meissner B, Matejka L. Description of the tensile stress-strain behaviour of filler-reinforced rubber-like networks using a langevin-theory-based approach: Part Ⅱ[J]. Polymer, 2001, 42 (3): 1143-1156.
[27] Meissner B, Matejka L. Description of the tensile stress-strain behavior of filler-reinforced rubber-like networks using a langevin-theory-based approach: Part I[J]. Polymer, 2000, 41 (21): 7749-7760.
[28] Meissner B. Tensile stress-strain behaviour of rubberlike networks up to break: theory and experimental comparison[J]. Polymer, 2000, 41 (21): 7827-7841.
[29] 宋名实. 聚合物网的网络结构同力学性能间相关性的研究——自由连接链的交联-缠结网大形变弹性分子理论[J]. 中国科学技术大学学报, 1985(03): 286-298.
[30] 宋名实. 聚合物网的网络结构同力学性能间相关性的研究——交联-缠结网弹性分子理论同实验的对比[J]. 中国科学技术大学学报, 1986(02): 162-174.
[31] Bokobza L. Filled elastomers: a new approach based on measurements of chain orientation[J]. Polymer, 2001, 42 (12): 5415-5423.
[32] Song M, Xia H S, Yao K J, Hourston D J. A study on phase morphology and surface properties of polyurethane/organoclay nanocomposite[J]. Eur Polym J, 2005, 41 (2): 259-266.
[33] Kohjiya S, Kato A, Ikeda Y. Visualization of nanostructure of soft matter by 3D-TEM: nanoparticles in a natural rubber matrix[J]. Prog Polym Sci, 2008, 33 (10): 979-997.
[34] Hamed G R, Hatfield S. On the role of bound rubber in carbon-black reinforcement[J]. Rubber Chem Technol, 1989, 62 (1): 143-156.
[35] Yu Q X. Handbook of materials for rubber industry. 2nd Ed[M]. Beijing: Chemistry Industry Press, 2007.
[36] Leblanc J L. Rubber-filler interactions and rheological properties in filled compounds[J]. Prog Polym Sci, 2002, 27 (4): 627-687.
[37] 张立群, 金日光, 耿海萍, 等. 短纤维橡胶复合材料临界长径比数学模型研究[J]. 复合材料学报, 1998, 15(03):85-91.
[38] 张立群, 金日光, 耿海萍, 等. 短纤维橡胶复合材料强度的理论研究Ⅰ:纵向拉伸强度的理论预测[J]. 复合材料学报, 1998, 15(04): 89-96.
[39] 高玉臣. 固体力学基础 [M]. 北京: 中国铁道出版社, 1999.
[40] Treloar L R G. The elasticity of a network of long-chain molecules. II [J]. Transactions of the Faraday Society, 1943, 39(2): 241-246.
[41] Mooney M. A theory of large elastic deformation [J]. Journal of Applied Physics, 1940, 11(9): 582-592.
[42] Yeoh O H. Characterization of elastic properties of carbon-black-filled rubber vulcanizates [J]. Rubber Chemistry and Technology, 1990, 63(5): 792-805.
[43] Ogden R W. Large deformation isotropic elasticity—on the correlation of theory and experiment for incompressible rubberlike Solids [J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1972, 326(1567): 565-584.
[44] Valanis K C. The strain-energy function of a hyperelastic material in terms of the extension ratios [J]. Journal of Applied Physics, 1967, 38(7): 2997-3002.
[45] Beda T, Chevalier Y. Hybrid continuum model for large elastic deformation of rubber [J]. Journal of Applied Physics, 2003, 94(4): 2701-2706.
[46] James H M, Guth E. Theory of the elastic properties of rubber [J]. The Journal of Chemical Physics, 1943, 11(10): 455-481.
[47] Flory P J, Rehner J. Statistical mechanics of cross-linked polymer networks i. rubberlike elasticity [J]. The Journal of Chemical Physics, 1943, 11(11): 512-520.
[48] Arruda E M, Boyce M C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials [J]. Journal of the Mechanics and Physics of Solids, 1993, 41(2): 389-412.
