银纹化高聚物的分形损伤模型
摘要
银纹化是玻璃态高聚物所特有的一种现象。聚合物的银纹损伤是一个复杂的多层次阶段,从微观层次的分子链间缠结链段的重排、滑移、取向、解缠及断链,到细观层次的银纹引发,生长及断裂,直到后继的微裂纹的产生、扩展、串接最终导致材料整体破坏。银纹能够承载一定的拉应力;银纹化高聚物的力学性能是银纹损伤和银纹增韧两方面竞争的结果,这说明银纹化高聚物损伤的模型不同于一般的损伤材料,应该反映它所特有的损伤机理。
在标准线性固体模型的基础上,通过引进率相关弹簧和作者已建立的非线性Bingham流体模型,建立了小变形条件下的高聚物一维非线性粘弹模型;并根据对应原理,将此模型推广到各向同性材料中,建立了三维非线性粘弹模型。其次,根据Noll三原则、功共轭原理、真应力原则,选择Updated Lagrange坐标系以及第二类P-K应力张量和Green应变张量,将小变形条件下的三维粘弹性本构进行推广,建立了Euler坐标系下的有限变形条件下的三维粘弹性模型。最后,根据非平衡态热力学及其内变量理论,建立了一维有限变形粘弹性模型。
首次引入分形理论对高聚物的银纹损伤进行研究。首先,根据银纹的特点阐述了其分形维数的区间为[0 , 2)。银纹的分形维数不仅表征了高聚物的空穴化程度而且表征了材料的微纤化水平。其次,在利用分形维数建立的损伤变量和韧化函数的基础上,定义了一个全新的概念:银纹变量。它可以表征银纹损伤和银纹增韧对材料的共同作用。在有限变形条件下,通过面积转换,定义了新的分形维数计算方法,建立了有限变形条件下的银纹变量。新的银纹变量能够更加客观的刻画材料的损伤程度,因为它有效地剔除有限变形过程中弹性变形和塑性变形对银纹分形维数的影响。最后,利用已建立的银纹变量,根据Kachanov-Rabotnov的有效应力理论,建立了银纹化高聚物在小变形条件和有限变形条件下的一维和三维的分形损伤模型。
利用分形维数对银纹进行了定量化分析。通过蠕变试验,采集了PMMA在不同应力和不同时间的蠕变银纹图像,并采用盒维法计算了其分形维数。试验证明,蠕变银纹引发的应力阀值随时间的增长呈指数关系降低,并最终趋于常数;蠕变银纹的分形维数与应力呈线性关系,与时间呈指数关系;在达到应力阀值的瞬间,能产生大量银纹,导致银纹的分形维数产生阶跃。根据实验结果,建立了蠕变银纹的分形维数与应力、时间的关系式。
The crazing phenomenon is unique to amorphous glassy polymers. The crazing damage evolves in three different levels: the orientating, untwisting and breaking of macromolecular chains in microscopic state; the initiation, growth and breakdown of crazes in mesoscopic layer; the formation, expansion and rupture of mesocracks in macroscopic view. A craze can sustain a definite amount of tensile stress and the mechanical properties of crazing polymers are the competitive result between crazing damage and toughening, which means the damage model of crazing polymers should be distinguished from other materials due to their particular damage mechanism.
Based on the standard linear solid model, a one-dimensional nonlinear viscoelastic model of polymers for small deformation is set up to describe strain- rate-dependency elasticity and nonlinear viscosity. The corresponding three- dimensional model is developed by generalizing the one-dimensional nonlinear viscoelastic model according to the correspondence principle.
The former construction serves as a starting point for the development of a three-dimensional, finite deformation, viscoelastic constitutive model. So the Updated Lagrange coordinate system and the second Piola-Kirchhoff stress tensor/the Green strain tensor are selected to extend small-strain model on the base of the Noll principles, the work conjugation theory and the true stress principle. A one-dimensional, finite strain, viscoelastic constitutive model is proposed according to the nonequilibrium thermodynamics and its internal variable theory.
The fractal theory is introduced to study crazes for the first time. Firstly, it is proved that the interval of fractal dimension of crazes is [0 , 2). The fractal dimension represents the fiberizing degree and the cavitating level of polymers. Secondly, a new concept—crazing variable is defined base on the damage variable and the toughening equation set up by the fractal dimension of crazes, which allows the two important properties of crazing: damage and toughening. The finite-strain crazing variable is proposed by use of the new computing method of fractal dimension modified by area transformation under the condition
在标准线性固体模型的基础上,通过引进率相关弹簧和作者已建立的非线性Bingham流体模型,建立了小变形条件下的高聚物一维非线性粘弹模型;并根据对应原理,将此模型推广到各向同性材料中,建立了三维非线性粘弹模型。其次,根据Noll三原则、功共轭原理、真应力原则,选择Updated Lagrange坐标系以及第二类P-K应力张量和Green应变张量,将小变形条件下的三维粘弹性本构进行推广,建立了Euler坐标系下的有限变形条件下的三维粘弹性模型。最后,根据非平衡态热力学及其内变量理论,建立了一维有限变形粘弹性模型。
首次引入分形理论对高聚物的银纹损伤进行研究。首先,根据银纹的特点阐述了其分形维数的区间为[0 , 2)。银纹的分形维数不仅表征了高聚物的空穴化程度而且表征了材料的微纤化水平。其次,在利用分形维数建立的损伤变量和韧化函数的基础上,定义了一个全新的概念:银纹变量。它可以表征银纹损伤和银纹增韧对材料的共同作用。在有限变形条件下,通过面积转换,定义了新的分形维数计算方法,建立了有限变形条件下的银纹变量。新的银纹变量能够更加客观的刻画材料的损伤程度,因为它有效地剔除有限变形过程中弹性变形和塑性变形对银纹分形维数的影响。最后,利用已建立的银纹变量,根据Kachanov-Rabotnov的有效应力理论,建立了银纹化高聚物在小变形条件和有限变形条件下的一维和三维的分形损伤模型。
利用分形维数对银纹进行了定量化分析。通过蠕变试验,采集了PMMA在不同应力和不同时间的蠕变银纹图像,并采用盒维法计算了其分形维数。试验证明,蠕变银纹引发的应力阀值随时间的增长呈指数关系降低,并最终趋于常数;蠕变银纹的分形维数与应力呈线性关系,与时间呈指数关系;在达到应力阀值的瞬间,能产生大量银纹,导致银纹的分形维数产生阶跃。根据实验结果,建立了蠕变银纹的分形维数与应力、时间的关系式。
The crazing phenomenon is unique to amorphous glassy polymers. The crazing damage evolves in three different levels: the orientating, untwisting and breaking of macromolecular chains in microscopic state; the initiation, growth and breakdown of crazes in mesoscopic layer; the formation, expansion and rupture of mesocracks in macroscopic view. A craze can sustain a definite amount of tensile stress and the mechanical properties of crazing polymers are the competitive result between crazing damage and toughening, which means the damage model of crazing polymers should be distinguished from other materials due to their particular damage mechanism.
