碳/碳复合材料疲劳寿命预测模型与分析方法研究
|
摘要
碳/碳（C/C）复合材料具有耐热性能及优异的力学性能，它既可以作为耐高温材料使用，又可作为功能结构材料使用。由于三维四向编织C/C复合材料内部结构复杂，人们对其疲劳寿命等力学特性的研究还很有限，这已成为其进一步推广应用的制约因素。因此，有必要通过对C/C复合材料的疲劳性能进行试验研究，分析其疲劳损伤模式，建立其疲劳寿命的预测模型，为其更加广泛应用提供理论支持。本文研究工作主要包括以下五个部分：
（1）碳纤维及C/C复合材料的静拉伸力学性能及疲劳特性试验研究。制作了单向C/C复合材料及三维四向编织C/C复合材料；测试了碳纤维束的拉伸强度及拉—拉疲劳特性，并对纤维单丝进行了强度测试；对单向C/C复合材料纵向、横向及面内剪切方向的静拉伸力学性能及拉—拉疲劳特性进行了试验研究；对三维四向编织C/C复合材料的纵向静拉伸力学性能及拉—拉疲劳特性进行了试验研究；测试单向C/C复合材料的纤维—基体界面强度及三维四向编织C/C复合材料的纤维束—基体界面强度。试验研究为C/C复合材料疲劳特性的理论预测提供了数据支持。
（2）单向C/C复合材料拉—拉疲劳寿命及剩余强度预测模型研究。基于单向C/C复合材料纵向拉伸强度的随机核模型，引入纤维单丝剩余强度二参数Weibull模型及纤维单丝—基体界面剩余强度模型，建立单向C/C复合材料纵向拉—拉疲劳寿命及剩余强度的预测模型，实现单向C/C复合材料纵向拉—拉疲劳寿命及剩余强度的预测。通过单向C/C复合材料算例分析表明本文所建立的疲劳寿命预测模型及剩余强度预测模型用于预测单向C/C复合材料疲劳寿命及剩余强度是可行的。
（3）三维四向编织复合材料细观结构模型和刚度预测模型研究。提出采用挤压切边椭圆面来描述相互挤压的纤维束横截面，建立了一种新的细观结构模型，该模型反映纤维束之间沿纤维束轴向不断变化的相互挤压变形造成纤维束横截面积沿纤维束轴向不断变化，基于刚度体积平均及柔度体积平均混合思想，引入所建立的细观结构模型，建立相应的刚度预测模型。用本文模型计算编织复合材料几何特性及工程弹性常数的数值结果与试件实测数据吻合，表明了模型的合理有效性。
（4）三维四向编织C/C复合材料纵向拉—拉疲劳寿命预测模型研究。基于单向复合材料纵向拉—拉疲劳寿命预测模型及剩余强度预测模型，将纤维束轴向拉应力与剪应力共同作用的蔡—希尔破坏准则及纤维—基体界面脱粘后纤维束发生断裂的破坏准则推广到疲劳加载情况，并作为三维四向编织复合材料疲劳损伤破坏准则，同时引入基体破坏准则，建立了考虑纤维单丝强度分散性的三维四向编织复合材料疲劳寿命预测模型。通过与实验结果对比，表明本文所建立的三维四向编织C/C复合材料疲劳寿命预测模型预测精度较好。
（5）三维四向编织C/C复合材料三维逐渐损伤有限元分析的强度与寿命预测方法研究。基于考虑纤维束间相互挤压接触的单胞模型，引入周期性位移边界条件及单向C/C复合材料的剩余强度模型和剩余刚度模型；采用Hashin失效判定准则判定纤维束的损伤类型，并提出相应的损伤退化模式及材料最终失效准则，实现对三维四向编织C/C复合材料在静载荷与疲劳载荷作用下的逐渐损伤破坏分析。试验验证表明，本文所建立的强度与寿命预测方法可以较好地预测静载荷和疲劳载荷作用下的损伤发生、扩展及最终失效。
Carbon/Carbon (C/C) composites have the advantages of high temperature performance andexcellent mechanical properties. It can be used as both high temperature structure materials andfunctional materials. However, researches on mechanical properties such as strength and fatigue life ofthree-dimensional and four-directional braided C/C composites are behindhand, because ofcomplexities of their microstructure. Such restriction has limited C/C composites for further application.Therefore, it is necessary to analyze fatigue damage modes of C/C composites through theexperimental research and to build models for predicting fatigue life of them, which can provide atheoretical support for their widely use. The main work done in this dissertation includes the followingfive parts:
(1) Experimental research on mechanical properties and fatigue characteristics of carbon fiber andC/C composites. Unidirectional and three-dimensional and four-directional braided C/C composites areprocessed. The tensile strength and tension-tension fatigue behaviour of carbon fibers yarn are tested.The tensile strength of carbon fibers is tested. The experimental research for tensile strength andtension-tension fatigue behavior of unidirectional C/C composites in the longitudinal, transverse andin-plane-shear directions is conducted. The tensile strength and tension-tension fatigue behaviour ofthree-dimensional and four-directional braided C/C composites in the longitudinal direction is tested.The fiber-matrix interfaces strengths of unidirectional C/C composites and fiber yarn-matrix interfacesstrengths of three-dimensional and four-directional braided C/C composites are tested. Theexperimental study provides a data support for the theoretical predictions on fatigue characteristics ofC/C composites.
(2) The model for predicting tension-tension fatigue life and residual strength of unidirectionalC/C composites is studied. Based on the random crack core theory and model for predicting thelongitudinal tensile strengths of unidirectional composites, the Weibull model describing residualstrength distribution of single fiber and the residual strength model of fiber-matrix interfaces is broughtin for building the tension-tension fatigue life and residual strength prediction model of unidirectionalC/C composites in the longitudinal direction. The tension-tension fatigue life and residual strength ofunidirectional C/C composites can be predicted by using the model.
(3) The research on microstructure model and stiffness prediction model of three-dimensional andfour-directional braided C/C composites. Elliptic with trimming is assumed to describe thecross-section of yarns, a new microstructure model of3D braided composites is established. The new model truly reflects the jamming pattern between yarns and its cross-section variation along the axial ofthe yarns. Based on the stiffness volume average method and flexibility volume average method,introducing the microstructure model which is established in this paper, a model to predict stiffness isthen established. The calculated simulation values of the geometric characteristics and elastic constantsof braided composites well agree with the measured values. The numerical result indicates theeffectiveness of the model.