[49] Boyce C M, Arruda M E. Constitutive models of rubber elasticity: A review [J]. Rubber Chemistry and Technology, 2000, 73(3): 504-523.
[50] Elías-Zúñiga A, Beatty M F. Constitutive equations for amended non-Gaussian network models of rubber elasticity [J]. International Journal of Engineering Science, 2002, 40(20): 2265-2294.
[51] Bonet J, Wood R D. Nonlinear continuum mechanics for finite element analysis [M]. UK: Cambridge University Press, 1997.
[52] Rivlin R S, Saunders D W. Large elastic deformations of isotropic materials. Ⅶ. experiments on the deformation of rubber[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 1951, 243(865): 251-288.
[53] Hart-Smith L J. Elasticity parameters for finite deformations of rubber-like materials [J]. Zeitschrift für angewandte Mathematik und Physik ZAMP, 1966, 17(5): 608-626.
[54] Gent A N. A new constitutive relation for rubber [J]. Rubber Chemistry and Technology, 1996, 69(1): 59-61.
[55] Yeoh O H, Fleming P D. A new attempt to reconcile the statistical and phenomenological theories of rubber elasticity [J]. Journal of Polymer Science Part B: Polymer Physics, 1997, 35(12): 1919-1931.
[56] Rivlin R S, Sawyers K N. The strain-energy function for elastomers [J]. Journal of Rheology, 1976, 20(4): 545-557.
[57] Treloar LRG. The physics of rubber elasticity [M]. Clarendon Press , Oxford University Press, 1975.
[58] Peng T J, Landel R F. Stored energy function of rubberlike materials derived from simple tensile data [J]. Journal of Applied Physics, 1972, 43(7): 3064-3067.
[59] Marckmann G, Verron E, Gornet L, et al. A theory of network alteration for the Mullins effect [J]. Journal of the Mechanics and Physics of Solids, 2002, 50(9): 2011-2028.
[60] 谭江华, 罗文波. 橡胶材料分子链网络本构模型的研究进展 [J]. 材料导报, 2008, 22(7): 31-34.
[61] Treloar L R G. The photoelastic properties of short-chain molecular networks [J]. Transactions of the Faraday Society, 1954, 50: 881-896.
[62] Wu P D, van der Giessen E. On improved network models for rubber elasticity and their applications to orientation hardening in glassy polymers [J]. Journal of the Mechanics and Physics of Solids, 1993, 41(3): 427-456.
[63] Tomita Y, Tanaka S. Prediction of deformation behavior of glassy polymers based on molecular chain network model [J]. International Journal of Solids and Structures, 1995, 32(23): 3423-3434.
[64] Heinrich G, Kaliske M. Theoretical and numerical formulation of a molecular based constitutive tube-model of rubber elasticity [J]. Computational and Theoretical Polymer Science, 1997, 7(3): 227-241.
[65] Kaliske M, Heinrich G. An extended tube-model for rubber elasticity: statistical-mechanical theory and finite element implementation [J]. Rubber Chemistry and Technology, 1999, 72(4): 602-632.
[66] Li F, Liu J, Yang H, et al. Numerical simulation and experimental verification of heat build-up for rubber compounds[J]. Polymer, 2016, 101:199-207.
[67] Li F, Liu F, Liu J, et al. Thermo-mechanical coupling analysis of transient temperature and rolling resistance for solid rubber tire: numerical simulation and experimental verification[J]. Composites Science and Technology, 2018, 167:404-410.
[68] 李凡珠.天然橡胶纳米复合材料的疲劳失效和滞后温升性能热力耦合的模拟研究[D]. 北京:北京化工大学,2017.
[69] Kraus G. Mechanical losses in carbon-black-filled rubbers[A]//Proceedings of the Journal of Applied Polymer Science: Applied Polymer Symposium[C], 1984.
[70] Ulmer J. Strain dependence of dynamic mechanical properties of carbon black-filled rubber compounds[J]. Rubber Chemistry and Technology, 1996, 69(1): 15-47.
