SiC纤维增强复合材料界面破坏与失效机理的研究
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摘要
界面的破坏与失效是考察纤维增强复合材料产生增韧效应的关键力学问题。本文主要研究了SiC／Ti-Al复合材料和陶瓷基复合材料的基体裂纹沿界面的偏移、纤维桥联增韧机理。考察了界面断裂特性的纤维拔出、多纤维／基体复合材料的拉伸应力-应变特性和拉伸强度、单纤维断裂后引起的相邻纤维中的应力集中、随机纤维桥联疲劳寿命和可靠性等问题。具体研究成果如下：
(1) 建立基体裂纹偏移／穿透有限元模型，并分析了相对裂纹扩展长度、材料参数、纤维体积分数对相对能量释放率的影响；给出了广泛使用的SiC／Ti-Al复合材料和陶瓷基复合材料最有利于基体裂纹偏移的弹性参数；并指出了含有纤维碳涂层时的优缺点。基于有限元结果和能量偏移准则，有效地评估了界面断裂韧性。
(2) 提出的桥联本构函数反映了桥联应力和基体裂纹展开位移之间无穷阶的非线性关系，且解释了桥联本构关系的上升和下降部分及其比率关系。通过计算桥联阻抗曲线，验证了纤维桥联中出现稳定基体裂纹增长阶段的物理特性；通过计算桥联载荷随基体裂纹长度的分布，证明桥联效应是纤维增强复合材料中主导的增韧机理；通过计算外载荷和载荷点位移的关系曲线，解释了从纤维桥联、纤维失效到纤维拔出的转换过程。
(3) 界面分离能释放率随界面分离长度的增加而减小。随分离界面摩擦应力的增加，纤维和基体剪切效应以及泊松效应抑制界面失效的能力增强，这是按剪滞理论所无法获得的结果。由纤维／基体热失配引起的热残余应力有利于抑制界面的失效。桥联本构关系(文[137，138]中)的幂指数n=0.5只适合于低摩擦应力和低界面断裂韧性的弱界面。
(4) 本文建立的有限元模型较好地模拟了复合材料拉伸破坏失效的过程，包括实时的界面分离和纤维断裂。GLS和HVDP模型在一定程度上低估了断裂纤维附近完整纤维中的应力集中。同时，由于热处理引起的热残余温度能改善复合材料的拉伸特性，进而提高复合材料最终拉伸强度。
(5) 在随机循环应力作用下，提出纤维桥联基体裂纹扩展的首次穿越扩散过程模型。证实了裂纹扩展尺寸对纤维桥联疲劳寿命和可靠性的影响。随基体裂纹扩展疲劳寿命和可靠性的分布呈现出两种不同的非线性下降特性。证明了韦布尔分布和对数正态分布对于模拟纤维桥联疲劳寿命随时间的分布具有一致性。
The damage and failure of the interface is a crucial mechanical problem for exploring the toughening effect in fiber-reinforced composites. For the SiC/Ti-Al composite and ceramic matrix composite, the primary research of this paper concentrates mainly on the matrix crack deflection along the interface and the fiber-bridging toughening mechanism. The fiber pull-out for exploring the interfacial fracture properties, the tensile stress-strain properties of the multi-fiber/matrix composites and the tensile strength, the stress concentration on the intact fibers near a broken fiber as well as the stochastic fiber bridging fatigue lifetime and reliability are investigated. The detailed research results are expressed as:
(1) The finite element model of matrix crack deflection/penetration is established and the effects on the relative energy release rate of the relative crack growth length, material parameters and fiber volume fraction are analyzed. The reason why the elastic parameters in the widely used SiC/Ti-Al composite and ceramic matrix composite favor the matrix crack deflection is given. The advantage and disadvantage of the fiber carbon coating are commonly pointed out. The interfacial fracture toughness is effectively evaluated based on the finite element results and the energy-based deflection criterion.
(2) The presented bridging constitutive function reflects an infinite-order non-linear relationship between the bridging stress and the matrix crack opening displacement, and interpretes the increasing and decreasing parts as well as their respective fractions. A stable matrix crack growth stage appearing in fiber bridging is confirmed by calculating the bridging resistance curve. The fact that the fiber bridging effect is a dominating toughening mechanism in fiber-reinforced composites is confirmed by calculating the distributions of bridging loads with the matrix crack length. The transformation process from fiber bridging, fiber failure to fiber pull-out is interpreted by calculating the load-displacement curve.
(3) The interfacial debonding energy decreases with increasing interface debond length. With increasing friction stress at the debonded interface, the abilities for the shear effects in the
(1) 建立基体裂纹偏移／穿透有限元模型，并分析了相对裂纹扩展长度、材料参数、纤维体积分数对相对能量释放率的影响；给出了广泛使用的SiC／Ti-Al复合材料和陶瓷基复合材料最有利于基体裂纹偏移的弹性参数；并指出了含有纤维碳涂层时的优缺点。基于有限元结果和能量偏移准则，有效地评估了界面断裂韧性。
(2) 提出的桥联本构函数反映了桥联应力和基体裂纹展开位移之间无穷阶的非线性关系，且解释了桥联本构关系的上升和下降部分及其比率关系。通过计算桥联阻抗曲线，验证了纤维桥联中出现稳定基体裂纹增长阶段的物理特性；通过计算桥联载荷随基体裂纹长度的分布，证明桥联效应是纤维增强复合材料中主导的增韧机理；通过计算外载荷和载荷点位移的关系曲线，解释了从纤维桥联、纤维失效到纤维拔出的转换过程。
(3) 界面分离能释放率随界面分离长度的增加而减小。随分离界面摩擦应力的增加，纤维和基体剪切效应以及泊松效应抑制界面失效的能力增强，这是按剪滞理论所无法获得的结果。由纤维／基体热失配引起的热残余应力有利于抑制界面的失效。桥联本构关系(文[137，138]中)的幂指数n=0.5只适合于低摩擦应力和低界面断裂韧性的弱界面。
(4) 本文建立的有限元模型较好地模拟了复合材料拉伸破坏失效的过程，包括实时的界面分离和纤维断裂。GLS和HVDP模型在一定程度上低估了断裂纤维附近完整纤维中的应力集中。同时，由于热处理引起的热残余温度能改善复合材料的拉伸特性，进而提高复合材料最终拉伸强度。
(5) 在随机循环应力作用下，提出纤维桥联基体裂纹扩展的首次穿越扩散过程模型。证实了裂纹扩展尺寸对纤维桥联疲劳寿命和可靠性的影响。随基体裂纹扩展疲劳寿命和可靠性的分布呈现出两种不同的非线性下降特性。证明了韦布尔分布和对数正态分布对于模拟纤维桥联疲劳寿命随时间的分布具有一致性。
The damage and failure of the interface is a crucial mechanical problem for exploring the toughening effect in fiber-reinforced composites. For the SiC/Ti-Al composite and ceramic matrix composite, the primary research of this paper concentrates mainly on the matrix crack deflection along the interface and the fiber-bridging toughening mechanism. The fiber pull-out for exploring the interfacial fracture properties, the tensile stress-strain properties of the multi-fiber/matrix composites and the tensile strength, the stress concentration on the intact fibers near a broken fiber as well as the stochastic fiber bridging fatigue lifetime and reliability are investigated. The detailed research results are expressed as:
(1) The finite element model of matrix crack deflection/penetration is established and the effects on the relative energy release rate of the relative crack growth length, material parameters and fiber volume fraction are analyzed. The reason why the elastic parameters in the widely used SiC/Ti-Al composite and ceramic matrix composite favor the matrix crack deflection is given. The advantage and disadvantage of the fiber carbon coating are commonly pointed out. The interfacial fracture toughness is effectively evaluated based on the finite element results and the energy-based deflection criterion.
(2) The presented bridging constitutive function reflects an infinite-order non-linear relationship between the bridging stress and the matrix crack opening displacement, and interpretes the increasing and decreasing parts as well as their respective fractions. A stable matrix crack growth stage appearing in fiber bridging is confirmed by calculating the bridging resistance curve. The fact that the fiber bridging effect is a dominating toughening mechanism in fiber-reinforced composites is confirmed by calculating the distributions of bridging loads with the matrix crack length. The transformation process from fiber bridging, fiber failure to fiber pull-out is interpreted by calculating the load-displacement curve.