Based on the standard linear solid model, a one-dimensional nonlinear viscoelastic model of polymers for small deformation is set up to describe strain- rate-dependency elasticity and nonlinear viscosity. The corresponding three- dimensional model is developed by generalizing the one-dimensional nonlinear viscoelastic model according to the correspondence principle.
The former construction serves as a starting point for the development of a three-dimensional, finite deformation, viscoelastic constitutive model. So the Updated Lagrange coordinate system and the second Piola-Kirchhoff stress tensor/the Green strain tensor are selected to extend small-strain model on the base of the Noll principles, the work conjugation theory and the true stress principle. A one-dimensional, finite strain, viscoelastic constitutive model is proposed according to the nonequilibrium thermodynamics and its internal variable theory.
The fractal theory is introduced to study crazes for the first time. Firstly, it is proved that the interval of fractal dimension of crazes is [0 , 2). The fractal dimension represents the fiberizing degree and the cavitating level of polymers. Secondly, a new concept—crazing variable is defined base on the damage variable and the toughening equation set up by the fractal dimension of crazes, which allows the two important properties of crazing: damage and toughening. The finite-strain crazing variable is proposed by use of the new computing method of fractal dimension modified by area transformation under the condition
引文
1 罗文波 , 杨挺青 , 张平 . 高聚物细观损伤演化的研究进展 . 力学进展. 2001, 31: 264~272
2 焦剑 ,雷渭媛 . 高聚物结构、性能与测试 . 化学工业出版社 , 2003: 452~479
3 李兆霞 . 损伤力学及其应用 . 科学出版社 , 2002: 101~102
4 W. T. Bjerkea, J. Lambrosb. Theoretical Development and Experimental Validation of a Thermally Dissipative Cohesive Zone Model for Dynamic Fracture of Amorphous Polymers. Journal of the Mechanics and Physics of Solids. 2003,51: 1147~1170
5 杨 挺 青 , 罗 文 波 , 危 银 涛 等 . 粘 弹 性 理 论 与 应 用 . 科 学 出 版 社 , 2004: 242~245
6 X. Lei, K. Masuda. Detailed Analysis of Acoustic Emission Activity During Catastrophic Fracture of Faults in Rock. Journal of Structural Geology. 2004, 26 :247~258
7 Sternstein, Meyers. In: Geil P H, Baer E, Wada Y. The Solid State of Polymer. New York: Marcel, 1974: 539~542
8 郑强 , 冯金茂等 . 聚合物增韧机理研究进展 . 高分子材料科学与工程. 1998, 4: 12~15
9 A. S. Argon, Hannoosh. Initiation of Crazes in Glassy Polymers. Solid Wastes Management Refuse Removal Journal. 1978: 445~470
10 E. Thomas. Structure and Properties of Polymers. In: Materials Science and Technology. Science Press, 1999: 618~677
11 A. S. Argon, M. M. Salama. Growth of Crazes in Glassy polymers. Phil Mag, 1977, 36: 1217~1234
12 J. Chern, R. Hsiao. A Generalizes Time-dependent Theory on Craze Initiation in Viscoelastic Media. Journal of Applied Physics. 1985, 57: 1823~1834.
13 A. S. Argon. Craze Plasticity in Low Molecular Weight Diluent-toughened Polystyrene. Journal of Applied Polymer Science. 1999, 72: 13~33
14 E. Schwier, A. S. Argon, Cohen. Craze Plasticity in a Series of Polystyrene/ Polybutadiene Di-block Copolymers with Spherical Morphology. Philosophical Magazine A: Physics of Condensed Matter, Defects and Mechanical Properties. 1985, 52: 581~603
15 E. J. Kramer. Microscopic and Molecular Fundamentals of Crazing. Advance in Polymer Science. 1983, 52-53: 1~56
16 E. J. Kramer. Craze Fibril Formation and Breakdown. Polymer Engineering Science. 1984, 24: 7612~770
17 B. D. Lauterwasser, E. J. Kramer. Microscopic Mechanisms and Mechanics of Craze Growth and Fracture. Philosophical Magazine A: Physics of Condensed Matter, Defects and Mechanical Properties. 1979, 39: 469~495
18 李强 , 贺子如 , 宋名实等 . 玻璃态高聚物细观损伤断裂统计力学 .力学进展. 1995, 25: 451~465
19 R. Estevez, M.G.A. Tijssens and E. V. Giessen. Modeling of the Competition between Shear Yielding and Crazing in Glassy Polymers. Journal of Mechanics and Physics of Solids. 2000, 48: 2585~2617
20 J. Qin, A. S. Argon and R.E. Cohen. Toughening of Glassy Polystyrene through Ternary Blending that Combines Low Molecular Weight Polybutadiene Diluents and ABS or HIPS-type Composite Particles. Journal of Applied Polymer Science. 1999, 71: 2319~2328
21 A. S. Argon, B. J. Gally. Selection of Crack-tip Slip System in the Thermal Arrest of Cleavage Cracks in Dislocation-free Silicon Single Crystals. Scripta Materialia. 2001, 45: 1287~1294;
22 T. Kazmierczak, A. Galeski and A. S. Argon. Plastic Deformation of Polyethylene Crystals as a Function of Crystal Thickness and Compression Rate. Polymer. 2005, 46: 8926~8936
23 S. Socrate, M. C. Boyce and A. Lazzeri. A Micromechanical Model for Multiple Crazing in High Impact Polystyrene. Mechanics ofMaterials. 2001, 33: 155~175