(4) The model for predicting tension-tension fatigue life of three-dimensional and four-directionalbraided C/C composites is studied. The criterion of yarn fracture after fiber-matrix interfacialdebonding and the Tsai-Hill criterion considering the axial tension and shear stress are extended fromstatic load to fatigue load. The new extended criteria, as well as matrix failure criterion are adopted asthe fatigue failure criteria of the three-dimensional and four-directional braided composites. Based onthe theory of the fatigue life and residual strength prediction model of unidirectional C/C composites,fatigue life prediction model of three-dimensional and four-directional braided C/C composites is built.Compared with the experimental results, the fatigue life prediction model is reasonable.
(5) The progressive damage method of predicting the strength and fatigue life ofthree-dimensional and four-directional braided C/C composites is studied. The Hashin-type failurecriteria are introduced into the method to detect damage for diverse damage modes, the criteria of thestructure catastrophe and the material property degradation rules are also established. Based on the theresidual strength degradation model and the residual stiffness degradation model of unidirectional C/Ccomposites, a progressive damage method of predicting the strength and fatigue life ofthree-dimensional and four-directional braided C/C composites is established by using the finiteelement method. The geometrical model considering the jamming pattern between yarns is applied inthe finite element method model coupled with the periodical displacement boundary conditions. Anexcellent agreement is found between date obtained from this study and the experiment.
（1）碳纤维及C/C复合材料的静拉伸力学性能及疲劳特性试验研究。制作了单向C/C复合材料及三维四向编织C/C复合材料；测试了碳纤维束的拉伸强度及拉—拉疲劳特性，并对纤维单丝进行了强度测试；对单向C/C复合材料纵向、横向及面内剪切方向的静拉伸力学性能及拉—拉疲劳特性进行了试验研究；对三维四向编织C/C复合材料的纵向静拉伸力学性能及拉—拉疲劳特性进行了试验研究；测试单向C/C复合材料的纤维—基体界面强度及三维四向编织C/C复合材料的纤维束—基体界面强度。试验研究为C/C复合材料疲劳特性的理论预测提供了数据支持。
（2）单向C/C复合材料拉—拉疲劳寿命及剩余强度预测模型研究。基于单向C/C复合材料纵向拉伸强度的随机核模型，引入纤维单丝剩余强度二参数Weibull模型及纤维单丝—基体界面剩余强度模型，建立单向C/C复合材料纵向拉—拉疲劳寿命及剩余强度的预测模型，实现单向C/C复合材料纵向拉—拉疲劳寿命及剩余强度的预测。通过单向C/C复合材料算例分析表明本文所建立的疲劳寿命预测模型及剩余强度预测模型用于预测单向C/C复合材料疲劳寿命及剩余强度是可行的。
（3）三维四向编织复合材料细观结构模型和刚度预测模型研究。提出采用挤压切边椭圆面来描述相互挤压的纤维束横截面，建立了一种新的细观结构模型，该模型反映纤维束之间沿纤维束轴向不断变化的相互挤压变形造成纤维束横截面积沿纤维束轴向不断变化，基于刚度体积平均及柔度体积平均混合思想，引入所建立的细观结构模型，建立相应的刚度预测模型。用本文模型计算编织复合材料几何特性及工程弹性常数的数值结果与试件实测数据吻合，表明了模型的合理有效性。
（4）三维四向编织C/C复合材料纵向拉—拉疲劳寿命预测模型研究。基于单向复合材料纵向拉—拉疲劳寿命预测模型及剩余强度预测模型，将纤维束轴向拉应力与剪应力共同作用的蔡—希尔破坏准则及纤维—基体界面脱粘后纤维束发生断裂的破坏准则推广到疲劳加载情况，并作为三维四向编织复合材料疲劳损伤破坏准则，同时引入基体破坏准则，建立了考虑纤维单丝强度分散性的三维四向编织复合材料疲劳寿命预测模型。通过与实验结果对比，表明本文所建立的三维四向编织C/C复合材料疲劳寿命预测模型预测精度较好。
（5）三维四向编织C/C复合材料三维逐渐损伤有限元分析的强度与寿命预测方法研究。基于考虑纤维束间相互挤压接触的单胞模型，引入周期性位移边界条件及单向C/C复合材料的剩余强度模型和剩余刚度模型；采用Hashin失效判定准则判定纤维束的损伤类型，并提出相应的损伤退化模式及材料最终失效准则，实现对三维四向编织C/C复合材料在静载荷与疲劳载荷作用下的逐渐损伤破坏分析。试验验证表明，本文所建立的强度与寿命预测方法可以较好地预测静载荷和疲劳载荷作用下的损伤发生、扩展及最终失效。
Carbon/Carbon (C/C) composites have the advantages of high temperature performance andexcellent mechanical properties. It can be used as both high temperature structure materials andfunctional materials. However, researches on mechanical properties such as strength and fatigue life ofthree-dimensional and four-directional braided C/C composites are behindhand, because ofcomplexities of their microstructure. Such restriction has limited C/C composites for further application.Therefore, it is necessary to analyze fatigue damage modes of C/C composites through theexperimental research and to build models for predicting fatigue life of them, which can provide atheoretical support for their widely use. The main work done in this dissertation includes the followingfive parts:
(1) Experimental research on mechanical properties and fatigue characteristics of carbon fiber andC/C composites. Unidirectional and three-dimensional and four-directional braided C/C composites areprocessed. The tensile strength and tension-tension fatigue behaviour of carbon fibers yarn are tested.The tensile strength of carbon fibers is tested. The experimental research for tensile strength andtension-tension fatigue behavior of unidirectional C/C composites in the longitudinal, transverse andin-plane-shear directions is conducted. The tensile strength and tension-tension fatigue behaviour ofthree-dimensional and four-directional braided C/C composites in the longitudinal direction is tested.The fiber-matrix interfaces strengths of unidirectional C/C composites and fiber yarn-matrix interfacesstrengths of three-dimensional and four-directional braided C/C composites are tested. Theexperimental study provides a data support for the theoretical predictions on fatigue characteristics ofC/C composites.
(2) The model for predicting tension-tension fatigue life and residual strength of unidirectionalC/C composites is studied. Based on the random crack core theory and model for predicting thelongitudinal tensile strengths of unidirectional composites, the Weibull model describing residualstrength distribution of single fiber and the residual strength model of fiber-matrix interfaces is broughtin for building the tension-tension fatigue life and residual strength prediction model of unidirectionalC/C composites in the longitudinal direction. The tension-tension fatigue life and residual strength ofunidirectional C/C composites can be predicted by using the model.