(3) The interfacial debonding energy decreases with increasing interface debond length. With increasing friction stress at the debonded interface, the abilities for the shear effects in the
引文
1．钱学森．现代力学[J]．力学与实践，1979，1(1)：4-9．
2．美国国防部关键技术计划[M]．中国国防科技信息中心，1992：11．
3. Iwashita N, Psomiadou E, Sawada Y. Effect of coupling treatment of carbon fiber surface on mechanical properties of carbon fiber reinforced carbon composites[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1998, 29 (8): 965-972.
4. Huang Z M. Micromechanical strength formulae of unidirectional composites[J]. Materials Letters, 1999, 40 (4): 164-169.
5. Huang Z M. Micromechanical modeling of fatigue strength of unidirectional fibrous composites[J]. International Journal of Fatigue, 2002, 24 (6): 659-670.
6. Lifshitz J M, Gov F, Gandelsman M. Instrumented low-velocity impact of CFRP beams[J]. International Journal of Impact Engineering, 1995,16 (2): 201-215.
7. Takeda M, Imai Y, lchikawa, et al. Thermal stability of SiC fiber prepared by an irradiationcuring process[J]. Composites Science and Technology, 1999, 59 (6): 793-799.
8. He J B fibers in continuous fiber eyerlein Irene J, Clarke D R. Load transfer from broken Al_2O_3-Al composites and dependence on local volume fraction[J]. Journal of the Mechanics and Physics of Solids, 1999, 3 (1): 465-502.
9. Wang Z, Xia Y M. Experimental evaluation of the strength distribution of fibers under high strain rates by bimodal Weibull distribution[J]. Composites Science and Technology, 1998, 57 (12): 1599-1607.
10. Beyerlein I J, Phoenix, S L. Statistics of fracture for an elastic notched composite lamina containing Weibull fibers-Part Ⅰ. Features from Monte-Carlo simulation[J]. Engineering Fracture Mechanics, 1997, 57 (2,3): 241-265..
11. Buryachenko V A, Pagano N J, Kim R Y, et al. Quantitative description and numerical simulation of random microstructures of composites and their effective elastic moduli[J]. International Journal of Solids and Structures, 2003, 40 (1): 47-72.
12. Van O, Douglas L, Dayal V. How isotropic are quasi-isotropic laminates[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 2003, 34 (1): 93-103.
13. Kumosa L, Armentrout D, Kumosa M. An evaluation of the critical conditions for the initiation of stress corrosion cracking in unidirectional E-glass/polymer composites[J]. Composites Science and Technology, 2001, 61 (4): 615-623.
14. Yamada R, Igawa N, Taguehi T. Thermal diffusivity/conductivity of Tyranno SA fiber-and Hi-Nicalon Type S fiber-reinforced 3-D SiC/SiC composites[J]. Journal of Nuclear Materials, 2004 (329-333): 497-501.
15. Feldman E. The effect of temperature-dependent material properties on elasto-viscoplastic buckling behaviour of non-uniformly heated MMC plates[J]. Composite Structures, 1996, 35 (1): 65-74.
16. Kagawa Y. Thermal shock damage in a two-dimensional SiC/SiC composite reinforced with woven SiC fibers[J]. Composites Science and Technology, 1997, 57 (5): 607-611.
17. Dalmaz A, Reynaud P, Rouby D, et al. Mechanical Behavior and Damage Development During Cyclic Fatigue at High-Temperature of a 2-5D Carbon/SiC Composite[J]. Composites Science and Technology, 1998, 58 (5): 693-699.
18. Durra I. Role of interracial and matrix creep during thermal cycling of continuous fiber reinforced metal-matrix composites[J]. Acta Materialia, 2000, 48 (5): 1055-1074.
19. Narayana Naik G, Krishna Murty A V, Gopalakrishnan S. A failure mechanism based failure theory for laminated composites including the effect of shear stress[J]. Composite Structures, 2005, 69 (2): 219-227.
20. Rebillat F, Lamon J, Guette A. The concept of a strong interface applied to SiC/SiC composites with a BN interphase[J]. Acta Materialia, 2000, 48 (18-19): 4609-4618.
21. Singh J P, Singh D, Sutaria M. Ceramic-composites: roles of fiber and interface[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1999, 30 (4): 445-450.
22 冼杏娟，李端义著．复合材料破坏分析及微观图谱[M]．科学出版社，1993：1-7．
23．王兴业等编著．复合材料力学分析与设计[M]．国防科技大学出版社，1999：98-137．
24，杨庆生著。复合材料细观结构力学与设计[M]．中国铁道出版社，2000：230-239．
25．杜善义，王彪编著．复合材料细观力学[M]．科学出版社，1998：1160．
26. Hashin Z. Thermoelastic properties of fiber composites with imperfect interface[J]. Mechanics of Materials, 1990, 8: 333-348.
27. Cook J, Gordon J E. A mechanism for the control of crack propagation in all-brittle systems[C]. Proc. Royal Society, 1964, 282: 508-520.
28. Goree J G, Gross R S. Analysis of an unidirectional composite containing broken fibers and matrix damage[J]. Engrg Fracture Mech., 1979, 13 (5): 563-578.
29. Barsoum M W, Kanguthar P, Wang A S D. Matrix crack initiation in ceramic matrix composite Ⅰ: Experiments and test results[J]. Composites Science and Technology, 1992 (44): 257-269.
30. He M Y, Hutchinson J W. Crack deflection at an interface between dissimilar elastic materials[J]. International Journal of Solids and Structure, 1989, 25 (1): 1053-1067.
31. He M Y, Evans A G, Hutchinson J W. Crack deflection at an interface between dissimilar elastic materials: role of residual stresses[J]. International Journal of Solids and Structure, 1994, 31(24): 3443-3455.
32. Ahn B K, Curtin W A, Parthasarathy T A, et al. Criteria for crack deflection/penetration criteria for fiber-reinforced ceramic matrix composites[J]. Composites Science and Technology, 1998, 58 (11): 1775-1784.
33. Susmit M, Raj N S. Effects of fiber coating properties on the crack deflection and penetration in fiber-reinforced ceramic composites[J]. Acta Materialia, 1997, 45(11): 4721-4731.
34. Kerans R J, Parthasarathy T A. Crack deflection in ceramic composites and fiber coating design criteria [J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1999, 30 (4): 521-524.
35. Lee W, Howard S J, Clegg W J. Growth of interface defects and its effect on crack deflection and toughening criteria [J]. Acta Materialia, 1996,44 (10): 3905-3922.
36. Martin E, Peters P W M, Leguillon D, et al. Conditions for matrix crack deflection at an interface in ceramic matrix composites [J]. Materials Science and Engineering: A, 1998, 250 (2): 291-302.
37. Martin E, Leguillon D, Lacroix C. A revisited criterion for crack deflection at an interface in a brittle biomaterial [J]. Composites Science and Technology, 2001, 61 (12): 1671-1679.
38.. Martin E, Leguillon D. Energetic conditions for interfacial failure in the vicinity of a matrix crack in brittle matrix composites [J]. International Journal of Solids and Structures, 2004, 41 (24-25): 6937-6948.
39. Ostertag C P. Influence of fiber and grain bridging on crack profiles in SiC fiber-reinforced alumina-matrix composites [J]. Materials Science and Engineering: A, 1999, 260 (1-2): 124-131.
40. Sun Y J, Singh R N. Determination of fiber bridging stress profile by debond length measurement [J]. Acta Materialia, 2000,48 (13): 3607-3619.
41. Raddatz O, Schneider G A, Mackens W, et al. Bridging stresses and R-curves in ceramic/metal composites [J]. Journal of the European Ceramic Society, 2000, 20 (13): 2261-2273.
42. Studer M, Peters K, Botsis J. Method for determination of crack bridging parameters using long optical fiber Bragg grating sensors [J]. Composites: Part B, 2003,34 (4): 347-359.
43.. Fernberg S P., Berglund L A. Bridging law and toughness characterisation of CSM and SMC composites [J]. Composites Science and Technology, 2001, 61(16): 2445-2454.
44. Begley M R, McMeeking R M. Fatigue crack growth with fiber failure in metal-matrix composites [J].. Composites Science and Technology, 1995,53 (4): 365-382.
45. Begley M R, McMeeking R M. Numerical analysis of fibre bridging and fatigue crack growth in metal matrix composite materials [J]. Materials Science and Engineering:A, 1995, 200 (1-2):12-20.
46. Budiansky B, Cui Y L. Toughening of ceramics by short aligned fibers [J]. Mechanics of Materials, 1995, 21 (2): 139-146.
47. Sarrafi-Nour G R, Coyle T W, Fett T. A weight function for the crack surface tractions in chevron-notched specimens [J]. Engineering Fracture Mechanics, 1998,59 (4): 439—445.