24 Y. Sha, C. Y. Hui and A. Ruina. Continum and Discrete Modeling of Craze Failure at a Crack Tip in a Glassy Polymer. Macromolecules.1995, 28: 2450~2459
25 揭敏 , 李银平 , 邓泽贤等 . 非晶高聚物裂尖银纹损伤场 . 应用力学学报. 1998, 15: 7~12
26 M. Jie, C. Y. Tang and Y. P. Li. Damage Evolution and Energy Dissipation of Polymers with Crazes. Theoretical and Applied Fracture Mechanics. 1998, 28: 165~174
27 B. P. Gearing, L. Anand. On Modeling the Deformation and Fracture Response of Glassy Polymers due to Shear-yielding and Crazing. International Journal of Solids and Structures. 2004, 41: 3125~3150
28 Wen-Bo Luo, Ting-Qing Yang and Xia-yu Wang. Time-dependent Craze Zone Growth at a Crack Tip in Polymer Solids. Polymer. 2004, 45: 3519~3525
29 罗文波 , 刘文娴 , 杨挺青等 . 一种 PMMA 银纹损伤演化的实验研究. 固体力学学报. 2004, 25: 171~175
30 李之达 , 周衍领 , 张嵘峰 . 蠕变条件下 PMMA 银纹损伤的试验研究. 湘潭大学自然科学学报. 2003, 12: 37~40
31 李强 , 贺子如 , 宋名实等 . 玻璃态高聚物细观损伤断裂统计力学 . 力学进展. 1995, 25: 451~465
32 李强 , 宋名实 , 唐敖庆 . 玻璃态高聚物的损伤和断裂非平衡态统计理论. 北京化工大学学报. 1996, 23: 14~22
33 李强 , 贺子如 , 宋名实等 . 玻璃态高聚物细观损伤断裂的非平衡统计理论. 中国科学, A 辑. 1995, 25:1082~1090
34 E . C . Marcelo, E. B. Becker, O . Sflebnem. Constitutive Modeling of Viscoelastic Materials with Damage - computational Aspects. Comput. Methods Appl. Mech. Engrg. 2001, 190: 2207~2226
35 T. Li, F. Grignon, D. J. Benson , K. S. Vecchio. Modeling the Elastic Properties and Damage Evolution in Ti-Al3Ti Metal-intermetallic Laminate (MIL ) Composites. Materials Science and Engineering A .2004, 374: 10~26
36 Dazhi Jiang, Dongwei Shu. Stress Distribution in Damaged Composite Laminates under Transverse Impact. Composite Structures. 2004, 63: 407~415
37 李兆霞 , 肖力光 , 佘颖禾 . 脆性固体损伤和局部软化的有限元分析. 计算结构力学及其应用.1996, 13(3):279~286
38 M.L. Boubakar , L. Vang, F. Trivaudey and D. Perreux. A Meso–macro Finite Element Modelling of Laminate Structures Part II: Time-dependent Behaviour. Composite Structures.2003, 60: 275~305
39 S. K.Rajesh, T. Ramesh. A Continuum Damage Model for Linear Viscoelastic Composite Materials. Mechanics of Materials .2003, 35: 463~480
40 M.L. Boubakar, F. Trivaudey, D. Perreux and L. Vang. A Meso-macro Finite Element Modelling of Laminate Structures Part I: Time-independent Behaviour. Composite Structures . 2002, 58 : 271~286
41 J.J. Xiong, R.A. Shenoi. A Two-stage Theory on Fatigue Damage and Life Prediction of Composites. Composites Science and Technology. 2004, 64: 1331~1343
42 L. Jiang, H. Wang, P. K. Liaw, C. R. Brooks and D. L. Klarstrom. Temperature Evolution during Low-cycle Fatigue of ULTIMET Alloy: Experiment and Modeling. Mechanics of Materials. 2004,36 : 73~84
43 E. Baron, M. B. Rubin, D. Z. Yankelevsky. Thermomechanical Constitutive Equations for the Dynamic Response of Ceramics. International Journal of Solids and Structures. 2003, 40: 4519~4548
44 金问鲁 . 固体的统一弹、粘、塑性理论 . 应用数学和力学 . 1999, 20, 3: 241~24
45 彭向和 ,曾祥国 . 蠕变—塑性交互作用的一种本构模型 . 应用力学学报. 1997, 14(3): 110~115
46 郭 宇 峰 , 吕 和 祥 , 冯 明 珲 . 粘 弹 塑 性 统 一 本 构 模 型 的 参 数 评 估 . 计算力学学报. 2003, 20(5): 597～601
47 Peiyin Lü, Qingbin Li, Yupu Song. Damage Constitutive of Concrete under Uniaxial Alternate Tension–compression Fatigue Loading Based on Double Bounding Surfaces. International Journal of Solids and Structures. 2004, 41: 3151~3166
48 L. Laiarinandrasana, R. Piques and A. Robisson. Visco-hyperelastic Model with Internal State Variable Coupled with Discontinuous Damage Concept under Total Lagrangian Formulation. International Journal of Plasticity. 2003, 19 : 977~1000
49 周柏卓 , 聂景旭 , 杨士杰 . 正交各向异性材料粘塑性损伤统一本构关系研究. 航空动力学报.1999,14(4):357~361
50 李兆霞 . 损伤力学及其应用 . 科学出版社 , 2002: 101~102
51 J. Kigami. Analysis on Fractals. China Machine Press. 2004 : 2~4
52 张济中 . 分形 . 清华大学出版社 , 1995: 302~304
53 戈 明 亮 . 混 沌 及 高 聚 物 的 混 沌 运 动 . 高 分 子 材 料 科 学 与 工 程 . 2004, 20: 17~20
54 A. I. Mohsen, A. I. Mahmoud and M. S. Islam. Fractal Dimension-a Messure of Fracture Toughness and Toughness of Concrete. Engineering Fracture Mechanics. 2003, 70: 125~137
55 M. M. Asasteh, A. Chudnovsky and J. W. Dudley II et al. Broadband Acoustic Emission Observations during Fracture Propagation in Rock-like Material. Int. J. Mech. Min. Sci. 1997, 34: 634~635
56 B. H. Choi, Z. Zhou and A. Chudnovsky et al. Fracture Initiation Associated with Chemical Degradation: Observation and Modeling. International Journal of Solids and Structures. 2005, 42: 681~695
57 陈顥 , 陈凌 . 分形几何学 . 地震出版社 , 1998: 66~67
58 B. B. Mandelbrot. Fractals-form, Chance and Dimension. W.H. Freeman and Company, 1977
59 Lei Weisheng, Chen Bingsen. Fractal Characterization of Some Fracture Phenomena. Engineering Fractal Mechanics. 1995, 50: 149~155
60 Q.A. Wang, A. L. Mehaute. Measuring Information Growth in Fractal Phase Space. Chaos, Soliton and Fractals. 2004, 21: 893~ 897
61 D. N. Winslow. The Fractal Nature of the Surface of Cement Paste. Cement Concrete Res. 1985, 15: 817~824