(3) The research on microstructure model and stiffness prediction model of three-dimensional andfour-directional braided C/C composites. Elliptic with trimming is assumed to describe thecross-section of yarns, a new microstructure model of3D braided composites is established. The new model truly reflects the jamming pattern between yarns and its cross-section variation along the axial ofthe yarns. Based on the stiffness volume average method and flexibility volume average method,introducing the microstructure model which is established in this paper, a model to predict stiffness isthen established. The calculated simulation values of the geometric characteristics and elastic constantsof braided composites well agree with the measured values. The numerical result indicates theeffectiveness of the model.
(4) The model for predicting tension-tension fatigue life of three-dimensional and four-directionalbraided C/C composites is studied. The criterion of yarn fracture after fiber-matrix interfacialdebonding and the Tsai-Hill criterion considering the axial tension and shear stress are extended fromstatic load to fatigue load. The new extended criteria, as well as matrix failure criterion are adopted asthe fatigue failure criteria of the three-dimensional and four-directional braided composites. Based onthe theory of the fatigue life and residual strength prediction model of unidirectional C/C composites,fatigue life prediction model of three-dimensional and four-directional braided C/C composites is built.Compared with the experimental results, the fatigue life prediction model is reasonable.
(5) The progressive damage method of predicting the strength and fatigue life ofthree-dimensional and four-directional braided C/C composites is studied. The Hashin-type failurecriteria are introduced into the method to detect damage for diverse damage modes, the criteria of thestructure catastrophe and the material property degradation rules are also established. Based on the theresidual strength degradation model and the residual stiffness degradation model of unidirectional C/Ccomposites, a progressive damage method of predicting the strength and fatigue life ofthree-dimensional and four-directional braided C/C composites is established by using the finiteelement method. The geometrical model considering the jamming pattern between yarns is applied inthe finite element method model coupled with the periodical displacement boundary conditions. Anexcellent agreement is found between date obtained from this study and the experiment.
引文
[1]王世驹.碳/碳复合材料氧化行为的研究[J].兵器材料科学与工程,1999,22(4):36~40.
[2]李贺军.碳/碳复合材料.新型碳材料,2001,16(2):79~80.
[3] Xue H, Li H J, Hou X H, et al. Flexual behavior of2D carbon-carbon composites fabricated bypressure gradient CVI[J]. New Carbon Mater,2004,19(4):289~293.
[4] Neumeister J, Jansson S, Leckie F. The effect of fiber architecture on the mechanical properties ofcarbon/carbon fiber composites[J]. Acta Mater,1996,44(2):573~585.
[5] Hiroshi Hatta, Keiji Suzuki, Tetsuro Shigei, et a1. Strength improvement by densification of C/Ccomposites[J]. Carbon.2001,39(1):83~90.
[6]嵇阿琳,李贺军,崔红.针刺炭纤维预制体的发展与应用[J].炭素科技,2010,29(3):23~27.
[7]孙乐民,李贺军,张守阳.沥青基炭/炭复合材料的弯曲断裂特征[J].新型炭材料,2001,16(3):28~31+41.
[8]熊信伯,李贺军.自发梯度炭/炭复合材料弯曲性能研究[J].新型炭材料,2001,16(4):22~26.
[9]王茂章,贺福.碳纤维的制造、性能及其应用[M].北京:科学出版社,1984.
[10] J X Zhao, K H Ding, J X Wei. Research on thermo physical properties and anti-thermal-vibrationproperties of C/C composites[J]. Acta Mater Compos Sinic,1987,4(4):45~50.
[11]袁辉.碳/碳复合材料刚度与强度预测模型研究[D].南京:南京航空航天大学,2009.
[12] Michael C H Lee, William T Short, Frank Abdi, et a1. A Math-Based Methodology for FatigueLongevity Prediction of3D Woven Fiberglass Reinforced Vinyl-ester Composites[C].2006SAEWorld Congress. Detroit, Michigan April2006:3~6.
[13]卢子兴,高镇同.应用微分方法确定复合泡沫塑料的杨氏模量[J].北京航空航天大学学报,1996,22(6):692~695.
[14] Roser B W. Mechanics of Fiber strengtherning Composite Materials[C]. Ohio, Matals Park:ASM，1965.
[15]韩杰才,黄玉东,赫晓东,杜善义.多向细编碳/碳复合材料界面力学性能测试与表征[J].复合材料学报,1995,12(4):72~78.
[16] Hiroshi Hatta, Ken Goto, Shinya Ikegaki, et al. Tensile strength and fiber/matrix interfacialproperties of2D-and3D-carbon/carbon composites[J]. Journal of the European Ceramic Society,2005,25(4):535~542.
[17] Yuko Furukawa, Hiroshi Hatta, Yasuo Kogo. Interfacial shear strength of C/C composites[J].Carbon,2003,41(9):1819~1826.
[18]孔宪仁,黄玉东,范洪涛,等.细编穿刺C/C复合材料不同层次界面剪切强度的测试分析[J].复合材料学报,2001,18(2):57~60.
[19] Takuya Aoki a, Yuhsuke Yamane, Toshio Ogasawara, et al. Measurements of fiber bundleinterfacial properties of three-dimensionally reinforced carbon/carbon composites up to2273K [J].carbon2007,45:459~467.
[20] Sines G, Yang Z, Vickers B D. Friction stress for carbon composite and carbon yarn during hightemperature creep[J]. Acta Metallurgica,1989,37(10):2673~2680.
[21]石荣,李贺军,杨峥,等.单向碳/碳复合材料的蠕变内应力[J].固体火箭技术,1995,18(4):59~62.
[22]赵秋雁,杨峥,朱小旗.碳/碳复合材料的高温持久性能测试及分析[J].宇航材料工艺,1996,(2):92~94.
[23] Gucer D E, Gurland J. Comparison of the statistics of two fracture modes[J]. Journal of theMechanics and Physics of Solids,1962,10(4):365~373.
[24] Curtin W A. Exact theory of fibre fragmentation in a singlefilament composite[J]. Journal ofMaterials Science,1991,26:5239~5253.
[25] Curtin W A. Stochastic damage evolution and failure in fibrereinforced composites[J]. Advancesin Applied Mechanics,1999,36:163~253.
[26] Hui C Y, Phoenix S L, Ibnabdeljalil M, et al. An exact closed form solution for fragmentation ofWeibull fibres in a single filament composite with applications to fibre-reinforced ceramics[J].Journal of the Mechanics and Physics of Solids,1995,43:1551~1585.