[71] Maier P G, Goritz D. Molecular interpretation of the Payne effect[J]. Kautschuk Gummi Kunststoffe, 1996, 49(1): 18-21.
[72] Meera A P, Said S, Grohens Y, et al. Nonlinear viscoelastic behavior of silica-filled natural rubber nanocomposites[J]. The Journal of Physical Chemistry C, 2009, 113(42): 17997-18002.
[73] Huber G, Vilgis T A, Heinrich G. Universal properties in the dynamical deformation of filled rubbers[J]. Journal of Physics: Condensed Matter, 1996, 8(29): 409.
[74] Lion A. Strain-dependent dynamic properties of filled rubber: a non-linear viscoelastic approach based on structural variables[J]. Rubber Chemistry and Technology, 1999, 72(2): 410-429.
[75] Du M, Guo B, Lei Y, et al. Carboxylated butadiene-styrene rubber/halloysite nanotube nanocomposites: interfacial interaction and performance[J]. Polymer, 2008, 49(22): 4871-4876.
[76] Keledi G, Hári J, Pukánszky B. Polymer nanocomposites: structure, interaction, and functionality[J]. Nanoscale, 2012, 4(6): 1919-1938.
[77] Meyers M A, McKittrick J, Chen P Y. Structural biological materials: critical mechanics-materials connections[J]. Science, 2013, 339(6121): 773-779.
[78] Gutsmann T, Hassenkam T, Cutroni J A, et al. Sacrificial bonds in polymer brushes from rat tail tendon functioning as nanoscale velcro[J]. Biophysical Journal, 2005, 89(1): 536-542.
[79] Gong J P, Katsuyama Y, Kurokawa T, et al. Double‐network hydrogels with extremely high mechanical strength[J]. Advanced Materials, 2003, 15(14): 1155-1158.
[80] Sun J Y, Zhao X, Illeperuma W R K, et al. Highly stretchable and tough hydrogels[J]. Nature, 2012, 489(7414): 133.
[81] Ducrot E, Chen Y, Bulters M, et al. Toughening elastomers with sacrificial bonds and watching them break[J]. Science, 2014, 344(6180): 186-189.
[82] Zhang X, Tang Z, Huang J, et al. Strikingly improved toughness of nonpolar rubber by incorporating sacrificial network at small fraction[J]. Journal of Polymer Science Part B: Polymer Physics, 2016, 54(8): 781-786.
[83] Mozhdehi D, Ayala S, Cromwell O R, et al. Self-healing multiphase polymers via dynamic metal–ligand interactions[J]. Journal of the American Chemical Society, 2014, 136(46): 16128-16131.
[84] Fantner G E, Oroudjev E, Schitter G, et al. Sacrificial bonds and hidden length: unraveling molecular mesostructures in tough materials[J]. Biophysical Journal, 2006, 90(4): 1411-1418.
[85] Wang W, Elbanna A. Crack propagation in bone on the scale of mineralized collagen fibrils: role of polymers with sacrificial bonds and hidden length[J]. Bone, 2014, 68: 20-31.
[86] Wang Z, Liu J, Wu S, et al. Novel percolation phenomena and mechanism of strengthening elastomers by nanofillers[J]. Physical Chemistry Chemical Physics, 2010, 12(12): 3014-3030.
[87] Li H, Yang L, Weng G, et al. Toughening rubbers with a hybrid filler network of graphene and carbon nanotubes[J]. Journal of Materials Chemistry A, 2015, 3(44): 22385-22392.
[88] Tang Z, Huang J, Guo B, et al. Bioinspired engineering of sacrificial metal-ligand bonds into elastomers with supramechanical performance and adaptive recovery[J]. Macromolecules, 2016, 49(5): 1781-1789.
[89] Chen Z, Lu H. Constructing sacrificial bonds and hidden lengths for ductile graphene/polyurethane elastomers with improved strength and toughness[J]. Journal of Materials Chemistry, 2012, 22(25): 12479-12490.
[90] Tanaka Y, Kuwabara R, Na Y H, et al. Determination of fracture energy of high strength double network hydrogels[J]. The Journal of Physical Chemistry B, 2005, 109(23): 11559-11562.