62 陈艳玲 , 杨问华 , 袁军华等 . 聚丙烯酰胺-醋酸铬与聚丙稀酰胺胶态分散凝胶的纳米颗粒自组织分形结构. 高分子学报. 2002, 5: 592~597
63 谭忠印 , 马金 , 王琛等 . 原子力显微镜对聚丙稀酰胺凝胶分形结构的研究. 中国科学, B. 1999,29:97~100
64 S. Amit, M. T. Louis and B. Gregory et al. Growth and Structure of Zirconium Hydrous Polymers in Aqueous Solutions. Journal of Colloid and Interface Science. 1997, 194: 470~481
65 荣利霞 , 魏柳荷 , 董宝中等 . 两亲性嵌段共聚物的同步辐射小角X 射线散射研究. 物理学报. 2002, 51: 1773~1777
66 吴秋菊 , 吴立新 , 漆宗能等 . 高磺化度聚丙胺体系中的分形结构研究. 高分子学报. 2000, 2: 172~175
67 赵永红 , 皇杰 藩 , 耿金 达等 . 岩 石破裂带的分维及变化特征 . 地质科学. 1994, 29:137~143
68 谢和平 . 分形-岩石力学导论 . 科学出版社 , 1996:129~148
69 Y. H. Lee, J. R. Carr and D. J. Barr et al. The Fractal Dimension as a Measure of the Roughness of Rock Discontinuity Profiles. Int. J. Mech. Min. Sci. 1990, 27: 453~464
70 A. M. Brandt, G. Prokopski. On the Fractal Dimension of Fracture Surfaces of Concrete Elements. Journal of Material Science. 1993, 28: 4762~4766
71 V. E. Saouma, C. C. Barton. Fractals, Fractures and Size Effects in Concrete. Journal of Engineering Mechanics. 1994, 120: 835~854
72 M. A. Issa, A. M. Hammad. Fractal Characterization of Fracture Surfaces in Mortar. Cement Concrete Res. 1993, 23: 7~12
73 M. A. Issa, A. M. Hammad, A. Chudnovsky. Correlation between Crack Tortuosity and Fracture Toughness in Cementitious Material. International Journal of Fractal. 1993, 60: 97~105
74 M. A. Issa, A. M. Hammad. Assessment and Evaluation of Fractal Dimension of Concrete Fracture Surface Digitized Images. Cement concrete Res. 1994, 24: 325~34
75 M. A. Issa, M. S. Islam, A. Chudnovsky. Size Effects in Concrete Fracture: Part I, Experimental Setup and Observations. International journal of Fractal. 2000, 102: 1~14.
76 R . Frederic, G. Fabrice. Inelastic Behavior Modelling of Concrete in Low and High Strain Rate Dynamics. Computers and Structures. 2003, 81: 1287`1299
77 R. Kunc, I. Prebil. Low-cycle fatigue properties of steel 42CrMo4. Materials Science and Engineering A. 2003 ,345: 278~285
78 Q . Li, L.Zhang and F. Ansari. Damage Constitutive for High Strength Concrete in Triaxial Cyclic Compression. International Journal of Solids and Structures. 2002, 39: 4013~4025
79 S. Baste. Inelastic Behaviour of Ceramic-matrix Composites. Composites Science and Technology. 2001, 61: 2285~2297
80 R.W. Meyer, L.A. Pruitt. The Effect of Cyclic True Strain on the Morphology, Structure and Relaxation Behavior of Ultra High Molecular Weight Polyethylene. Polymer. 2001,42: 5293~5306
81 王 泽 云 , 刘 立 , 刘 宝 县 . 岩 石 微 结 构 与 微 裂 纹 的 损 伤 演 化 特 征 . 岩石力学与工程学报. 2002, 51:1773~1777
82 Y. H. Zhao. Crack Pattern Evolution and a Fractal Damage Constitutive Model for Rock. Journal of Rock Mech. Min. Sci. 1998, 35: 349-366
83 赵 永 红 . 岩 石 弹 脆 性 分 维 损 伤 本 构 模 型 . 地 质 科 学 . 1997, 32: 487~494
84 Y. H. Zhao. Fractal Variation of Fracturing in Compresses Rock Specimen. Chinese Science Bulletin. 1995, 40: 1277~1281
85 A. Billi, F. Salvini and F. Storti. The damage zone-fault core transition in carbonate rocks: implications for fault growth, structure and permeability. Journal of Structural Geology. 2003, 25: 1779~1794
86 段庆泉 , 刘彩平 , 鞠杨 , 谢和平 . 混凝土压临界裂纹扩展的分形效应. 中国矿业大学学报. 2006, 35:70~74
87 谢卫红 , 高峰 , 谢和平 . 细观尺度下岩石热变形破坏的试验研究 . 试验力学. 2005, 12:628~634
88 H. P. Xie, D. J. Sanderson. Fractal Effects of Crack Propagation on Dynamic Stress Intensity Factors and Crack Velocities. International Journal of Fracture. 1996, 74: 29~42
89 H. P. Xie, J. A. Wang, W. H. Xie. Photoelastic Study of the Contact Mechanics of Fractal Joints. Journal of Rock Mech. Min. Sci. 1997, 34: 865~874
90 徐志斌 , 谢和平 . 断裂构造的分形分布与其损伤演化的关系 . 武汉理工大学学报. 2004, 26: 29~34
91 A. Carpinteri, B. Chiaia, P. Cornetti. A Fractal Theory for the Mechanics of Elastic Materials. Materials Science and Engineering A. 2004, 365: 235`240
92 A. Carpinteri, B. Chiaia, P. Cornetti. A Scale-invariant Cohesive Crack Model for Quasi-brittle Materials. Engineering Fracture Mechanics. 2002, 69: 207~217
93 A. Carpinteri, B. Chiaia, P. Cornetti. The Elastic Problem for Fractal Media: Basic Theory and Finite Element Formulation. Computers and Structures. 2004, 82: 499~508
94 A. Carpinteri, G. Ferro, G. Ventura. The Partition of Unity Quadrature in Element-free Crack Modeling. Computers and Structures. 2003, 81: 1783~1794
95 A. Carpinteri, M. Paggi. Size-scale Effects on the Friction Coefficient. International Journal of Solids and Structures. 2005, 42: 2901~2910
96 B. Chiaia. Fracture Mechanisms Induced in a Brittle Material by a Hard Cutting Indenter. International Journal of Solids and Structures. 2001, 38: 7747~7768
97 A. Carpinteri, B. Chiaia, P. Cornetti. A Mesoscopic Theory of Damage and Fracture in Heterogeneous Materials. Theoretical and Applied Fracture Mechanics. 2004,41: 43~50