48. Herrmann D J, Hillberry B M. A new approach to the analysis of unidirectional titanium matrix composites with bridge and unbridged cracks [J]. Engineering Fracture Mechanics, 1997, 56 (5): 711-726.
49. Song G M, Zhou Y, Sun Y. Modeling of fiber toughening in fiber-reinforced ceramic composites [J]. Ceramics International, 1999,25 (3): 257-260.
50. Mumm D R, Faber K T. Interfacial debonding and sliding in brittle-matrix composites measured using an improved fiber pullout technique[J]. Acta Metallurgica Materialia, 1995, 43 (3): 1259-1270.
51. Verma R, Ghosh K, Merrick H, et al. Measurement of interracial shear properties of composites of Ti-1100 alloy reinforced with SCS-6 SiC monofilament fiber[J]. Materials Science and Engineering: A, 1995, 191 (1-2): 151-163.
52. Young R J, Bannister D J, Andrews M C, et al. Analysis of the single-fibre pull-out test by means of Raman spectroscopy: Part Ⅱ-Micromechanics of deformation for an aramid/epoxy system[J]. Composites Science and Technology, 1995, 53 (4): 411-421.
53. Harmia T, Friedrich K. Fracture toughness and failure mechanisms in unreinforced and long-glass-fibre-reinforced PA66/PP blends[J]. Composites Science and Technology, 1995, 53 (4):. 423-430.
54. Xia Z, Curtin W A. Tough-to-brittle transitions in ceramic-matrix composites with increasing interfacial shear stress[J]. Acta Materialia, 2000, 48 (20): 4879-4892.
55. Cherepanov G P, Esparragoza I E. The problem of fiber pullout[J]. Materials Science and Engineering: A, 1995, 203 (1-2): 332-342.
56. Zhou L M, Mai Y M, Ye L. Analysis of fibre push-out test based on the fracrure mechanics approach[J]. Composites Engineering, 5 (10-11): 1199-1219.
57. Quek M Y. Stress transfer at a partially bonded fibre/matrix interface[J]. International Journal of Adhesion and Adhesives, 2002, 22 (4): 303-310.
58. Lin G, Geubelle P H, Sottos N R. Simulation of fiber debonding with friction in a model composite pushout test[J]. International Journal of Solids and Structures, 2001, 38 (46-47): 8547-8562
59. Schreyer H L, Peffer A. Fiber pullout based on a one-dimensional model of decohesion[J], Mechanics of Materials, 2000, 32 (12): 821-836.
60. Tsai K H, Kim K S. The micromechanics of fiber pull-out[J]. Journal of the Mechanics and Physics of Solids, 1996, 44 (7): 1147-1177.
61. Marotzke C, Qiao, L. Interracial crack propagation arising in single-fiber pull-out tests[J]. Composites Science and Technology, 1997, 57 (8): 887-897.
62. Beckert W, Lauke B. Finite element calculation of energy release rate for single-fibre pull-out test[J]. Computational Materials Science, 1996, 5 (1-3): 1-11
63. Hedgepeth J M, Dyke V P. Local stress concentrations in imperfect filimentary composite materials[J]. Journal of composite material, 1967 (1): 294-309.
64. Beyerlein I J, Landis C M. Shear-lag model for failure simulations of unidirectional fiber composites including matrix stiffness[J]. Mechanics of Materials, 1999, 31 (5): 331-350.
65. Jiang X Y, Gao Q. Stress-transfer analysis for fibre/matrix interfaces in short-fibre-reinforced composites[J]. Composites Science and Technology, 2001, 61 (10): 1359-1366.
66. Hsueh C H. Crack-wake interracial debonding criteria for fiber-reinforced composites[J]. Acta Materialia, 1996, 44 (6): 2211-2216.
67. Hsueh C H, Young R J, Yang X. Stress transfer in a model composite containing a single embedded fiber[J]. Acta Materialia, 1997, 45 (4): 1469-1476.
68. Hsueh C H, Becher P F. Interfacial shear debonding problems in fiber-reinforced ceramic composites [J], Acta Materialia, 1998, 46 (9): 3237-3245.
69. Nairn J A, Mendels D A. On the use of planar shear-lag methods for stress-transfer analysis of multilayered composites [J]. Mechanics of Materials, 2001,33 (6): 335-362.
70. Nairn J A. Energy release rate analysis for adhesive and laminate double cantilever beam specimens emphasizing the effect of residual stresses [J]. International Journal of Adhesion and Adhesives, 2000, 20 (1): 59-70.
71. Zhang S Y. A new model for the energy release rate of fibre/matrix interfacial fracture. Composites Science and Technology, 1998, 58 (1): 163-166.
72. Zhang S Y. Debonding and Cracking Energy Release Rate of the Fiber/Matrix Interface [J]. Composites Science and Technology, 1998, 58 (3-4): 331-335.
73. Zhang S Y. A simple approach to the evaluation of fiber/matrix interfacial shear strength and fracture toughness, A simple approach to the evaluation of fiber/matrix interfacial shear strength and fracture toughness [J]. Composites Science and Technology, 2000, 60 (1):. 145-148.
74. Curtin W A. Theory of mechanical properties of ceramic matrix composites. J. Am. Ceram. Soc [C]. 1991, 74 (11), 2837-2845.
75. Lissart N, Lamon J. Damage and failure in ceramic matrix minicomposites: experimental study and model [J]. Acta Materalia, 1997,45 (3): 1025-1044.
76. Wu E M, Robinson C S. Computational micro-mechanics for probabilistic failure of fiber composites in tension [J]. Composites Science and Technology, 1997,58 (9): 1421—1432.
77. Bednarcyk B A, Arnold S M. Micromechanics-based deformation and failure prediction for longitudinally reinforced titanium composites [J]. Composites Science and Technology, 2001,61 (5): 705-729.
78. Gonzalez C, Llorca J. Micromechanical modelling of deformation and failure in Ti-6Al-4V/SiC composites [J]. Acta Materialia, 2001,49 (17): 3505-3519.
79. Landis C M, Beyerlein I J, McMeeking R M. Micromechanical simulation of the failure of fiber reinforced composites [J]. Journal of the Mechanics and Physics of Solids, 2000,48 (3): 621-648.
80. Curtin W A. Theory of mechanical properties of ceramic-matrix composites [J]. Journal of American Ceramic Society, 1991,76 (1): 2837-2845.
81. Mackay R A, Draper S L, Ritttter A M, et al. A comparision of the mechanical properties and microstructure of intermetallic matrix composites fabricated by two different methods [J]. Metallic Transactions, 1991,25 (1): 1443-1455.
82. Weber C H, Du Z Z, Zok F W. High temperature deformation and fracture of a fiber reinforced titanium matrix composites [J]. Acta Materalia, 1996, 44 (2): 683-695.
83. Gaffney K M, Botsis J. Deformation and fracture of a uniaxially reinforced composite material [J]. Composites Science and Technology, 1999, 59 (12): 1847-1859.
84. Xu J, Cox B N, Mcglockton M A, et al. A binary model of textile composites-II: The elastic regime [J]. Acta metallica, 1995,43 (1): 3511-3524.
85. Cox B N, Carter W C, Fleck N A. A binary model of textile composites-I: Formations[J]. Acta metalliea, 1995, 42 (1): 3463-3479.
86. Zhou S J, Curtin W A. Faliure of fiber composites: a lattice Green function model[J]. Acta Materialia, 1995, 43 (1): 3093-3104.
87. Ibnabdeljalil M, Curtin W A. Strength and reliability of fiber-reinforced composites: localized load-sharing and associated size effects[J]. International Journal of Solids and Structures, 1997, 34 (21): 2649-2668.
88. Ibnabdeljalil M, Curtin W A. Strength and reliability of notched fiber-reinforced composites[J]. Acta Materialia, 1997, 45 (9): 3641-3652.
89. Beyerlein I J, Phoenix S L. Stress concentrations around multiple fiber breaks in an elastic matrix with local yielding or debonding using quadratic influence superposition[J]. Journal of the Mechanics and Physics of Solids, 1996, 44 (12): 1997-2039.
90. Mahesh S, Beyerlein I J, Phoenix S L. Size and heterogeneity effects on the strength of fibrous composites[J]. Physica D, 1999, 133 (1-4): 371-389:
91. Beyerlein I J, Phoenix S, Sastry L, et al. Comparison of shear-lag theory and continuum fracture mechanics for modeling fiber and matrix stresses in an elastic cracked composite lamina[J]. International Journal of Solids and Structures, 1996, 33 (18): 2543-2574.