[27] Turon A, Costa J, Maim P, et al. A progressive damage model for unidirectional fibre-reinforcedcomposites based on fibre fragmentation. Part I: Formulation[J]. Composites Science andTechnology,2005,65:2039~2048.
[28] Zweben C. Tensile failure of fiber composites[J]. AIAA,1968,6(12):2325~2331.
[29]范赋群,曾庆敦.单向纤维增强复合材料的随机扩大临界核理论[J].中国科学(A辑),1994,(2):210~217.
[30] QingDun Zeng. A random critical-core theory of microdamage in interply hybrid composites:IIultimate failure[J]. Composites Science and Technology,1994,54(4):481~487.
[31] Yasuhiro Tanabe, Takuya Yoshimura, Tomoyuki Watanabe, et al. Fatigue of C/C composites inbending and in shear modes[J]. Carbon,2004,(42):1~6.
[32] A K Roy. Tensile fatigue behavior of a coated two-dimensional carbon/Carbon compositelaminate[J]. J Compos Technol Rea,1996,(18):202~208.
[33] A Ozturk．The influence of cyclic fatigue damage on the fracture toughness of carbon/carbonComposites[J]. J Bionmed Mater Res,1996,27A:641~646.
[34] A Ozturk, Moore R E. Tensile fatigue behavior of tightly WOVen carbon/carbon composites[J].Composites,1992,(23):39~46.
[35] H Mahfuz, M Maniruzzaman, J Krishagopalan, et a1. Effect of stress ratio on fatigue life ofcarbon/carbon composites[J]. Theoretical and Applied Fracture Mechanics,1995,(24):121~131.
[36] J C Williams, S W Yurgartis, J C Moosbrugger. Interlaminar shear fatigue damage evolution of2D carbon/carbon composites[J]. J Comp Mater,1996,30(7):785~799.
[37] K Goto，H Hatta，D Katsu，T Machida．Tensile fatigue of a laminated carbon/carbon compositesat room temperature[J]. Carbon,2003,(41):1249~1255.
[38]冯翃翎. C/C复合材料疲劳性能的研究[D].西安：西北工业大学,2006.
[39] Yang J M，Ma C L，Chou T W. Fiber inclination model of three dimensional textile structuralcomposites[J]. Journal of Composite Materials,1986,20(5):472~484.
[40] Li W, Hammad M, EI Shiekh A. Structural analysis of3-Dbraided performs for composites[J].Journal of Textile Institute,1990,81(4):491~514.
[41] Du Guangwu，Ko F K. Unit cell geometry of3-D braided structures[J]. Journal of ReinforcedPlastics and Composites,1993,12(7):752~768.
[42] Wang Y Q, W ang A S D. On the topological yarn structure of3-D rectangular and tubular braidedperforms [J]. Composites Science and Technology,1994,51(4):575~586.
[43] W u D L. Three-cell model and5D braided structural com posites[J]. Composites Science andTechnology,1996,56(3):225~233.
[44] Byun H, Chou T W. Process-microstructure relationships of2-step and4-step braidedcomposites[J]. Composites Science and Technology,1999,56(3):235~251.
[45] Chen L, Tao X M, Choy C L. On the microstructure of three-dimensional braided preforms[J].Composites Science and Technology,1999,59(3):391~404.
[46]徐焜,许希武.四步法三维矩形编织复合材料的细观结构模型[J].复合材料学报,2006,23(5):154~160.
[47] Makoto Ito. Effects of yarn undulation on the stress and deformation of textile composites[D].University of Delaware,1995.
[48]李嘉禄,刘谦.三维编织复合材料中纤维束横截面形状的研究[J].复合材料学报,2001,18(2):9~13.
[49]沈美玲.三向碳/碳复合材料拉伸性能测试方法研究[J].宇航材料工艺,1994,(6):62~67.
[50] Hiroshi Hatta, Ken Goto, Shinya Ikegaki, et al. Tensile strength and fiber/matrix interfacialproperties of2D-and3D-carbon/carbon composites[J]. Journal of the European Ceramic Society,2005,25(4):535~542.
[51] Peter B Pollock. Tensile failure in2-D carbon-carbon composites[J]. Carbon,1990,28(5):717~732.
[52] Lomov S V, Barburski M, Stoilova Tz, et al. Carbon composites based on multiaxial multiplystitched preforms. Part3: Biaxial tension, picture frame and compression tests of the performs[J].Composites Part A,2005,36(9):1188~1206.
[53]韩红梅. C/C复合材料的力学性能及损伤演变研究[D].西安:西北工业大学,2002.
[54]郑锡涛三维编织复合材料细观结构与力学性能分析[D].西安:西北工业大学,2003.
[55]李典森,卢子兴,卢文书.三维四向编织复合材料刚度和强度的理论预测[J].应用数学和力学,2008,(29)2:149~156
[56]王波.三维编织复合材料力学行为研究[D].西安:西北工业大学,2003.
[57]卢子兴,刘振国,麦汉超,等.三维编织复合材料强度的数值预测[J].北京航空航天大学学报,2002.(28)5:563~565.
[58]徐焜,许希武.三维编织复合材料渐进损伤的非线性数值分析[J].力学学报,2007.(39)2:398~407.
[59] Hashin Z. Failure criteria for unidirectional fiber composites[J]. Journal of Applied Mechanics,1980,47:329~335.
[60] Fang Guo-dong, Liang Jun, Wang Bao-lai Progressive damage and nonlinear analysis of3Dfour-directional braided composites under unidirectional tension[J]. Composite Structures，2009，(89);126~133.
[61]李嘉禄,杨红娜,寇长河.三维编织复合材料的疲劳性能[J].复合材料学报,(22)4:172~176.
[62]缪晓玲.三维编织C/C复合材料的疲劳行为及损伤演变研究[D].西安：西北工业大学,2006.
[63]肖来元,左惟炜,廖道训.三维编织复合材料威布尔概率分布数学模型[J].华中科技大学学报，2007,(35)12:56~61.
[64]王丹勇.层合板接头损伤失效与疲劳寿命研究[D].南京：南京航空航天大学博士论文,2006.
[65] Yang J N, Jones D L, Yang S H, et al.. A stiffness degradation model for graphite/epoxylaminates[J]. Journal of Composite Materials,1990,24:753~769.
[66] Lee J H. An experimental and analytical investigation of the stiffness degradation of graphite/epoxy composite laminates under cyclic loading[D]. The George Washington University,1989.
[67] Harris B, Gathercole N, Lee J A, et al. Life-prediction for constant-stress fatigue in carbon-fibrecomposites[C]. Philosophical Transactions of the Royal Society of London,1997,355:1259~1294.