98 T. Sugama, J. R. Fair, A. P. Reed. Polymetallosiloxane Coatings Derived from Two-step, Acid-base Catalyzed Sol Precursors for Corrosion Protection of Aluminum Substrates. Journal of Coatings Technology. 1993, 65: 27~36
99 J. Botsis, G. Oerter, K. Friedrich. Fatigue Fracture in Polypropylene with Different Spherulitic Sizes. Annual Technical Conference - ANTEC, Conference Proceedings.1996, 3: 3294`3300
100 H. Tobushi, T.Hashimoto, S. Hayashi and E.Yamada. Thermomechanical Constitutive Modeling in Shape Memory Polymer of Polyurethane Series. Journal of Intelligent Material Systems and Structures. 1997 ,8: 711~718
101 吴衡毅 , 马钢 , 夏源明 . PMMA 低、中应变率单向拉伸力学性能的试验研究. 试验力学. 2005, 20:193~199
102 S. W. Park. Analytical Modeling of Viscoelastic Dampers for Structural and Vibration Control. International Journal of Solids and Structures. 2001, 38: 8065~8092
103 M. Kaliske, L. Nasdala and H. Rothert. On Damage Modelling for Elastic and Viscoelastic Materials at Large Strain. Computers and Structures. 2001,79: 2133~2141
104 李勇 , 闫学成 , 释清海 . 对橡胶材料流变模型的探讨 . 橡塑技术与装备. 2003, 9: 1~4
105 Y. Li, J. A. Wu and X. W. Du. Viscoelastic Constitutive Model of Unvulcanizated Rubber. Polymer & Polymer Composites.2005,13: 727~736
106 Y. Li, Y. M. Long, Y. S. Wang and J. A. Wu. Nonlinear Constitutive Model of Charged Rubber. International Rubber Conference, Beijing, 2004. Beijing, 2004, C: 364~369
107 Y. S. Wang, X. W. Du. Non-linear Constitutive Model of Uncured Epoxy Resin. Journal of Macromolecular Science, Physics. 2005, 44: 177~184
108 M. G. A. Tijssens, E. Giessen and L. J. Sluys. Simulation of Mode I Crack Growth in Polymers by Crazing. International Journal of Solids and Structures. 2000, 37: 7307~7327
109 S. Basu, D. K. Mahajan, E. V. Giessen. Micromechanics of the Growth of a Craze Fibril in Glassy Polymers. Polymer. 2005,46:7504~7518
110 C.G.F. Gerlach and F.P.E. Dunne. An Elastic-viscoplastic LargeDeformation Model and its Application to particle filled polymer film. Computational Materials Science. 1994,3: 146~158
111 T. Ebeling, A. Hiltner, E. Baer. Effect of Peel Rate and Temperature on Delamination Toughness of PC–SAN Microlayers. Polymer. 1999, 40: 1525~1536
112 I. M. Ward. Mechanical Properties of Solid Polymers. Second. Wiley- interscience Edition, 1983: 476~477
113 C. He, A. M. Donald. Morphology of a Deformed Rubber Toughened Polymethylmethacrylate Film under Tensile Strain. Journal of Material Science. 1997, 32: 5661~5667
114 Melick, Bressers and Toonder et al. A Micro-indentation Method for Probing the Craze-initiation Stress in Glassy Polymers. Polymer. 2003, 44: 2481~2491
115 I. M. Ward. Mechanical properties of solid polymers. Wiley- interscience,2 nd edition, 1983: 476~477
116 A. D. Drozdov, J. C. Christiansen. The Effect of Strain Rate on the Viscoplastic Behavior of Isotactic Polypropylene at Finite Strains. Polymer. 2003, 44: 1211~1228
117 杨 光 松 . 损 伤 力 学 与 复 合 材 料 损 伤 . 国 防 工 业 出 版 社 . 1995: 84~85
118 A. Khan and H. Zhang. Finite Deformation of a Polymer: Experiments and Modeling. International Journal of Plasticity. 2001.17: 1167~1188
119 黄筑平 . 连续介质力学基础 . 高等教育出版社 . 2003: 78~200
120 R. J. Oxborough, P. B. Bowden. A General Critical-strain Criterion for Crazing in Amorphous Glassy Polymers. Phil Mag.1973, 28: 547~559
121 周太全 , 李兆霞 , 贾军波 . 弹塑性损伤分析的参变量变分原理 . 东南大学学报. 2001, 31:67~71
122 李柏林 , 林建国 , 姚新 . 蠕变损伤统一本构方程的特性分析及优化. 中国机械工程. 2002,13: 1696~1700
123 盛冬发 , 程昌钧 , 扶名福 . 损伤粘弹性力学的广义变分原理及应用.应用数学和力学. 2004, 25: 345~353
2 焦剑 ,雷渭媛 . 高聚物结构、性能与测试 . 化学工业出版社 , 2003: 452~479
3 李兆霞 . 损伤力学及其应用 . 科学出版社 , 2002: 101~102
4 W. T. Bjerkea, J. Lambrosb. Theoretical Development and Experimental Validation of a Thermally Dissipative Cohesive Zone Model for Dynamic Fracture of Amorphous Polymers. Journal of the Mechanics and Physics of Solids. 2003,51: 1147~1170
5 杨 挺 青 , 罗 文 波 , 危 银 涛 等 . 粘 弹 性 理 论 与 应 用 . 科 学 出 版 社 , 2004: 242~245
6 X. Lei, K. Masuda. Detailed Analysis of Acoustic Emission Activity During Catastrophic Fracture of Faults in Rock. Journal of Structural Geology. 2004, 26 :247~258
7 Sternstein, Meyers. In: Geil P H, Baer E, Wada Y. The Solid State of Polymer. New York: Marcel, 1974: 539~542
8 郑强 , 冯金茂等 . 聚合物增韧机理研究进展 . 高分子材料科学与工程. 1998, 4: 12~15
9 A. S. Argon, Hannoosh. Initiation of Crazes in Glassy Polymers. Solid Wastes Management Refuse Removal Journal. 1978: 445~470
10 E. Thomas. Structure and Properties of Polymers. In: Materials Science and Technology. Science Press, 1999: 618~677
11 A. S. Argon, M. M. Salama. Growth of Crazes in Glassy polymers. Phil Mag, 1977, 36: 1217~1234
12 J. Chern, R. Hsiao. A Generalizes Time-dependent Theory on Craze Initiation in Viscoelastic Media. Journal of Applied Physics. 1985, 57: 1823~1834.