92. Ibnabdeljalil M, Phoenix S L. Scalings in the statistical failure of brittle matrix composites with discontinuous fibers-1. Analysis and Monte Carlo simulations[J]. Acta Metallurgica Materialia, 1995, 43 (8): 2975-2983.
93. Ismar H, Streicher F. Modelling and simulation of the mechanical behavior of ceramic matrix composites as shown by the example of SiC/SiC[J]. Computational Materials Science, 1999, 16 (1-4): 17-24.
94. Cheng T L, Qiao R, Xia Y M. A Monte Carlo simulation of damage and failure process with crack saturation for unidirectional fiber reinforced: ceramic composites[J]. Composites Science and Technology, 2004, 64 (13-14): 2251-2260.
95. Ananth C R, Voleti S R, Chandra N. Effect of fiber fracture and interracial debonding on the evolution of damage in metal matrix composites[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1998, 29 (9-10): 1203-1211.
96. Xia Z, Curtin W A, Okabe T. Green's function vs. shear-lag models of damage and failure in fiber composites[J]. Composites Science and Technology, 2002, 62 (10-11): 1279-1288.
97. Xia Z, Okabe T, Curtin W A. Shear-lag versus finite element models for stress transfer in fiber-reinforced composites[J]. Composites Science and Technology, 2002, 62 (9): 1141-1149.
98. Xia Z, Curtin W A, Peters P W M. Multiscale modeling of failure in metal matrix composites[J]. Acta Materialia, 2001, 49 (2): 273-287.
99. Zaretsky E V. Design for life, plan for death[J]. Machine Design,1994, 66 (15): 55-59.
100. Bao G, Hutchinson J W, McMeeking R M. Particle Reinforcement of Ductile Matrices Against Plastic Flow and Creep[J]. Acta metall, mater., 1991, 39 (8): 1871-1882.
101. Rauchs G, Thomason P F, Withers P J. Finite element modelling of frictional bridging during fatigue crack growth in fibre-reinforced metal matrix composites[J]. Computational Materials Science, 2002, 25 (1-2): 166-173.
102. Rauchs G, Withers P J. Computational assessment of the influence of load ratio on fatigue crack growth in fibre-reinforced metal matrix composites[J]. International Journal of Fatigue, 2002, 24 (12): 1205-1211.
103. Guo Y J, Wu W R. A phenomenological model for predicting crack growth in fiber-reinforced metal laminates under constant-amplitude loading[J]. Composites Science and Technology, 1999, 59 (12): 1825-1831.
104. Barney C, Cardona D C, Bowen P. Fatigue crack growth resistance from unbridged defects in continuous fibre reinforced metal matrix composites[J]. International Journal of Fatigue, 1998, 20 (4): 279-289.
105. Botsis J, Zhao D. Fatigue fracture process in a model composite[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1997, 28 (7): 657-666.
106. Kruzic J J, Cannon R M, Ager J W, et al. Fatigue threshold R-curvees for predicting reliability of ceramics under cyclic loading[J]. Acta Materialia, 2005, 53 (9): 2595-2605.
107. Kruzic J J, Campbell J P, Ritchie R O. On the fatigue behavior of γ-based titanimn aluminides: role of small cracks[J]. Acta Materialia, 1999, 47(3): 801-816.
108. Kruzic J J, Nalla R K, Kinney J H, et al. Crack blunting, crack bridging and resistance-curve fracture mechanics in dentin: effect of hydration[J]. Biomaterials, 2003, 24(28): 5209-5221.
109. Wang P C, Jeng S M, Yang J M. Characterization and modeling of stiffness reduction in SCS-6-Ti composites under low cycle fatigue loading[J]. Materials Science and Engineering: A, 1995, 200 (1-2): 173-180.
110. Wang P C, Jeng S M, Yang J M, et al. Fatigue life prediction of fiberoreinforced titanium matrix composites[J]. Acta Materialia, 1996, 44 (3): 11097-1108.
111. Wang P C, Yang J M. Simulation of fatigue cracking and life distribution of SCS-6 fiber-reinforced orthorhombic titanium aluminide composites[J]. Materials Science and Engineering: A, 1997, 222 (2): 101-108.
112. Wang P C, Her Y C, Yang J M. Fatigue behavior and damage modeling of SCS-6/titanium/titanium aluminide hybrid laminated composite[J]. Materials Science and Engineering: A, 1998, 245 (1): 100-108.
113. Xia Z H, Peters P W M, Dudek H J. Finite element modelling of fatigue crack initiation in SiC-fibre reinforced titanium alloys[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 2000, 31 (20): 1031-1037.
114. Xia Z H, Curtin W A. Life prediction of titanium MMCs under low-cycle fatigue[J]. Acta Materialia, 2001, 49 (9): 1633-1646.
115. Williams M L. The Stresses Around a Fault or Crack in Dissimilar Media[J]. Bulletin of the Seismological Society of America, 1959, 49 (2): 199-204,
116. Dundurs J. Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading[J]. Journal of applied Mechanics, 1969, 36: 650-652.
117. Erdogan F. Stress Distribution in a Nonhomogeneous Elastic Plane With Cracks[J]. Journal of Applied Mechanics, 1963, 30: 232-236.
118. Erdogan F. Stress Distribution in Bonded Dissimilar Materials With Cracks[J]. Journal of Applied Mechanics, 1965, 32: 403-410.
119. Rice J R, Sih O C. Plane Problems of Cracks in Dissimilar Media[J]. Journal of Applied Mechanics, 1965, 32: 418-423.
120. Hutchinson J W, Mear M E, Rice J R. Crack Paralleling an Interface Between Dissimilar Materials[J]. Journal of Applied Mechanics, 1987, 54: 828-832.
121. Rice JR. Elastic Fracture Mechanics Concepts for Interfacial Cracks[J]. Journal of Applied Mechanics, 1988, 55: 98-103.
122. Zak A R, Williams M L. Crack point stress singularities at a bi-material interface[J]. Journal of Applied Mechanics, 1963, 30: 142-143.
123. Gupta V, Yuan J, Martinez D. Calculation, Measurement, and Control of Interface Strength in Composites[J]. Journal of American Ceramic Socrety, 1993, 76 (15): 305-315.
124. Lacroix C, Leguillon D, Martin E. The influence of an interphase on the deflection of a matrix crack in a ceramic-matrix composite[J]. Composites Science and Technology, 2002, 62 (4): 519-5123.
125. Liu Y F, Tanaka Y, Masuda C. Debonding mechanisms in the presence of an interphase in composites[J]. Acta Materialia 1998, 46 (15): 5237-5247.
126. Akser E O, Choy K L. Finite element analysis of the stress distribution in a thermally and transversely loaded Ti-6Al-4V/SiC fibre composite[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 2001, 32 (2): 243-251.
127. Carrere N, Martin E, Lamon J. The influence of the interphase and associated interfaces on the deflection of matrix cracks in ceramic matrix composites[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 2000, 31 (11): 1179-1190.
128. Hinoki T, Yang W, Nozawa T, et al. Improvement of mechanical properties of SiC/SiC composites by various surface treatments of fibers[J]. Journal of Nuclear Materials, 2001, 289 (1-2): 23-29.
129. Wang Y Q, Zhou B L. Effect of a fiber coating on the fabrication of fiber reinforced metal-matrix composites[J]. Journal of Materials Processing Technology, 1998, 73 (1-3): 78-81.
130. Cui Y L. On the strength of fiber reinforced ceramic composites containing an elliptic hole[J]. Mechanics of Materials, 1995, 19 (2-3): 239-249.
131. Majumda B S, Newaz G M. Constituent damage mechanisms in metal matrix composites under fatigue loading and their effects on fatigue life[J]. Materials Science and Engineering, 1995, 200 (1-2): 114-129.
132. Murakami H. Stress intensity factors handbook[M]. Oxford: Pergamon Press, 1986.
133. Cao J W, Sakai M. The crack-face fiber bridging of a 2D-C/C-composite[J]. Carbon, 1996, 34 (3): 387-395.
134. Barenblatt G L. The mathematical theory of equilibrium cracks in brittle fracture[J]. Advanced Applied Mechanics, 1962, 7: 55-129.
135. Lawn B R. In Fracture of brittle Solid[M]. Cambridge: Cambridge University Press, 1993.
136. Marshall D B, Cox B N, Evans A G. The mechanics of matrix cracking in brittle-matrix fiber composites[J], Acta metall, mater., 1985, 33 (11): 2013-2021.