[68] Gathercole N, Reiter H, Adam T, et al. Life prediction for fatigue of T800/5435carbon-fibrecomposites:2constant amplitude loading[J]. International Journal of Fatigue,1994,16:523~532.
[69] Coleman B D. On the strength of classical fibers and fiber bundles[J]. J Mech Phys Solids,1958(7):60~70.
[70] Phani K K. Evaluation of single-fiber strength distribution fiber bundle strength[J]. MaterialsScience,1988,23:941~945.
[71] Militky J. Tensile properties of modified PET fibers[J]. Textile Science,2001,93:112~117.
[72]王丹勇,温卫东.复合材料单向层合板损伤失效试验研究[J].复合材料学报,2007,24(5):142~148.
[73]黄曦.碳纤维增强复合材料层合板疲劳寿命与剩余强度试验研究[D].南京：南京航空航天大学,2006.
[74] Coleman B D. On the strength of classical fibers and fiber bundles [J]. Journal of the Mechanicsand Physics of Solids,1958,6(1):60~70.
[75] Phani K K. Evaluation of single-fiber strength distribution fiber bundle strength[J]. MaterialsScience,1988,23:941~945.
[76] Militky J. Tensile properties of modified PET fibers[J]. Textile Science,2001,93:112~117.
[77]罗祖道,王震鸣.复合材料力学进展[M].北京大学出版社.1992:62~65,94~95.
[78]国家技术监督局. GB/T16779-1997纤维增强塑料层合板拉—拉疲劳性能试验方法[S].北京:中国标准出版社,1997.
[79]国家技术监督局. GB/T3354-1999定向纤维增强塑料拉伸性能试验方法[S].北京:中国标准出版社,1999.
[80]国家技术监督局. GB/T5258-1995纤维增强塑料薄层板压缩性能试验方法[S].北京:中国标准出版社,1995.
[81] Chamis C C. Simplified composite micromechanics equations for strength, fracture toughness,impact, resistance and environmental effects[R]. NASA, TM-83696,1984.
[82]沈观林,胡更开.复合材料力学[M].长沙:清华大学出版社,2007:221~231.
[83]杜善义,王彪.复合材料细观力学[M].北京:科学出版社,1998:5~117.
[84] Rosen B W. Tensile failure of fibrous composites[J]. AIAA Journal,1964,2(11):1985~1991.
[85] Smith R L. A probability model for fibrous composites with local load sharing[C]. Proceedings ofthe Royal Society of London, Series A,1980,372:539~553.
[86] Pheonix S L, Smith R L. A comparison of probabilistic techniques for the strength of fibrousmaterials under local load-sharing among fibers[J]. International Journal of Solids and Structures,1983,19(6):479~496.
[87] Kelly A, Tyson W R. Tensile properties of fiber reinforced metals: copper-tungsten and copper-molybdenum[J]. Journal of the Mechanics and Physics of Solids,2000,48:621~648.
[88]范斌群.单向纤维增强复合材料的载荷集中因子和裂纹扩展统计理论[J].固体力学学报,1981,3:287~295.
[89] Rosen B W. Mechanics of composite strengthening in fiber composite materials[J]. Americansociety for metals.1965:37~65.
[90] Zweben C, Rosen B W. A statistical theory of material strength application to compositematerials[J]. Mech phys solids.1970,18:189~206.
[91] Scop, P.M, Argon, A.S. Statistical theory of strength of laminated composites II[J]. J.Compos.Mater.19693,30~47.
[92]杨庆生.复合材料细观结构力学与设计[M].北京:中国铁道出版社,2000.
[93] Ma C L, Yang J M, Chou T W．Elastic stiffness of three-dimensional braided textile structuralcomposites[C]. Whitney J M. Composite Materials: Testing and Design. Philadelphia: AmericanSociety for Testing Material,1986:404~421.
[94]陈利,李嘉禄,李学明,邱冠雄.三维方形编织预制件的纱线编织结构[J].复合材料学报,2000,17(3):1~5.
[95]卢子兴,杨振宇,刘振国.三维四向编织复合材料结构模型的几何特性[J].北京航空航天大学学报,2006,32(1):92~96.
[96]杨振宇,卢子兴,刘振国,李仲平.三维四向编织复合材料力学性能的有限元分析[J].复合材料学报,2005，22(5):155~161.
[97]徐焜,许希武.三维编织复合材料弹性性能数值预测及细观应力分析[J].复合材料学报,2007,24(3):178~185.
[98] GD Fang, J Liang, Y Wang, et al.The effect of yarn distortion on the mechanical properties of3Dfour-directional braided composites[J]. Composites Part A.2009,40(4):343~350.
[99] Fang Guo-dong, Liang Jun, Wang Bao-lai. Progressive damage and nonlinear analysis of3Dfour-directional braided composites under unidirectional tension[J]. Composite Structures,2009，(89):126~133.
[100]汪星明,邢誉峰.三维编织复合材料研究进展[J].航空学报,2010,31(5):914~927.
[101] Chamis C C. M echanics of composites materials:Past, present and future[J]. Journal ofComposites Technology and Research,1989,11(1):3~14.
[102]徐翔星. C/SiC陶瓷基复合材料的X射线无损检测研究[D].西安:西北工业大学.2003.
[103]陈利,徐正亚.三维五向编织复合材料中纱线横截面形状实验分析[J].复合材料学报,2007,24(4):128~132.
[104]方国东.三维四向碳/环氧编织复合材料积累损伤及失效分析[D].哈尔滨工业大学.2010.
[105]温卫东,邵将,崔海涛,等.三维四向编织复合材料的弹性性能预测研究[J].航空动力学报,2019,24(11):2514~2520.
[106]徐焜,许希武,田静.小编织角三维编织复合材料拉伸强度模型[J].航空学报,2007,28(2):294~300.
[107] Zuo Weiwei, Xiao Laiyuan, Liao Daoxun. Statistical strength analyses of the3-D braidedcomposites[J]. Composites Science and Technology,2007,67:2095~2102.
[108] Chamis C C. Mechanics of composites materials:Past, present and future[J]. Journal ofComposites Technology and Research,1989,11(1):3~14.
[109]周玉.陶瓷材料学[M].北京:科学出版社,2004.
[110] Xia Z H, Zhang Y F, Ellyin F. A unified periodical boundary condition s for representativevolume elements of composites and applications[J]. International Journal of Solids and Structures,2003,40(8):1907~1921.
[111] Xia Z H, Zhou C W, Yong Q L, et al. On select ion of repeated unit cell model and applicationof unified periodic boundary conditions in micromechanical analysis of composites[J].International Journal of Solids and Structures,2006,43(2):266~278.
[112]张超,许希武,毛见春.三维编织复合材料渐进损伤模拟及强度预测[J].复合材料学报,2011,28(2):222~230.
[113] Shokrich M M, Lessard L B. Progressive fatigue damage modeling of composite materials, part I:modeling[J]. Journal of Composite Materials,2000,34:1056~1080.
[114] Shokrich M M, Lessard L B. Progressive fatigue damage modeling of composite materials, partII: material characterization and model verification[J]. Journal of Composite Materials,2000,34:1081~1116.
[115] Tserpes K I, Papanikos P, Labeas G, etal. Fatigue damage accumulation and residual strengthassessment of CFRP laminates[J]. Composite Structure,2004,63:219~230.
[116] Hashin Z. Fatigue failure criteria for combined cyclic stress[J]. International Journal of Fracture,1981,17:101~109.
[2]李贺军.碳/碳复合材料.新型碳材料,2001,16(2):79~80.
[3] Xue H, Li H J, Hou X H, et al. Flexual behavior of2D carbon-carbon composites fabricated bypressure gradient CVI[J]. New Carbon Mater,2004,19(4):289~293.
[4] Neumeister J, Jansson S, Leckie F. The effect of fiber architecture on the mechanical properties ofcarbon/carbon fiber composites[J]. Acta Mater,1996,44(2):573~585.
[5] Hiroshi Hatta, Keiji Suzuki, Tetsuro Shigei, et a1. Strength improvement by densification of C/Ccomposites[J]. Carbon.2001,39(1):83~90.
[6]嵇阿琳,李贺军,崔红.针刺炭纤维预制体的发展与应用[J].炭素科技,2010,29(3):23~27.
[7]孙乐民,李贺军,张守阳.沥青基炭/炭复合材料的弯曲断裂特征[J].新型炭材料,2001,16(3):28~31+41.
[8]熊信伯,李贺军.自发梯度炭/炭复合材料弯曲性能研究[J].新型炭材料,2001,16(4):22~26.
[9]王茂章,贺福.碳纤维的制造、性能及其应用[M].北京:科学出版社,1984.
[10] J X Zhao, K H Ding, J X Wei. Research on thermo physical properties and anti-thermal-vibrationproperties of C/C composites[J]. Acta Mater Compos Sinic,1987,4(4):45~50.
[11]袁辉.碳/碳复合材料刚度与强度预测模型研究[D].南京:南京航空航天大学,2009.
[12] Michael C H Lee, William T Short, Frank Abdi, et a1. A Math-Based Methodology for FatigueLongevity Prediction of3D Woven Fiberglass Reinforced Vinyl-ester Composites[C].2006SAEWorld Congress. Detroit, Michigan April2006:3~6.
[13]卢子兴,高镇同.应用微分方法确定复合泡沫塑料的杨氏模量[J].北京航空航天大学学报,1996,22(6):692~695.
[14] Roser B W. Mechanics of Fiber strengtherning Composite Materials[C]. Ohio, Matals Park:ASM，1965.
[15]韩杰才,黄玉东,赫晓东,杜善义.多向细编碳/碳复合材料界面力学性能测试与表征[J].复合材料学报,1995,12(4):72~78.
[16] Hiroshi Hatta, Ken Goto, Shinya Ikegaki, et al. Tensile strength and fiber/matrix interfacialproperties of2D-and3D-carbon/carbon composites[J]. Journal of the European Ceramic Society,2005,25(4):535~542.
[17] Yuko Furukawa, Hiroshi Hatta, Yasuo Kogo. Interfacial shear strength of C/C composites[J].Carbon,2003,41(9):1819~1826.
[18]孔宪仁,黄玉东,范洪涛,等.细编穿刺C/C复合材料不同层次界面剪切强度的测试分析[J].复合材料学报,2001,18(2):57~60.
[19] Takuya Aoki a, Yuhsuke Yamane, Toshio Ogasawara, et al. Measurements of fiber bundleinterfacial properties of three-dimensionally reinforced carbon/carbon composites up to2273K [J].carbon2007,45:459~467.
[20] Sines G, Yang Z, Vickers B D. Friction stress for carbon composite and carbon yarn during hightemperature creep[J]. Acta Metallurgica,1989,37(10):2673~2680.
[21]石荣,李贺军,杨峥,等.单向碳/碳复合材料的蠕变内应力[J].固体火箭技术,1995,18(4):59~62.
[22]赵秋雁,杨峥,朱小旗.碳/碳复合材料的高温持久性能测试及分析[J].宇航材料工艺,1996,(2):92~94.
[23] Gucer D E, Gurland J. Comparison of the statistics of two fracture modes[J]. Journal of theMechanics and Physics of Solids,1962,10(4):365~373.
[24] Curtin W A. Exact theory of fibre fragmentation in a singlefilament composite[J]. Journal ofMaterials Science,1991,26:5239~5253.
[25] Curtin W A. Stochastic damage evolution and failure in fibrereinforced composites[J]. Advancesin Applied Mechanics,1999,36:163~253.
[26] Hui C Y, Phoenix S L, Ibnabdeljalil M, et al. An exact closed form solution for fragmentation ofWeibull fibres in a single filament composite with applications to fibre-reinforced ceramics[J].Journal of the Mechanics and Physics of Solids,1995,43:1551~1585.
[27] Turon A, Costa J, Maim P, et al. A progressive damage model for unidirectional fibre-reinforcedcomposites based on fibre fragmentation. Part I: Formulation[J]. Composites Science andTechnology,2005,65:2039~2048.
[28] Zweben C. Tensile failure of fiber composites[J]. AIAA,1968,6(12):2325~2331.
[29]范赋群,曾庆敦.单向纤维增强复合材料的随机扩大临界核理论[J].中国科学(A辑),1994,(2):210~217.
[30] QingDun Zeng. A random critical-core theory of microdamage in interply hybrid composites:IIultimate failure[J]. Composites Science and Technology,1994,54(4):481~487.
[31] Yasuhiro Tanabe, Takuya Yoshimura, Tomoyuki Watanabe, et al. Fatigue of C/C composites inbending and in shear modes[J]. Carbon,2004,(42):1~6.
[32] A K Roy. Tensile fatigue behavior of a coated two-dimensional carbon/Carbon compositelaminate[J]. J Compos Technol Rea,1996,(18):202~208.
[33] A Ozturk．The influence of cyclic fatigue damage on the fracture toughness of carbon/carbonComposites[J]. J Bionmed Mater Res,1996,27A:641~646.
[34] A Ozturk, Moore R E. Tensile fatigue behavior of tightly WOVen carbon/carbon composites[J].Composites,1992,(23):39~46.
[35] H Mahfuz, M Maniruzzaman, J Krishagopalan, et a1. Effect of stress ratio on fatigue life ofcarbon/carbon composites[J]. Theoretical and Applied Fracture Mechanics,1995,(24):121~131.
[36] J C Williams, S W Yurgartis, J C Moosbrugger. Interlaminar shear fatigue damage evolution of2D carbon/carbon composites[J]. J Comp Mater,1996,30(7):785~799.
[37] K Goto，H Hatta，D Katsu，T Machida．Tensile fatigue of a laminated carbon/carbon compositesat room temperature[J]. Carbon,2003,(41):1249~1255.
[38]冯翃翎. C/C复合材料疲劳性能的研究[D].西安：西北工业大学,2006.
[39] Yang J M，Ma C L，Chou T W. Fiber inclination model of three dimensional textile structuralcomposites[J]. Journal of Composite Materials,1986,20(5):472~484.
[40] Li W, Hammad M, EI Shiekh A. Structural analysis of3-Dbraided performs for composites[J].Journal of Textile Institute,1990,81(4):491~514.
[41] Du Guangwu，Ko F K. Unit cell geometry of3-D braided structures[J]. Journal of ReinforcedPlastics and Composites,1993,12(7):752~768.
[42] Wang Y Q, W ang A S D. On the topological yarn structure of3-D rectangular and tubular braidedperforms [J]. Composites Science and Technology,1994,51(4):575~586.
[43] W u D L. Three-cell model and5D braided structural com posites[J]. Composites Science andTechnology,1996,56(3):225~233.
[44] Byun H, Chou T W. Process-microstructure relationships of2-step and4-step braidedcomposites[J]. Composites Science and Technology,1999,56(3):235~251.
[45] Chen L, Tao X M, Choy C L. On the microstructure of three-dimensional braided preforms[J].Composites Science and Technology,1999,59(3):391~404.
[46]徐焜,许希武.四步法三维矩形编织复合材料的细观结构模型[J].复合材料学报,2006,23(5):154~160.
[47] Makoto Ito. Effects of yarn undulation on the stress and deformation of textile composites[D].University of Delaware,1995.
[48]李嘉禄,刘谦.三维编织复合材料中纤维束横截面形状的研究[J].复合材料学报,2001,18(2):9~13.
[49]沈美玲.三向碳/碳复合材料拉伸性能测试方法研究[J].宇航材料工艺,1994,(6):62~67.
[50] Hiroshi Hatta, Ken Goto, Shinya Ikegaki, et al. Tensile strength and fiber/matrix interfacialproperties of2D-and3D-carbon/carbon composites[J]. Journal of the European Ceramic Society,2005,25(4):535~542.
[51] Peter B Pollock. Tensile failure in2-D carbon-carbon composites[J]. Carbon,1990,28(5):717~732.
[52] Lomov S V, Barburski M, Stoilova Tz, et al. Carbon composites based on multiaxial multiplystitched preforms. Part3: Biaxial tension, picture frame and compression tests of the performs[J].Composites Part A,2005,36(9):1188~1206.
[53]韩红梅. C/C复合材料的力学性能及损伤演变研究[D].西安:西北工业大学,2002.
[54]郑锡涛三维编织复合材料细观结构与力学性能分析[D].西安:西北工业大学,2003.
[55]李典森,卢子兴,卢文书.三维四向编织复合材料刚度和强度的理论预测[J].应用数学和力学,2008,(29)2:149~156
[56]王波.三维编织复合材料力学行为研究[D].西安:西北工业大学,2003.
[57]卢子兴,刘振国,麦汉超,等.三维编织复合材料强度的数值预测[J].北京航空航天大学学报,2002.(28)5:563~565.
[58]徐焜,许希武.三维编织复合材料渐进损伤的非线性数值分析[J].力学学报,2007.(39)2:398~407.
[59] Hashin Z. Failure criteria for unidirectional fiber composites[J]. Journal of Applied Mechanics,1980,47:329~335.
[60] Fang Guo-dong, Liang Jun, Wang Bao-lai Progressive damage and nonlinear analysis of3Dfour-directional braided composites under unidirectional tension[J]. Composite Structures，2009，(89);126~133.
[61]李嘉禄,杨红娜,寇长河.三维编织复合材料的疲劳性能[J].复合材料学报,(22)4:172~176.
[62]缪晓玲.三维编织C/C复合材料的疲劳行为及损伤演变研究[D].西安：西北工业大学,2006.
[63]肖来元,左惟炜,廖道训.三维编织复合材料威布尔概率分布数学模型[J].华中科技大学学报，2007,(35)12:56~61.
[64]王丹勇.层合板接头损伤失效与疲劳寿命研究[D].南京：南京航空航天大学博士论文,2006.
[65] Yang J N, Jones D L, Yang S H, et al.. A stiffness degradation model for graphite/epoxylaminates[J]. Journal of Composite Materials,1990,24:753~769.
[66] Lee J H. An experimental and analytical investigation of the stiffness degradation of graphite/epoxy composite laminates under cyclic loading[D]. The George Washington University,1989.
[67] Harris B, Gathercole N, Lee J A, et al. Life-prediction for constant-stress fatigue in carbon-fibrecomposites[C]. Philosophical Transactions of the Royal Society of London,1997,355:1259~1294.
[68] Gathercole N, Reiter H, Adam T, et al. Life prediction for fatigue of T800/5435carbon-fibrecomposites:2constant amplitude loading[J]. International Journal of Fatigue,1994,16:523~532.
[69] Coleman B D. On the strength of classical fibers and fiber bundles[J]. J Mech Phys Solids,1958(7):60~70.
[70] Phani K K. Evaluation of single-fiber strength distribution fiber bundle strength[J]. MaterialsScience,1988,23:941~945.
[71] Militky J. Tensile properties of modified PET fibers[J]. Textile Science,2001,93:112~117.
[72]王丹勇,温卫东.复合材料单向层合板损伤失效试验研究[J].复合材料学报,2007,24(5):142~148.
[73]黄曦.碳纤维增强复合材料层合板疲劳寿命与剩余强度试验研究[D].南京：南京航空航天大学,2006.
[74] Coleman B D. On the strength of classical fibers and fiber bundles [J]. Journal of the Mechanicsand Physics of Solids,1958,6(1):60~70.
[75] Phani K K. Evaluation of single-fiber strength distribution fiber bundle strength[J]. MaterialsScience,1988,23:941~945.
[76] Militky J. Tensile properties of modified PET fibers[J]. Textile Science,2001,93:112~117.
[77]罗祖道,王震鸣.复合材料力学进展[M].北京大学出版社.1992:62~65,94~95.
[78]国家技术监督局. GB/T16779-1997纤维增强塑料层合板拉—拉疲劳性能试验方法[S].北京:中国标准出版社,1997.
[79]国家技术监督局. GB/T3354-1999定向纤维增强塑料拉伸性能试验方法[S].北京:中国标准出版社,1999.
[80]国家技术监督局. GB/T5258-1995纤维增强塑料薄层板压缩性能试验方法[S].北京:中国标准出版社,1995.
[81] Chamis C C. Simplified composite micromechanics equations for strength, fracture toughness,impact, resistance and environmental effects[R]. NASA, TM-83696,1984.
[82]沈观林,胡更开.复合材料力学[M].长沙:清华大学出版社,2007:221~231.
[83]杜善义,王彪.复合材料细观力学[M].北京:科学出版社,1998:5~117.
[84] Rosen B W. Tensile failure of fibrous composites[J]. AIAA Journal,1964,2(11):1985~1991.
[85] Smith R L. A probability model for fibrous composites with local load sharing[C]. Proceedings ofthe Royal Society of London, Series A,1980,372:539~553.
[86] Pheonix S L, Smith R L. A comparison of probabilistic techniques for the strength of fibrousmaterials under local load-sharing among fibers[J]. International Journal of Solids and Structures,1983,19(6):479~496.
[87] Kelly A, Tyson W R. Tensile properties of fiber reinforced metals: copper-tungsten and copper-molybdenum[J]. Journal of the Mechanics and Physics of Solids,2000,48:621~648.
[88]范斌群.单向纤维增强复合材料的载荷集中因子和裂纹扩展统计理论[J].固体力学学报,1981,3:287~295.
[89] Rosen B W. Mechanics of composite strengthening in fiber composite materials[J]. Americansociety for metals.1965:37~65.
[90] Zweben C, Rosen B W. A statistical theory of material strength application to compositematerials[J]. Mech phys solids.1970,18:189~206.
[91] Scop, P.M, Argon, A.S. Statistical theory of strength of laminated composites II[J]. J.Compos.Mater.19693,30~47.
[92]杨庆生.复合材料细观结构力学与设计[M].北京:中国铁道出版社,2000.
[93] Ma C L, Yang J M, Chou T W．Elastic stiffness of three-dimensional braided textile structuralcomposites[C]. Whitney J M. Composite Materials: Testing and Design. Philadelphia: AmericanSociety for Testing Material,1986:404~421.
[94]陈利,李嘉禄,李学明,邱冠雄.三维方形编织预制件的纱线编织结构[J].复合材料学报,2000,17(3):1~5.
[95]卢子兴,杨振宇,刘振国.三维四向编织复合材料结构模型的几何特性[J].北京航空航天大学学报,2006,32(1):92~96.
[96]杨振宇,卢子兴,刘振国,李仲平.三维四向编织复合材料力学性能的有限元分析[J].复合材料学报,2005，22(5):155~161.
[97]徐焜,许希武.三维编织复合材料弹性性能数值预测及细观应力分析[J].复合材料学报,2007,24(3):178~185.
[98] GD Fang, J Liang, Y Wang, et al.The effect of yarn distortion on the mechanical properties of3Dfour-directional braided composites[J]. Composites Part A.2009,40(4):343~350.
[99] Fang Guo-dong, Liang Jun, Wang Bao-lai. Progressive damage and nonlinear analysis of3Dfour-directional braided composites under unidirectional tension[J]. Composite Structures,2009，(89):126~133.
[100]汪星明,邢誉峰.三维编织复合材料研究进展[J].航空学报,2010,31(5):914~927.
[101] Chamis C C. M echanics of composites materials:Past, present and future[J]. Journal ofComposites Technology and Research,1989,11(1):3~14.
[102]徐翔星. C/SiC陶瓷基复合材料的X射线无损检测研究[D].西安:西北工业大学.2003.
[103]陈利,徐正亚.三维五向编织复合材料中纱线横截面形状实验分析[J].复合材料学报,2007,24(4):128~132.
[104]方国东.三维四向碳/环氧编织复合材料积累损伤及失效分析[D].哈尔滨工业大学.2010.
[105]温卫东,邵将,崔海涛,等.三维四向编织复合材料的弹性性能预测研究[J].航空动力学报,2019,24(11):2514~2520.
[106]徐焜,许希武,田静.小编织角三维编织复合材料拉伸强度模型[J].航空学报,2007,28(2):294~300.
[107] Zuo Weiwei, Xiao Laiyuan, Liao Daoxun. Statistical strength analyses of the3-D braidedcomposites[J]. Composites Science and Technology,2007,67:2095~2102.
[108] Chamis C C. Mechanics of composites materials:Past, present and future[J]. Journal ofComposites Technology and Research,1989,11(1):3~14.
[109]周玉.陶瓷材料学[M].北京:科学出版社,2004.
[110] Xia Z H, Zhang Y F, Ellyin F. A unified periodical boundary condition s for representativevolume elements of composites and applications[J]. International Journal of Solids and Structures,2003,40(8):1907~1921.
[111] Xia Z H, Zhou C W, Yong Q L, et al. On select ion of repeated unit cell model and applicationof unified periodic boundary conditions in micromechanical analysis of composites[J].International Journal of Solids and Structures,2006,43(2):266~278.
[112]张超,许希武,毛见春.三维编织复合材料渐进损伤模拟及强度预测[J].复合材料学报,2011,28(2):222~230.
[113] Shokrich M M, Lessard L B. Progressive fatigue damage modeling of composite materials, part I:modeling[J]. Journal of Composite Materials,2000,34:1056~1080.
[114] Shokrich M M, Lessard L B. Progressive fatigue damage modeling of composite materials, partII: material characterization and model verification[J]. Journal of Composite Materials,2000,34:1081~1116.
[115] Tserpes K I, Papanikos P, Labeas G, etal. Fatigue damage accumulation and residual strengthassessment of CFRP laminates[J]. Composite Structure,2004,63:219~230.
[116] Hashin Z. Fatigue failure criteria for combined cyclic stress[J]. International Journal of Fracture,1981,17:101~109.