13 A. S. Argon. Craze Plasticity in Low Molecular Weight Diluent-toughened Polystyrene. Journal of Applied Polymer Science. 1999, 72: 13~33
14 E. Schwier, A. S. Argon, Cohen. Craze Plasticity in a Series of Polystyrene/ Polybutadiene Di-block Copolymers with Spherical Morphology. Philosophical Magazine A: Physics of Condensed Matter, Defects and Mechanical Properties. 1985, 52: 581~603
15 E. J. Kramer. Microscopic and Molecular Fundamentals of Crazing. Advance in Polymer Science. 1983, 52-53: 1~56
16 E. J. Kramer. Craze Fibril Formation and Breakdown. Polymer Engineering Science. 1984, 24: 7612~770
17 B. D. Lauterwasser, E. J. Kramer. Microscopic Mechanisms and Mechanics of Craze Growth and Fracture. Philosophical Magazine A: Physics of Condensed Matter, Defects and Mechanical Properties. 1979, 39: 469~495
18 李强 , 贺子如 , 宋名实等 . 玻璃态高聚物细观损伤断裂统计力学 .力学进展. 1995, 25: 451~465
19 R. Estevez, M.G.A. Tijssens and E. V. Giessen. Modeling of the Competition between Shear Yielding and Crazing in Glassy Polymers. Journal of Mechanics and Physics of Solids. 2000, 48: 2585~2617
20 J. Qin, A. S. Argon and R.E. Cohen. Toughening of Glassy Polystyrene through Ternary Blending that Combines Low Molecular Weight Polybutadiene Diluents and ABS or HIPS-type Composite Particles. Journal of Applied Polymer Science. 1999, 71: 2319~2328
21 A. S. Argon, B. J. Gally. Selection of Crack-tip Slip System in the Thermal Arrest of Cleavage Cracks in Dislocation-free Silicon Single Crystals. Scripta Materialia. 2001, 45: 1287~1294;
22 T. Kazmierczak, A. Galeski and A. S. Argon. Plastic Deformation of Polyethylene Crystals as a Function of Crystal Thickness and Compression Rate. Polymer. 2005, 46: 8926~8936
23 S. Socrate, M. C. Boyce and A. Lazzeri. A Micromechanical Model for Multiple Crazing in High Impact Polystyrene. Mechanics ofMaterials. 2001, 33: 155~175
24 Y. Sha, C. Y. Hui and A. Ruina. Continum and Discrete Modeling of Craze Failure at a Crack Tip in a Glassy Polymer. Macromolecules.1995, 28: 2450~2459
25 揭敏 , 李银平 , 邓泽贤等 . 非晶高聚物裂尖银纹损伤场 . 应用力学学报. 1998, 15: 7~12
26 M. Jie, C. Y. Tang and Y. P. Li. Damage Evolution and Energy Dissipation of Polymers with Crazes. Theoretical and Applied Fracture Mechanics. 1998, 28: 165~174
27 B. P. Gearing, L. Anand. On Modeling the Deformation and Fracture Response of Glassy Polymers due to Shear-yielding and Crazing. International Journal of Solids and Structures. 2004, 41: 3125~3150
28 Wen-Bo Luo, Ting-Qing Yang and Xia-yu Wang. Time-dependent Craze Zone Growth at a Crack Tip in Polymer Solids. Polymer. 2004, 45: 3519~3525
29 罗文波 , 刘文娴 , 杨挺青等 . 一种 PMMA 银纹损伤演化的实验研究. 固体力学学报. 2004, 25: 171~175
30 李之达 , 周衍领 , 张嵘峰 . 蠕变条件下 PMMA 银纹损伤的试验研究. 湘潭大学自然科学学报. 2003, 12: 37~40
31 李强 , 贺子如 , 宋名实等 . 玻璃态高聚物细观损伤断裂统计力学 . 力学进展. 1995, 25: 451~465
32 李强 , 宋名实 , 唐敖庆 . 玻璃态高聚物的损伤和断裂非平衡态统计理论. 北京化工大学学报. 1996, 23: 14~22
33 李强 , 贺子如 , 宋名实等 . 玻璃态高聚物细观损伤断裂的非平衡统计理论. 中国科学, A 辑. 1995, 25:1082~1090
34 E . C . Marcelo, E. B. Becker, O . Sflebnem. Constitutive Modeling of Viscoelastic Materials with Damage - computational Aspects. Comput. Methods Appl. Mech. Engrg. 2001, 190: 2207~2226
35 T. Li, F. Grignon, D. J. Benson , K. S. Vecchio. Modeling the Elastic Properties and Damage Evolution in Ti-Al3Ti Metal-intermetallic Laminate (MIL ) Composites. Materials Science and Engineering A .2004, 374: 10~26
36 Dazhi Jiang, Dongwei Shu. Stress Distribution in Damaged Composite Laminates under Transverse Impact. Composite Structures. 2004, 63: 407~415
37 李兆霞 , 肖力光 , 佘颖禾 . 脆性固体损伤和局部软化的有限元分析. 计算结构力学及其应用.1996, 13(3):279~286
38 M.L. Boubakar , L. Vang, F. Trivaudey and D. Perreux. A Meso–macro Finite Element Modelling of Laminate Structures Part II: Time-dependent Behaviour. Composite Structures.2003, 60: 275~305
39 S. K.Rajesh, T. Ramesh. A Continuum Damage Model for Linear Viscoelastic Composite Materials. Mechanics of Materials .2003, 35: 463~480
40 M.L. Boubakar, F. Trivaudey, D. Perreux and L. Vang. A Meso-macro Finite Element Modelling of Laminate Structures Part I: Time-independent Behaviour. Composite Structures . 2002, 58 : 271~286
41 J.J. Xiong, R.A. Shenoi. A Two-stage Theory on Fatigue Damage and Life Prediction of Composites. Composites Science and Technology. 2004, 64: 1331~1343
42 L. Jiang, H. Wang, P. K. Liaw, C. R. Brooks and D. L. Klarstrom. Temperature Evolution during Low-cycle Fatigue of ULTIMET Alloy: Experiment and Modeling. Mechanics of Materials. 2004,36 : 73~84
43 E. Baron, M. B. Rubin, D. Z. Yankelevsky. Thermomechanical Constitutive Equations for the Dynamic Response of Ceramics. International Journal of Solids and Structures. 2003, 40: 4519~4548
44 金问鲁 . 固体的统一弹、粘、塑性理论 . 应用数学和力学 . 1999, 20, 3: 241~24
45 彭向和 ,曾祥国 . 蠕变—塑性交互作用的一种本构模型 . 应用力学学报. 1997, 14(3): 110~115
46 郭 宇 峰 , 吕 和 祥 , 冯 明 珲 . 粘 弹 塑 性 统 一 本 构 模 型 的 参 数 评 估 . 计算力学学报. 2003, 20(5): 597～601
47 Peiyin Lü, Qingbin Li, Yupu Song. Damage Constitutive of Concrete under Uniaxial Alternate Tension–compression Fatigue Loading Based on Double Bounding Surfaces. International Journal of Solids and Structures. 2004, 41: 3151~3166