137. Marshall M B, Cox B N. A J-integral method for calculating steady-state matrix cracking stresses in composites[J]. Mechanics of Materials, 1988, 7(4): 127-133.
138. McCartney L N. Mechanics of matrix cracking in brittle-matrix fiber-reinforced composites[J]. Proc. R. Soe. Lond., 1987, 409: 329-333.
139. Raddatz O, Schneider G A, Claussen N. Modelling of R-curve behaviour in ceramic/metal composites[J]. Acta Materialia, 1998, 46 (18): 6381-6395.
140. Rouby D, Brenet P, Conchin F, et al. Direct measurement of crack-bridging tractions: A new approach to the fracture behaviour of ceramic/ceramic composites[J]. Composites Science and Technology, 1996, 56 (7): 817-823.
141. Sakai M, Matsuyama R, Miyajima T. The pull-out and failure of a fiber bundle in a carbon fiber reinforced carbon matrix composite[J]. Carbon, 2000, 38 (15): 2123-2131.
142. Chiang Y C. On fiber debonding and matrix cracking in fiber-reinforced ceramics[J]. Comp. Sci. Technol., 2001, 61(12): 1743-1756.
143. Budiansky B, Evans A G, Hutchinson J W. Fiber-matrix debonding effects on cracking in aligned fiber ceramic composites[J]. International Journal of Solids and Structures, 1995, 32 (3-4): 315-328.
144. Preuss M, Rauchs G, Doel T J A, et al. Measurements of fibre bridging during fatigue crack growth in Ti/SiC fibre metal matrix compositesv[J]. Acta Materialia, 2003, 51(4): 1045-1057.
145. Honda K, Kagawa Y, Mai Y W. Effects of relative sliding distance on the frictional stress transfer in fiber-reinforced ceramics[J]. Materials Science and Engineering: A, 1998, 252 (1): 53-63.
146. Warrier SG, Maruyama B, Majumdar BS, et al. Behavior of several interfaces during fatigue crack growth in SiC/Ti-6Al-4V composites[J]. Materials Science and Engineering: A, 1999, 259 (2): 189-200.
147. Wu W, Verpoest I, Varna J. Prediction of energy release rate due to the growth of an interface crack by variational analysis[J]. Comp. Sci. Teehnol., 2000, 60 (3): 351-360.
148. Mao X N, Zhou L, Zhou Y G, et al. Characteristic of principle properties and microstructure of TP-650 Particles reinforced titanium matrix Composites[J]. Rare metal materials and engineering, 2004, 33 (6): 620-623 (in chinese).
149. Chandra N, Ananth-C R. Analysis of interracial behavior in MMCs and IMCs by the use of thin-slice push-out tests[J]. Composites Science and Technology, 1995, 54 (1): 87-100.
150. Okabe T, Takeda N, Kamoshida Y, et al. A 3D shear-lag model considering micro-damage and statistical strength prediction of unidirectional fiber-reinforced composites[J]. Composites Science and Technology, 2001, 61 (12): 1773-1787.
151. Gonzalez C, Llorca J. Micromechanical modelling of deformation and failure in Ti-6A1-4V/SiC composites[J]. Acta Materialia, 2001, 49 (17): 3505-3519.
152. Majumdar B S, Newaz G M. Inelastic deformation of metal matrix composites: plasticity and damage mechanisms[J]. Philosophical Magazine A, 1992, 66 (2): 187-212.
153. Fiedler B. Klisch A, Schulte K. Stress concentrations in multiple fibre model composites[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1998, 29 (9-10): 1013-1019.
154. Leucht R, Dudek H J. Properties of SiC fibre reinforced titanium alloys processed by fibre coating and hot isostatic pressing[J]. Materials Science and Engineering: A, 1994, 188: 201-210.
155. Cox B N. Scaling relations for bridged cracks[J]. Mech. of Mater., 1993, 15: 87-98.
156. MeMeeking R M, Evans A G. Matrix fatigue cracking in fiber composites[J]. Mech. Mater., 1990, 9: 217-227.
157. Greaves I, Yates J R. The growth of freely initialing fatigue cracks in an unnotched SiC/titanium composite[J]. International Journal of Fatigne, 1997, 19 (2): 151-159.
2．美国国防部关键技术计划[M]．中国国防科技信息中心，1992：11．
3. Iwashita N, Psomiadou E, Sawada Y. Effect of coupling treatment of carbon fiber surface on mechanical properties of carbon fiber reinforced carbon composites[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1998, 29 (8): 965-972.
4. Huang Z M. Micromechanical strength formulae of unidirectional composites[J]. Materials Letters, 1999, 40 (4): 164-169.
5. Huang Z M. Micromechanical modeling of fatigue strength of unidirectional fibrous composites[J]. International Journal of Fatigue, 2002, 24 (6): 659-670.
6. Lifshitz J M, Gov F, Gandelsman M. Instrumented low-velocity impact of CFRP beams[J]. International Journal of Impact Engineering, 1995,16 (2): 201-215.
7. Takeda M, Imai Y, lchikawa, et al. Thermal stability of SiC fiber prepared by an irradiationcuring process[J]. Composites Science and Technology, 1999, 59 (6): 793-799.
8. He J B fibers in continuous fiber eyerlein Irene J, Clarke D R. Load transfer from broken Al_2O_3-Al composites and dependence on local volume fraction[J]. Journal of the Mechanics and Physics of Solids, 1999, 3 (1): 465-502.
9. Wang Z, Xia Y M. Experimental evaluation of the strength distribution of fibers under high strain rates by bimodal Weibull distribution[J]. Composites Science and Technology, 1998, 57 (12): 1599-1607.
10. Beyerlein I J, Phoenix, S L. Statistics of fracture for an elastic notched composite lamina containing Weibull fibers-Part Ⅰ. Features from Monte-Carlo simulation[J]. Engineering Fracture Mechanics, 1997, 57 (2,3): 241-265..
11. Buryachenko V A, Pagano N J, Kim R Y, et al. Quantitative description and numerical simulation of random microstructures of composites and their effective elastic moduli[J]. International Journal of Solids and Structures, 2003, 40 (1): 47-72.
12. Van O, Douglas L, Dayal V. How isotropic are quasi-isotropic laminates[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 2003, 34 (1): 93-103.
13. Kumosa L, Armentrout D, Kumosa M. An evaluation of the critical conditions for the initiation of stress corrosion cracking in unidirectional E-glass/polymer composites[J]. Composites Science and Technology, 2001, 61 (4): 615-623.
14. Yamada R, Igawa N, Taguehi T. Thermal diffusivity/conductivity of Tyranno SA fiber-and Hi-Nicalon Type S fiber-reinforced 3-D SiC/SiC composites[J]. Journal of Nuclear Materials, 2004 (329-333): 497-501.
15. Feldman E. The effect of temperature-dependent material properties on elasto-viscoplastic buckling behaviour of non-uniformly heated MMC plates[J]. Composite Structures, 1996, 35 (1): 65-74.
16. Kagawa Y. Thermal shock damage in a two-dimensional SiC/SiC composite reinforced with woven SiC fibers[J]. Composites Science and Technology, 1997, 57 (5): 607-611.
17. Dalmaz A, Reynaud P, Rouby D, et al. Mechanical Behavior and Damage Development During Cyclic Fatigue at High-Temperature of a 2-5D Carbon/SiC Composite[J]. Composites Science and Technology, 1998, 58 (5): 693-699.
18. Durra I. Role of interracial and matrix creep during thermal cycling of continuous fiber reinforced metal-matrix composites[J]. Acta Materialia, 2000, 48 (5): 1055-1074.
19. Narayana Naik G, Krishna Murty A V, Gopalakrishnan S. A failure mechanism based failure theory for laminated composites including the effect of shear stress[J]. Composite Structures, 2005, 69 (2): 219-227.
20. Rebillat F, Lamon J, Guette A. The concept of a strong interface applied to SiC/SiC composites with a BN interphase[J]. Acta Materialia, 2000, 48 (18-19): 4609-4618.
21. Singh J P, Singh D, Sutaria M. Ceramic-composites: roles of fiber and interface[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1999, 30 (4): 445-450.
22 冼杏娟，李端义著．复合材料破坏分析及微观图谱[M]．科学出版社，1993：1-7．
23．王兴业等编著．复合材料力学分析与设计[M]．国防科技大学出版社，1999：98-137．
24，杨庆生著。复合材料细观结构力学与设计[M]．中国铁道出版社，2000：230-239．
25．杜善义，王彪编著．复合材料细观力学[M]．科学出版社，1998：1160．
26. Hashin Z. Thermoelastic properties of fiber composites with imperfect interface[J]. Mechanics of Materials, 1990, 8: 333-348.
27. Cook J, Gordon J E. A mechanism for the control of crack propagation in all-brittle systems[C]. Proc. Royal Society, 1964, 282: 508-520.
28. Goree J G, Gross R S. Analysis of an unidirectional composite containing broken fibers and matrix damage[J]. Engrg Fracture Mech., 1979, 13 (5): 563-578.
29. Barsoum M W, Kanguthar P, Wang A S D. Matrix crack initiation in ceramic matrix composite Ⅰ: Experiments and test results[J]. Composites Science and Technology, 1992 (44): 257-269.
30. He M Y, Hutchinson J W. Crack deflection at an interface between dissimilar elastic materials[J]. International Journal of Solids and Structure, 1989, 25 (1): 1053-1067.
31. He M Y, Evans A G, Hutchinson J W. Crack deflection at an interface between dissimilar elastic materials: role of residual stresses[J]. International Journal of Solids and Structure, 1994, 31(24): 3443-3455.
32. Ahn B K, Curtin W A, Parthasarathy T A, et al. Criteria for crack deflection/penetration criteria for fiber-reinforced ceramic matrix composites[J]. Composites Science and Technology, 1998, 58 (11): 1775-1784.
33. Susmit M, Raj N S. Effects of fiber coating properties on the crack deflection and penetration in fiber-reinforced ceramic composites[J]. Acta Materialia, 1997, 45(11): 4721-4731.
34. Kerans R J, Parthasarathy T A. Crack deflection in ceramic composites and fiber coating design criteria [J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1999, 30 (4): 521-524.
35. Lee W, Howard S J, Clegg W J. Growth of interface defects and its effect on crack deflection and toughening criteria [J]. Acta Materialia, 1996,44 (10): 3905-3922.
36. Martin E, Peters P W M, Leguillon D, et al. Conditions for matrix crack deflection at an interface in ceramic matrix composites [J]. Materials Science and Engineering: A, 1998, 250 (2): 291-302.
37. Martin E, Leguillon D, Lacroix C. A revisited criterion for crack deflection at an interface in a brittle biomaterial [J]. Composites Science and Technology, 2001, 61 (12): 1671-1679.
38.. Martin E, Leguillon D. Energetic conditions for interfacial failure in the vicinity of a matrix crack in brittle matrix composites [J]. International Journal of Solids and Structures, 2004, 41 (24-25): 6937-6948.
39. Ostertag C P. Influence of fiber and grain bridging on crack profiles in SiC fiber-reinforced alumina-matrix composites [J]. Materials Science and Engineering: A, 1999, 260 (1-2): 124-131.
40. Sun Y J, Singh R N. Determination of fiber bridging stress profile by debond length measurement [J]. Acta Materialia, 2000,48 (13): 3607-3619.
41. Raddatz O, Schneider G A, Mackens W, et al. Bridging stresses and R-curves in ceramic/metal composites [J]. Journal of the European Ceramic Society, 2000, 20 (13): 2261-2273.
42. Studer M, Peters K, Botsis J. Method for determination of crack bridging parameters using long optical fiber Bragg grating sensors [J]. Composites: Part B, 2003,34 (4): 347-359.
43.. Fernberg S P., Berglund L A. Bridging law and toughness characterisation of CSM and SMC composites [J]. Composites Science and Technology, 2001, 61(16): 2445-2454.
44. Begley M R, McMeeking R M. Fatigue crack growth with fiber failure in metal-matrix composites [J].. Composites Science and Technology, 1995,53 (4): 365-382.
45. Begley M R, McMeeking R M. Numerical analysis of fibre bridging and fatigue crack growth in metal matrix composite materials [J]. Materials Science and Engineering:A, 1995, 200 (1-2):12-20.
46. Budiansky B, Cui Y L. Toughening of ceramics by short aligned fibers [J]. Mechanics of Materials, 1995, 21 (2): 139-146.
47. Sarrafi-Nour G R, Coyle T W, Fett T. A weight function for the crack surface tractions in chevron-notched specimens [J]. Engineering Fracture Mechanics, 1998,59 (4): 439—445.
48. Herrmann D J, Hillberry B M. A new approach to the analysis of unidirectional titanium matrix composites with bridge and unbridged cracks [J]. Engineering Fracture Mechanics, 1997, 56 (5): 711-726.
49. Song G M, Zhou Y, Sun Y. Modeling of fiber toughening in fiber-reinforced ceramic composites [J]. Ceramics International, 1999,25 (3): 257-260.
50. Mumm D R, Faber K T. Interfacial debonding and sliding in brittle-matrix composites measured using an improved fiber pullout technique[J]. Acta Metallurgica Materialia, 1995, 43 (3): 1259-1270.
51. Verma R, Ghosh K, Merrick H, et al. Measurement of interracial shear properties of composites of Ti-1100 alloy reinforced with SCS-6 SiC monofilament fiber[J]. Materials Science and Engineering: A, 1995, 191 (1-2): 151-163.
52. Young R J, Bannister D J, Andrews M C, et al. Analysis of the single-fibre pull-out test by means of Raman spectroscopy: Part Ⅱ-Micromechanics of deformation for an aramid/epoxy system[J]. Composites Science and Technology, 1995, 53 (4): 411-421.
53. Harmia T, Friedrich K. Fracture toughness and failure mechanisms in unreinforced and long-glass-fibre-reinforced PA66/PP blends[J]. Composites Science and Technology, 1995, 53 (4):. 423-430.
54. Xia Z, Curtin W A. Tough-to-brittle transitions in ceramic-matrix composites with increasing interfacial shear stress[J]. Acta Materialia, 2000, 48 (20): 4879-4892.
55. Cherepanov G P, Esparragoza I E. The problem of fiber pullout[J]. Materials Science and Engineering: A, 1995, 203 (1-2): 332-342.
56. Zhou L M, Mai Y M, Ye L. Analysis of fibre push-out test based on the fracrure mechanics approach[J]. Composites Engineering, 5 (10-11): 1199-1219.
57. Quek M Y. Stress transfer at a partially bonded fibre/matrix interface[J]. International Journal of Adhesion and Adhesives, 2002, 22 (4): 303-310.
58. Lin G, Geubelle P H, Sottos N R. Simulation of fiber debonding with friction in a model composite pushout test[J]. International Journal of Solids and Structures, 2001, 38 (46-47): 8547-8562
59. Schreyer H L, Peffer A. Fiber pullout based on a one-dimensional model of decohesion[J], Mechanics of Materials, 2000, 32 (12): 821-836.
60. Tsai K H, Kim K S. The micromechanics of fiber pull-out[J]. Journal of the Mechanics and Physics of Solids, 1996, 44 (7): 1147-1177.
61. Marotzke C, Qiao, L. Interracial crack propagation arising in single-fiber pull-out tests[J]. Composites Science and Technology, 1997, 57 (8): 887-897.
62. Beckert W, Lauke B. Finite element calculation of energy release rate for single-fibre pull-out test[J]. Computational Materials Science, 1996, 5 (1-3): 1-11
63. Hedgepeth J M, Dyke V P. Local stress concentrations in imperfect filimentary composite materials[J]. Journal of composite material, 1967 (1): 294-309.
64. Beyerlein I J, Landis C M. Shear-lag model for failure simulations of unidirectional fiber composites including matrix stiffness[J]. Mechanics of Materials, 1999, 31 (5): 331-350.
65. Jiang X Y, Gao Q. Stress-transfer analysis for fibre/matrix interfaces in short-fibre-reinforced composites[J]. Composites Science and Technology, 2001, 61 (10): 1359-1366.
66. Hsueh C H. Crack-wake interracial debonding criteria for fiber-reinforced composites[J]. Acta Materialia, 1996, 44 (6): 2211-2216.
67. Hsueh C H, Young R J, Yang X. Stress transfer in a model composite containing a single embedded fiber[J]. Acta Materialia, 1997, 45 (4): 1469-1476.
68. Hsueh C H, Becher P F. Interfacial shear debonding problems in fiber-reinforced ceramic composites [J], Acta Materialia, 1998, 46 (9): 3237-3245.
69. Nairn J A, Mendels D A. On the use of planar shear-lag methods for stress-transfer analysis of multilayered composites [J]. Mechanics of Materials, 2001,33 (6): 335-362.
70. Nairn J A. Energy release rate analysis for adhesive and laminate double cantilever beam specimens emphasizing the effect of residual stresses [J]. International Journal of Adhesion and Adhesives, 2000, 20 (1): 59-70.
71. Zhang S Y. A new model for the energy release rate of fibre/matrix interfacial fracture. Composites Science and Technology, 1998, 58 (1): 163-166.
72. Zhang S Y. Debonding and Cracking Energy Release Rate of the Fiber/Matrix Interface [J]. Composites Science and Technology, 1998, 58 (3-4): 331-335.
73. Zhang S Y. A simple approach to the evaluation of fiber/matrix interfacial shear strength and fracture toughness, A simple approach to the evaluation of fiber/matrix interfacial shear strength and fracture toughness [J]. Composites Science and Technology, 2000, 60 (1):. 145-148.
74. Curtin W A. Theory of mechanical properties of ceramic matrix composites. J. Am. Ceram. Soc [C]. 1991, 74 (11), 2837-2845.
75. Lissart N, Lamon J. Damage and failure in ceramic matrix minicomposites: experimental study and model [J]. Acta Materalia, 1997,45 (3): 1025-1044.
76. Wu E M, Robinson C S. Computational micro-mechanics for probabilistic failure of fiber composites in tension [J]. Composites Science and Technology, 1997,58 (9): 1421—1432.
77. Bednarcyk B A, Arnold S M. Micromechanics-based deformation and failure prediction for longitudinally reinforced titanium composites [J]. Composites Science and Technology, 2001,61 (5): 705-729.
78. Gonzalez C, Llorca J. Micromechanical modelling of deformation and failure in Ti-6Al-4V/SiC composites [J]. Acta Materialia, 2001,49 (17): 3505-3519.
79. Landis C M, Beyerlein I J, McMeeking R M. Micromechanical simulation of the failure of fiber reinforced composites [J]. Journal of the Mechanics and Physics of Solids, 2000,48 (3): 621-648.
80. Curtin W A. Theory of mechanical properties of ceramic-matrix composites [J]. Journal of American Ceramic Society, 1991,76 (1): 2837-2845.
81. Mackay R A, Draper S L, Ritttter A M, et al. A comparision of the mechanical properties and microstructure of intermetallic matrix composites fabricated by two different methods [J]. Metallic Transactions, 1991,25 (1): 1443-1455.
82. Weber C H, Du Z Z, Zok F W. High temperature deformation and fracture of a fiber reinforced titanium matrix composites [J]. Acta Materalia, 1996, 44 (2): 683-695.
83. Gaffney K M, Botsis J. Deformation and fracture of a uniaxially reinforced composite material [J]. Composites Science and Technology, 1999, 59 (12): 1847-1859.
84. Xu J, Cox B N, Mcglockton M A, et al. A binary model of textile composites-II: The elastic regime [J]. Acta metallica, 1995,43 (1): 3511-3524.
85. Cox B N, Carter W C, Fleck N A. A binary model of textile composites-I: Formations[J]. Acta metalliea, 1995, 42 (1): 3463-3479.
86. Zhou S J, Curtin W A. Faliure of fiber composites: a lattice Green function model[J]. Acta Materialia, 1995, 43 (1): 3093-3104.
87. Ibnabdeljalil M, Curtin W A. Strength and reliability of fiber-reinforced composites: localized load-sharing and associated size effects[J]. International Journal of Solids and Structures, 1997, 34 (21): 2649-2668.
88. Ibnabdeljalil M, Curtin W A. Strength and reliability of notched fiber-reinforced composites[J]. Acta Materialia, 1997, 45 (9): 3641-3652.
89. Beyerlein I J, Phoenix S L. Stress concentrations around multiple fiber breaks in an elastic matrix with local yielding or debonding using quadratic influence superposition[J]. Journal of the Mechanics and Physics of Solids, 1996, 44 (12): 1997-2039.
90. Mahesh S, Beyerlein I J, Phoenix S L. Size and heterogeneity effects on the strength of fibrous composites[J]. Physica D, 1999, 133 (1-4): 371-389:
91. Beyerlein I J, Phoenix S, Sastry L, et al. Comparison of shear-lag theory and continuum fracture mechanics for modeling fiber and matrix stresses in an elastic cracked composite lamina[J]. International Journal of Solids and Structures, 1996, 33 (18): 2543-2574.
92. Ibnabdeljalil M, Phoenix S L. Scalings in the statistical failure of brittle matrix composites with discontinuous fibers-1. Analysis and Monte Carlo simulations[J]. Acta Metallurgica Materialia, 1995, 43 (8): 2975-2983.
93. Ismar H, Streicher F. Modelling and simulation of the mechanical behavior of ceramic matrix composites as shown by the example of SiC/SiC[J]. Computational Materials Science, 1999, 16 (1-4): 17-24.
94. Cheng T L, Qiao R, Xia Y M. A Monte Carlo simulation of damage and failure process with crack saturation for unidirectional fiber reinforced: ceramic composites[J]. Composites Science and Technology, 2004, 64 (13-14): 2251-2260.
95. Ananth C R, Voleti S R, Chandra N. Effect of fiber fracture and interracial debonding on the evolution of damage in metal matrix composites[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1998, 29 (9-10): 1203-1211.
96. Xia Z, Curtin W A, Okabe T. Green's function vs. shear-lag models of damage and failure in fiber composites[J]. Composites Science and Technology, 2002, 62 (10-11): 1279-1288.
97. Xia Z, Okabe T, Curtin W A. Shear-lag versus finite element models for stress transfer in fiber-reinforced composites[J]. Composites Science and Technology, 2002, 62 (9): 1141-1149.
98. Xia Z, Curtin W A, Peters P W M. Multiscale modeling of failure in metal matrix composites[J]. Acta Materialia, 2001, 49 (2): 273-287.
99. Zaretsky E V. Design for life, plan for death[J]. Machine Design,1994, 66 (15): 55-59.
100. Bao G, Hutchinson J W, McMeeking R M. Particle Reinforcement of Ductile Matrices Against Plastic Flow and Creep[J]. Acta metall, mater., 1991, 39 (8): 1871-1882.
101. Rauchs G, Thomason P F, Withers P J. Finite element modelling of frictional bridging during fatigue crack growth in fibre-reinforced metal matrix composites[J]. Computational Materials Science, 2002, 25 (1-2): 166-173.
102. Rauchs G, Withers P J. Computational assessment of the influence of load ratio on fatigue crack growth in fibre-reinforced metal matrix composites[J]. International Journal of Fatigue, 2002, 24 (12): 1205-1211.
103. Guo Y J, Wu W R. A phenomenological model for predicting crack growth in fiber-reinforced metal laminates under constant-amplitude loading[J]. Composites Science and Technology, 1999, 59 (12): 1825-1831.
104. Barney C, Cardona D C, Bowen P. Fatigue crack growth resistance from unbridged defects in continuous fibre reinforced metal matrix composites[J]. International Journal of Fatigue, 1998, 20 (4): 279-289.
105. Botsis J, Zhao D. Fatigue fracture process in a model composite[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1997, 28 (7): 657-666.
106. Kruzic J J, Cannon R M, Ager J W, et al. Fatigue threshold R-curvees for predicting reliability of ceramics under cyclic loading[J]. Acta Materialia, 2005, 53 (9): 2595-2605.
107. Kruzic J J, Campbell J P, Ritchie R O. On the fatigue behavior of γ-based titanimn aluminides: role of small cracks[J]. Acta Materialia, 1999, 47(3): 801-816.
108. Kruzic J J, Nalla R K, Kinney J H, et al. Crack blunting, crack bridging and resistance-curve fracture mechanics in dentin: effect of hydration[J]. Biomaterials, 2003, 24(28): 5209-5221.
109. Wang P C, Jeng S M, Yang J M. Characterization and modeling of stiffness reduction in SCS-6-Ti composites under low cycle fatigue loading[J]. Materials Science and Engineering: A, 1995, 200 (1-2): 173-180.
110. Wang P C, Jeng S M, Yang J M, et al. Fatigue life prediction of fiberoreinforced titanium matrix composites[J]. Acta Materialia, 1996, 44 (3): 11097-1108.
111. Wang P C, Yang J M. Simulation of fatigue cracking and life distribution of SCS-6 fiber-reinforced orthorhombic titanium aluminide composites[J]. Materials Science and Engineering: A, 1997, 222 (2): 101-108.
112. Wang P C, Her Y C, Yang J M. Fatigue behavior and damage modeling of SCS-6/titanium/titanium aluminide hybrid laminated composite[J]. Materials Science and Engineering: A, 1998, 245 (1): 100-108.
113. Xia Z H, Peters P W M, Dudek H J. Finite element modelling of fatigue crack initiation in SiC-fibre reinforced titanium alloys[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 2000, 31 (20): 1031-1037.
114. Xia Z H, Curtin W A. Life prediction of titanium MMCs under low-cycle fatigue[J]. Acta Materialia, 2001, 49 (9): 1633-1646.
115. Williams M L. The Stresses Around a Fault or Crack in Dissimilar Media[J]. Bulletin of the Seismological Society of America, 1959, 49 (2): 199-204,
116. Dundurs J. Edge-bonded dissimilar orthogonal elastic wedges under normal and shear loading[J]. Journal of applied Mechanics, 1969, 36: 650-652.
117. Erdogan F. Stress Distribution in a Nonhomogeneous Elastic Plane With Cracks[J]. Journal of Applied Mechanics, 1963, 30: 232-236.
118. Erdogan F. Stress Distribution in Bonded Dissimilar Materials With Cracks[J]. Journal of Applied Mechanics, 1965, 32: 403-410.
119. Rice J R, Sih O C. Plane Problems of Cracks in Dissimilar Media[J]. Journal of Applied Mechanics, 1965, 32: 418-423.
120. Hutchinson J W, Mear M E, Rice J R. Crack Paralleling an Interface Between Dissimilar Materials[J]. Journal of Applied Mechanics, 1987, 54: 828-832.
121. Rice JR. Elastic Fracture Mechanics Concepts for Interfacial Cracks[J]. Journal of Applied Mechanics, 1988, 55: 98-103.
122. Zak A R, Williams M L. Crack point stress singularities at a bi-material interface[J]. Journal of Applied Mechanics, 1963, 30: 142-143.
123. Gupta V, Yuan J, Martinez D. Calculation, Measurement, and Control of Interface Strength in Composites[J]. Journal of American Ceramic Socrety, 1993, 76 (15): 305-315.
124. Lacroix C, Leguillon D, Martin E. The influence of an interphase on the deflection of a matrix crack in a ceramic-matrix composite[J]. Composites Science and Technology, 2002, 62 (4): 519-5123.
125. Liu Y F, Tanaka Y, Masuda C. Debonding mechanisms in the presence of an interphase in composites[J]. Acta Materialia 1998, 46 (15): 5237-5247.
126. Akser E O, Choy K L. Finite element analysis of the stress distribution in a thermally and transversely loaded Ti-6Al-4V/SiC fibre composite[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 2001, 32 (2): 243-251.
127. Carrere N, Martin E, Lamon J. The influence of the interphase and associated interfaces on the deflection of matrix cracks in ceramic matrix composites[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 2000, 31 (11): 1179-1190.
128. Hinoki T, Yang W, Nozawa T, et al. Improvement of mechanical properties of SiC/SiC composites by various surface treatments of fibers[J]. Journal of Nuclear Materials, 2001, 289 (1-2): 23-29.
129. Wang Y Q, Zhou B L. Effect of a fiber coating on the fabrication of fiber reinforced metal-matrix composites[J]. Journal of Materials Processing Technology, 1998, 73 (1-3): 78-81.
130. Cui Y L. On the strength of fiber reinforced ceramic composites containing an elliptic hole[J]. Mechanics of Materials, 1995, 19 (2-3): 239-249.
131. Majumda B S, Newaz G M. Constituent damage mechanisms in metal matrix composites under fatigue loading and their effects on fatigue life[J]. Materials Science and Engineering, 1995, 200 (1-2): 114-129.
132. Murakami H. Stress intensity factors handbook[M]. Oxford: Pergamon Press, 1986.
133. Cao J W, Sakai M. The crack-face fiber bridging of a 2D-C/C-composite[J]. Carbon, 1996, 34 (3): 387-395.
134. Barenblatt G L. The mathematical theory of equilibrium cracks in brittle fracture[J]. Advanced Applied Mechanics, 1962, 7: 55-129.
135. Lawn B R. In Fracture of brittle Solid[M]. Cambridge: Cambridge University Press, 1993.
136. Marshall D B, Cox B N, Evans A G. The mechanics of matrix cracking in brittle-matrix fiber composites[J], Acta metall, mater., 1985, 33 (11): 2013-2021.
137. Marshall M B, Cox B N. A J-integral method for calculating steady-state matrix cracking stresses in composites[J]. Mechanics of Materials, 1988, 7(4): 127-133.
138. McCartney L N. Mechanics of matrix cracking in brittle-matrix fiber-reinforced composites[J]. Proc. R. Soe. Lond., 1987, 409: 329-333.
139. Raddatz O, Schneider G A, Claussen N. Modelling of R-curve behaviour in ceramic/metal composites[J]. Acta Materialia, 1998, 46 (18): 6381-6395.
140. Rouby D, Brenet P, Conchin F, et al. Direct measurement of crack-bridging tractions: A new approach to the fracture behaviour of ceramic/ceramic composites[J]. Composites Science and Technology, 1996, 56 (7): 817-823.
141. Sakai M, Matsuyama R, Miyajima T. The pull-out and failure of a fiber bundle in a carbon fiber reinforced carbon matrix composite[J]. Carbon, 2000, 38 (15): 2123-2131.
142. Chiang Y C. On fiber debonding and matrix cracking in fiber-reinforced ceramics[J]. Comp. Sci. Technol., 2001, 61(12): 1743-1756.
143. Budiansky B, Evans A G, Hutchinson J W. Fiber-matrix debonding effects on cracking in aligned fiber ceramic composites[J]. International Journal of Solids and Structures, 1995, 32 (3-4): 315-328.
144. Preuss M, Rauchs G, Doel T J A, et al. Measurements of fibre bridging during fatigue crack growth in Ti/SiC fibre metal matrix compositesv[J]. Acta Materialia, 2003, 51(4): 1045-1057.
145. Honda K, Kagawa Y, Mai Y W. Effects of relative sliding distance on the frictional stress transfer in fiber-reinforced ceramics[J]. Materials Science and Engineering: A, 1998, 252 (1): 53-63.
146. Warrier SG, Maruyama B, Majumdar BS, et al. Behavior of several interfaces during fatigue crack growth in SiC/Ti-6Al-4V composites[J]. Materials Science and Engineering: A, 1999, 259 (2): 189-200.
147. Wu W, Verpoest I, Varna J. Prediction of energy release rate due to the growth of an interface crack by variational analysis[J]. Comp. Sci. Teehnol., 2000, 60 (3): 351-360.
148. Mao X N, Zhou L, Zhou Y G, et al. Characteristic of principle properties and microstructure of TP-650 Particles reinforced titanium matrix Composites[J]. Rare metal materials and engineering, 2004, 33 (6): 620-623 (in chinese).
149. Chandra N, Ananth-C R. Analysis of interracial behavior in MMCs and IMCs by the use of thin-slice push-out tests[J]. Composites Science and Technology, 1995, 54 (1): 87-100.
150. Okabe T, Takeda N, Kamoshida Y, et al. A 3D shear-lag model considering micro-damage and statistical strength prediction of unidirectional fiber-reinforced composites[J]. Composites Science and Technology, 2001, 61 (12): 1773-1787.
151. Gonzalez C, Llorca J. Micromechanical modelling of deformation and failure in Ti-6A1-4V/SiC composites[J]. Acta Materialia, 2001, 49 (17): 3505-3519.
152. Majumdar B S, Newaz G M. Inelastic deformation of metal matrix composites: plasticity and damage mechanisms[J]. Philosophical Magazine A, 1992, 66 (2): 187-212.
153. Fiedler B. Klisch A, Schulte K. Stress concentrations in multiple fibre model composites[J]. Composites Part A: Applied Science and Manufacturing (Incorporating Composites and Composites Manufacturing), 1998, 29 (9-10): 1013-1019.
154. Leucht R, Dudek H J. Properties of SiC fibre reinforced titanium alloys processed by fibre coating and hot isostatic pressing[J]. Materials Science and Engineering: A, 1994, 188: 201-210.
155. Cox B N. Scaling relations for bridged cracks[J]. Mech. of Mater., 1993, 15: 87-98.
156. MeMeeking R M, Evans A G. Matrix fatigue cracking in fiber composites[J]. Mech. Mater., 1990, 9: 217-227.
157. Greaves I, Yates J R. The growth of freely initialing fatigue cracks in an unnotched SiC/titanium composite[J]. International Journal of Fatigne, 1997, 19 (2): 151-159.