48 L. Laiarinandrasana, R. Piques and A. Robisson. Visco-hyperelastic Model with Internal State Variable Coupled with Discontinuous Damage Concept under Total Lagrangian Formulation. International Journal of Plasticity. 2003, 19 : 977~1000
49 周柏卓 , 聂景旭 , 杨士杰 . 正交各向异性材料粘塑性损伤统一本构关系研究. 航空动力学报.1999,14(4):357~361
50 李兆霞 . 损伤力学及其应用 . 科学出版社 , 2002: 101~102
51 J. Kigami. Analysis on Fractals. China Machine Press. 2004 : 2~4
52 张济中 . 分形 . 清华大学出版社 , 1995: 302~304
53 戈 明 亮 . 混 沌 及 高 聚 物 的 混 沌 运 动 . 高 分 子 材 料 科 学 与 工 程 . 2004, 20: 17~20
54 A. I. Mohsen, A. I. Mahmoud and M. S. Islam. Fractal Dimension-a Messure of Fracture Toughness and Toughness of Concrete. Engineering Fracture Mechanics. 2003, 70: 125~137
55 M. M. Asasteh, A. Chudnovsky and J. W. Dudley II et al. Broadband Acoustic Emission Observations during Fracture Propagation in Rock-like Material. Int. J. Mech. Min. Sci. 1997, 34: 634~635
56 B. H. Choi, Z. Zhou and A. Chudnovsky et al. Fracture Initiation Associated with Chemical Degradation: Observation and Modeling. International Journal of Solids and Structures. 2005, 42: 681~695
57 陈顥 , 陈凌 . 分形几何学 . 地震出版社 , 1998: 66~67
58 B. B. Mandelbrot. Fractals-form, Chance and Dimension. W.H. Freeman and Company, 1977
59 Lei Weisheng, Chen Bingsen. Fractal Characterization of Some Fracture Phenomena. Engineering Fractal Mechanics. 1995, 50: 149~155
60 Q.A. Wang, A. L. Mehaute. Measuring Information Growth in Fractal Phase Space. Chaos, Soliton and Fractals. 2004, 21: 893~ 897
61 D. N. Winslow. The Fractal Nature of the Surface of Cement Paste. Cement Concrete Res. 1985, 15: 817~824
62 陈艳玲 , 杨问华 , 袁军华等 . 聚丙烯酰胺-醋酸铬与聚丙稀酰胺胶态分散凝胶的纳米颗粒自组织分形结构. 高分子学报. 2002, 5: 592~597
63 谭忠印 , 马金 , 王琛等 . 原子力显微镜对聚丙稀酰胺凝胶分形结构的研究. 中国科学, B. 1999,29:97~100
64 S. Amit, M. T. Louis and B. Gregory et al. Growth and Structure of Zirconium Hydrous Polymers in Aqueous Solutions. Journal of Colloid and Interface Science. 1997, 194: 470~481
65 荣利霞 , 魏柳荷 , 董宝中等 . 两亲性嵌段共聚物的同步辐射小角X 射线散射研究. 物理学报. 2002, 51: 1773~1777
66 吴秋菊 , 吴立新 , 漆宗能等 . 高磺化度聚丙胺体系中的分形结构研究. 高分子学报. 2000, 2: 172~175
67 赵永红 , 皇杰 藩 , 耿金 达等 . 岩 石破裂带的分维及变化特征 . 地质科学. 1994, 29:137~143
68 谢和平 . 分形-岩石力学导论 . 科学出版社 , 1996:129~148
69 Y. H. Lee, J. R. Carr and D. J. Barr et al. The Fractal Dimension as a Measure of the Roughness of Rock Discontinuity Profiles. Int. J. Mech. Min. Sci. 1990, 27: 453~464
70 A. M. Brandt, G. Prokopski. On the Fractal Dimension of Fracture Surfaces of Concrete Elements. Journal of Material Science. 1993, 28: 4762~4766
71 V. E. Saouma, C. C. Barton. Fractals, Fractures and Size Effects in Concrete. Journal of Engineering Mechanics. 1994, 120: 835~854
72 M. A. Issa, A. M. Hammad. Fractal Characterization of Fracture Surfaces in Mortar. Cement Concrete Res. 1993, 23: 7~12
73 M. A. Issa, A. M. Hammad, A. Chudnovsky. Correlation between Crack Tortuosity and Fracture Toughness in Cementitious Material. International Journal of Fractal. 1993, 60: 97~105
74 M. A. Issa, A. M. Hammad. Assessment and Evaluation of Fractal Dimension of Concrete Fracture Surface Digitized Images. Cement concrete Res. 1994, 24: 325~34
75 M. A. Issa, M. S. Islam, A. Chudnovsky. Size Effects in Concrete Fracture: Part I, Experimental Setup and Observations. International journal of Fractal. 2000, 102: 1~14.
76 R . Frederic, G. Fabrice. Inelastic Behavior Modelling of Concrete in Low and High Strain Rate Dynamics. Computers and Structures. 2003, 81: 1287`1299
77 R. Kunc, I. Prebil. Low-cycle fatigue properties of steel 42CrMo4. Materials Science and Engineering A. 2003 ,345: 278~285
78 Q . Li, L.Zhang and F. Ansari. Damage Constitutive for High Strength Concrete in Triaxial Cyclic Compression. International Journal of Solids and Structures. 2002, 39: 4013~4025
79 S. Baste. Inelastic Behaviour of Ceramic-matrix Composites. Composites Science and Technology. 2001, 61: 2285~2297
80 R.W. Meyer, L.A. Pruitt. The Effect of Cyclic True Strain on the Morphology, Structure and Relaxation Behavior of Ultra High Molecular Weight Polyethylene. Polymer. 2001,42: 5293~5306
81 王 泽 云 , 刘 立 , 刘 宝 县 . 岩 石 微 结 构 与 微 裂 纹 的 损 伤 演 化 特 征 . 岩石力学与工程学报. 2002, 51:1773~1777
82 Y. H. Zhao. Crack Pattern Evolution and a Fractal Damage Constitutive Model for Rock. Journal of Rock Mech. Min. Sci. 1998, 35: 349-366
83 赵 永 红 . 岩 石 弹 脆 性 分 维 损 伤 本 构 模 型 . 地 质 科 学 . 1997, 32: 487~494
84 Y. H. Zhao. Fractal Variation of Fracturing in Compresses Rock Specimen. Chinese Science Bulletin. 1995, 40: 1277~1281
85 A. Billi, F. Salvini and F. Storti. The damage zone-fault core transition in carbonate rocks: implications for fault growth, structure and permeability. Journal of Structural Geology. 2003, 25: 1779~1794
86 段庆泉 , 刘彩平 , 鞠杨 , 谢和平 . 混凝土压临界裂纹扩展的分形效应. 中国矿业大学学报. 2006, 35:70~74
87 谢卫红 , 高峰 , 谢和平 . 细观尺度下岩石热变形破坏的试验研究 . 试验力学. 2005, 12:628~634
88 H. P. Xie, D. J. Sanderson. Fractal Effects of Crack Propagation on Dynamic Stress Intensity Factors and Crack Velocities. International Journal of Fracture. 1996, 74: 29~42
89 H. P. Xie, J. A. Wang, W. H. Xie. Photoelastic Study of the Contact Mechanics of Fractal Joints. Journal of Rock Mech. Min. Sci. 1997, 34: 865~874
90 徐志斌 , 谢和平 . 断裂构造的分形分布与其损伤演化的关系 . 武汉理工大学学报. 2004, 26: 29~34
91 A. Carpinteri, B. Chiaia, P. Cornetti. A Fractal Theory for the Mechanics of Elastic Materials. Materials Science and Engineering A. 2004, 365: 235`240
92 A. Carpinteri, B. Chiaia, P. Cornetti. A Scale-invariant Cohesive Crack Model for Quasi-brittle Materials. Engineering Fracture Mechanics. 2002, 69: 207~217
93 A. Carpinteri, B. Chiaia, P. Cornetti. The Elastic Problem for Fractal Media: Basic Theory and Finite Element Formulation. Computers and Structures. 2004, 82: 499~508
94 A. Carpinteri, G. Ferro, G. Ventura. The Partition of Unity Quadrature in Element-free Crack Modeling. Computers and Structures. 2003, 81: 1783~1794
95 A. Carpinteri, M. Paggi. Size-scale Effects on the Friction Coefficient. International Journal of Solids and Structures. 2005, 42: 2901~2910
96 B. Chiaia. Fracture Mechanisms Induced in a Brittle Material by a Hard Cutting Indenter. International Journal of Solids and Structures. 2001, 38: 7747~7768
97 A. Carpinteri, B. Chiaia, P. Cornetti. A Mesoscopic Theory of Damage and Fracture in Heterogeneous Materials. Theoretical and Applied Fracture Mechanics. 2004,41: 43~50
98 T. Sugama, J. R. Fair, A. P. Reed. Polymetallosiloxane Coatings Derived from Two-step, Acid-base Catalyzed Sol Precursors for Corrosion Protection of Aluminum Substrates. Journal of Coatings Technology. 1993, 65: 27~36
99 J. Botsis, G. Oerter, K. Friedrich. Fatigue Fracture in Polypropylene with Different Spherulitic Sizes. Annual Technical Conference - ANTEC, Conference Proceedings.1996, 3: 3294`3300
100 H. Tobushi, T.Hashimoto, S. Hayashi and E.Yamada. Thermomechanical Constitutive Modeling in Shape Memory Polymer of Polyurethane Series. Journal of Intelligent Material Systems and Structures. 1997 ,8: 711~718
101 吴衡毅 , 马钢 , 夏源明 . PMMA 低、中应变率单向拉伸力学性能的试验研究. 试验力学. 2005, 20:193~199
102 S. W. Park. Analytical Modeling of Viscoelastic Dampers for Structural and Vibration Control. International Journal of Solids and Structures. 2001, 38: 8065~8092
103 M. Kaliske, L. Nasdala and H. Rothert. On Damage Modelling for Elastic and Viscoelastic Materials at Large Strain. Computers and Structures. 2001,79: 2133~2141
104 李勇 , 闫学成 , 释清海 . 对橡胶材料流变模型的探讨 . 橡塑技术与装备. 2003, 9: 1~4
105 Y. Li, J. A. Wu and X. W. Du. Viscoelastic Constitutive Model of Unvulcanizated Rubber. Polymer & Polymer Composites.2005,13: 727~736
106 Y. Li, Y. M. Long, Y. S. Wang and J. A. Wu. Nonlinear Constitutive Model of Charged Rubber. International Rubber Conference, Beijing, 2004. Beijing, 2004, C: 364~369
107 Y. S. Wang, X. W. Du. Non-linear Constitutive Model of Uncured Epoxy Resin. Journal of Macromolecular Science, Physics. 2005, 44: 177~184
108 M. G. A. Tijssens, E. Giessen and L. J. Sluys. Simulation of Mode I Crack Growth in Polymers by Crazing. International Journal of Solids and Structures. 2000, 37: 7307~7327
109 S. Basu, D. K. Mahajan, E. V. Giessen. Micromechanics of the Growth of a Craze Fibril in Glassy Polymers. Polymer. 2005,46:7504~7518
110 C.G.F. Gerlach and F.P.E. Dunne. An Elastic-viscoplastic LargeDeformation Model and its Application to particle filled polymer film. Computational Materials Science. 1994,3: 146~158
111 T. Ebeling, A. Hiltner, E. Baer. Effect of Peel Rate and Temperature on Delamination Toughness of PC–SAN Microlayers. Polymer. 1999, 40: 1525~1536
112 I. M. Ward. Mechanical Properties of Solid Polymers. Second. Wiley- interscience Edition, 1983: 476~477
113 C. He, A. M. Donald. Morphology of a Deformed Rubber Toughened Polymethylmethacrylate Film under Tensile Strain. Journal of Material Science. 1997, 32: 5661~5667
114 Melick, Bressers and Toonder et al. A Micro-indentation Method for Probing the Craze-initiation Stress in Glassy Polymers. Polymer. 2003, 44: 2481~2491
115 I. M. Ward. Mechanical properties of solid polymers. Wiley- interscience,2 nd edition, 1983: 476~477
116 A. D. Drozdov, J. C. Christiansen. The Effect of Strain Rate on the Viscoplastic Behavior of Isotactic Polypropylene at Finite Strains. Polymer. 2003, 44: 1211~1228
117 杨 光 松 . 损 伤 力 学 与 复 合 材 料 损 伤 . 国 防 工 业 出 版 社 . 1995: 84~85
118 A. Khan and H. Zhang. Finite Deformation of a Polymer: Experiments and Modeling. International Journal of Plasticity. 2001.17: 1167~1188
119 黄筑平 . 连续介质力学基础 . 高等教育出版社 . 2003: 78~200
120 R. J. Oxborough, P. B. Bowden. A General Critical-strain Criterion for Crazing in Amorphous Glassy Polymers. Phil Mag.1973, 28: 547~559
121 周太全 , 李兆霞 , 贾军波 . 弹塑性损伤分析的参变量变分原理 . 东南大学学报. 2001, 31:67~71
122 李柏林 , 林建国 , 姚新 . 蠕变损伤统一本构方程的特性分析及优化. 中国机械工程. 2002,13: 1696~1700
123 盛冬发 , 程昌钧 , 扶名福 . 损伤粘弹性力学的广义变分原理及应用.应用数学和力学. 2004, 25: 345~353
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |