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复合材料层合板分层损伤数值模拟方法研究现状

李西宁 王悦舜 周新房

李西宁, 王悦舜, 周新房. 复合材料层合板分层损伤数值模拟方法研究现状[J]. 复合材料学报, 2021, 38(4): 1076-1086. doi: 10.13801/j.cnki.fhclxb.20210302.006
引用本文: 李西宁, 王悦舜, 周新房. 复合材料层合板分层损伤数值模拟方法研究现状[J]. 复合材料学报, 2021, 38(4): 1076-1086. doi: 10.13801/j.cnki.fhclxb.20210302.006
LI Xining, WANG Yueshun, ZHOU Xinfang. Status of numerical simulation methods for delamination damage of composite laminates[J]. Acta Materiae Compositae Sinica, 2021, 38(4): 1076-1086. doi: 10.13801/j.cnki.fhclxb.20210302.006
Citation: LI Xining, WANG Yueshun, ZHOU Xinfang. Status of numerical simulation methods for delamination damage of composite laminates[J]. Acta Materiae Compositae Sinica, 2021, 38(4): 1076-1086. doi: 10.13801/j.cnki.fhclxb.20210302.006

复合材料层合板分层损伤数值模拟方法研究现状

doi: 10.13801/j.cnki.fhclxb.20210302.006
详细信息
    通讯作者:

    李西宁,博士,副教授,硕士生导师,研究方向为基于MFC的曲壳结构动态形状控制 E-mail:lixining@nwpu.edu.cn

  • 中图分类号: TB332;V250

Status of numerical simulation methods for delamination damage of composite laminates

  • 摘要: 复合材料层合板在航空航天等领域受到广泛应用,分层损伤作为复合材料层合板主要的损伤形式,对复合材料结构的强度和刚度有显著的影响,是限制其重大工程应用的热点问题之一。通过实验的方法对复合材料结构进行研究,往往需要耗费大量的时间和成本,成熟的有限元数值模拟技术可以较低成本实现复合材料结构的分层行为模拟,成为分层损伤研究的重要手段。本文从数值模拟角度总结了国内外在纤维增强复合材料分层损伤取得的研究成果,并对目前主要的方法虚拟裂纹闭合技术(VCCT)、内聚力模型(CZM)及扩展有限元法(XFEM)进行阐述。最后,对其发展方向进行了展望。

     

  • 图  1  复合材料在飞机上的应用

    Figure  1.  Application of composite materials in aircraft

    图  2  虚拟裂纹闭合示意图

    Figure  2.  Sketch of virtual crack closure technique

    图  3  典型裂纹能量释放率G随裂纹长度a变化曲线[16]

    Figure  3.  Curve of typical crack energy release rate G with crack length a[16]

    图  4  Cohesive单元示意图

    Figure  4.  Schematic diagram of Cohesive cell

    图  5  不同的内聚力模型本构关系

    Figure  5.  Constitutive relations of different cohesive models

  • [1] 杜善义, 关志东. 我国大型客机先进复合材料技术应对策略思考[J]. 复合材料学报, 2008, 25(1):1-10. doi: 10.3321/j.issn:1000-3851.2008.01.001

    DU Shanyi, GAUN Zhidong. Strategic considerations for development of advances composite technology for large commercial aircraft in china[J]. Acta Materiae Compo-sitae Sinica,2008,25(1):1-10(in Chinese). doi: 10.3321/j.issn:1000-3851.2008.01.001
    [2] 赵丽滨, 龚愉, 张建宇. 纤维增强复合材料层合板分层行为研究进展[J]. 航空学报, 2019, 40(1):166-194.

    ZHAO Libin, GONG Yu, ZHANG Jianyu. A survey on delamination growth behavior in fiber reinforced compo-site laminates[J]. Acta Aeronautica et Astronautica Sinica,2019,40(1):166-194(in Chinese).
    [3] 庄蔚敏, 王楠, 吴迪, 等. 碳纤维复合材料层合板三点弯曲损伤仿真研究[J]. 机械工程学报, 2019, 55(10):109-114. doi: 10.3901/JME.2019.10.109

    ZHUANG Weimin, WANG Nan, WU Di, et al. Simulation and analysis of the damage of carbon fiber composite laminates under three point bending load[J]. Journal of Mechanical Engineering,2019,55(10):109-114(in Chinese). doi: 10.3901/JME.2019.10.109
    [4] HILLERBORG A, MODEER M, PETERSSON P. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements[J]. Cement and Concrete Research,1976,6(6):773-782. doi: 10.1016/0008-8846(76)90007-7
    [5] CARTER B, WAWRZYNEK P, INGRAFFEA A. Automated 3-D crack growth simulation[J]. International Journal for Numerical Methods in Engineering,2000,47(3):229-258.
    [6] KIM J, SIMONE A, DUARTE C. Mesh refinement strategies without mapping of nonlinear solutions for the generalized and standard FEM analysis of 3-D cohesive fractures[J]. International Journal for Numerical Methods in Engineering,2017,109(2):235-258. doi: 10.1002/nme.5286
    [7] KRUEGER R. Virtual crack closure technique: History, approach, and applications[J]. Applied Mechanics Reviews,2004,57(2):109-143. doi: 10.1115/1.1595677
    [8] HEIDARI-RARANI M, SAYEDAIN M. Finite element modeling strategies for 2D and 3D delamination propagation in composite DCB specimens using VCCT, CZM and XFEM approaches[J]. Theoretical and Applied Fracture Mechanics,2019,103(3):102246.
    [9] OKINEN J, KANERVA M. Simulation of delamination growth at CFRP-tungsten aerospace laminates using VCCT and CZM modelling techniques[J]. Applied Composite Materials,2019,26(7):709-721.
    [10] RYBICKI E F, KANNINEN M F. A finite element calculation of stress intensity factors by a modified crack closure integral[J]. Engineering Fracture Mechanics,1997,9(4):931-938.
    [11] SHIVAKUMAR K N, TAN P W, NEWMAN J J. A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies[J]. International Journal of Facture,1988,36(1):43-50.
    [12] RAJU I S, SISTLA R, KRISHNAMURTHY T. Fracture mechanics analyses for skin-stiffener debondingt[J]. Engineering Fracture Mechanics,1996,54(3):371-385. doi: 10.1016/0013-7944(95)00184-0
    [13] XIE D, SHERRILL B, BIGGERS J. Strain energy release rate calculation for a moving delamination front of arbitrary shape based on the VCCT: Part I and Part II[J]. Engineering Fracture Mechanics,2006,73(6):771-785. doi: 10.1016/j.engfracmech.2005.07.013
    [14] FAWAZ S A. Application of virtual crack closure technique to calculate stress intensity factors for through cracks with an elliptical crack front[J]. Engineering Fracture Mechanics,1998,59(3):327-342. doi: 10.1016/S0013-7944(97)00126-4
    [15] IRWIN G R. One set fast crack propagation in high steel and aluminum alloys[C]. Sagamore Research Conference Proceedings, 1956, 2(32): 289-305.
    [16] 王自强, 陈少华. 高等断裂力学(精)[M]. 北京: 科学出版社, 2009: 124-140.

    WANG Ziqiang, CHEN Shaohua. Higher fracture mechanics[M]. Beijing: Science Publishing, 2009: 124-140(in Chinese).
    [17] GRIFFITH A A. The phenomena of rupture and flow in solids[J]. Philosophical Transactions of the Royal Society of London A,1921,221(6):163-198.
    [18] PIETROPAOLI Elisa, RICCIO Aniello. Formulation and assessment of an enhanced finite elementprocedure for the analysis of delamination growth phenomena in composite structures[J]. Composites Science and Technology,2011,71(6):836-846. doi: 10.1016/j.compscitech.2011.01.026
    [19] RAIMONDO A, RICCIO A. Inter-laminar and intra-laminar damage evolution in composite panels with skin-stringer debonding under compression[J]. Composites Part B: Engineering,2016,94(12):139-151.
    [20] LI H C H, DHARMAWAN F, HERSZBERG I, et al. Fracture behaviour of composite maritime T-joints[J]. Composite Structures,2006,75(1):339-350.
    [21] TAWK I, NAVARRO P, FERRERO J F, et al. Composite delamination modelling using a multi-layered solid element[J]. Composites Science and Technology,2010,70(2):207-214. doi: 10.1016/j.compscitech.2009.10.008
    [22] PANIGRAHI S K, PRADHAN B. Three dimensional failure analysis and damage propagation behavior of, adhesively bonded single lap joints in laminated FRP composites[J]. Journal of Reinforced Plastics and Composites,2007,26(2):183-201. doi: 10.1177/0731684407070026
    [23] 周立明, 孟广伟, 王晖, 等. 基于光滑有限元的含裂纹复合材料的虚拟裂纹闭合法[J]. 湖南大学学报(自然科学版), 2014, 41(8):36-40.

    ZHOU Liming, MENG Guangwei, WANG Hui, et al. Virtual crack closure technique based on smoothed finite element method for composite materials with cracks[J]. Journal of Hunan University (Natural Science),2014,41(8):36-40(in Chinese).
    [24] 陈玉良, 程宸, 万水, 等. 基于虚拟裂纹闭合法计算组合材料的应变能释放率[J]. 玻璃钢/复合材料, 2013, 4(3):8-12.

    CHEN Yuliang, CHENG Chen, WAN Shui, et al. Based on virtual crack close technique the calculation of strain energy release rete for composite material[J]. Journal of FRP/Composites,2013,4(3):8-12(in Chinese).
    [25] 孟令兵, 陈普会. 层压复合材料分层扩展分析的虚拟裂纹闭合技术及其应用[J]. 复合材料学报, 2010, 27(1):190-195.

    MENG Lingbing, CHEN Puhui. Virtual crack closure technique for delamination growth analysis of laminated composites and its application[J]. Acta Materiae Compositae Sinica,2010,27(1):190-195(in Chinese).
    [26] MAGI F, MAIO D D, SEVER I. Validation of initial crack propagation under vibration fatigue by Finite Element analysis[J]. International Journal of Fatigue,2017,104(6):183-194.
    [27] CARVALHO N V D, KRUEGER R, MABSON G E, et al. Combining progressive nodal release with the virtual crack closure technique to model fatigue delamination growth without re-meshing[C]//2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. 2018.
    [28] 杜洪雨, 奚晓波, 孟力华, 等. 含分层损伤的复合材料层压板后屈曲及低周疲劳分层扩展有限元模拟研究[J]. 玻璃钢/复合材料, 2018(6):39-43.

    DU Hongyu, XI Xiaobo, MENG Lihua, et al. Finite element of post-buckled delamination of composite laminate with preliminary debond subjected to static and fatigue loads[J]. Journal of FRP/Composites,2018(6):39-43(in Chinese).
    [29] 孙益军, 林智育. 含分层损伤复合材料层板压缩分层疲劳扩展研究[J]. 航空制造技术, 2015(9):77-81.

    SUN Yijun, LIN Zhiyu. Progressive delamination growth in composites laminates under compressive fatigue load[J]. Aeronautical Manufacturing Technology,2015(9):77-81(in Chinese).
    [30] 熊伟华. 含分层损伤复合材料层合板疲劳分层扩展研究[D]. 南京: 南京航空航天大学, 2015.

    XIONG Weihua. Delamination growth in composite laminates[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2015(in Chinese).
    [31] DUGDALE D S. Yielding of steel sheets containing slits[J]. Journal of Mechanics & Physics of Solid,1960,8(2):100-104.
    [32] BARENBLATT G I. The mathematical theory of equilibrium cracks in brittle fracture[J]. Advances in Applied Mechanics,1962,7(8):55-129.
    [33] NEEDLEMAN A. A continuum model for void nucleation by inclusion debonding[J]. Journal of Applied Mechanics,1987,54(3):525-531. doi: 10.1115/1.3173064
    [34] NEEDLEMAN A. An analysis of decohesion along an imperfect interface[J]. International Journal of Fracture,1990,42(5):21-40.
    [35] LIU P F, ISLAM M M. A nonlinear cohesive model for mixed-mode delamination of composite laminates[J]. Composite Structures,2013,106(6):47-56.
    [36] TVERGAARD V, HUTCHINSON J W. The relation between crack growth resistance and fracture process parameters in elastic-plastic solids[J]. Journal of the Mechanics and Physics of Solids,1992,40(6):1377-1397. doi: 10.1016/0022-5096(92)90020-3
    [37] MI Y, CRISFIELD M A, DAVIES G A O, et al. Progressive delamination using interface elements[J]. Journal of Composite Materials,1998,32(14):1246-1272. doi: 10.1177/002199839803201401
    [38] ALLIX O, LADEVÉZE P, CORIGLIANO A. Damage analysis of interlaminar fracture specimens[J]. Composite Structures,1995,31(1):61-74. doi: 10.1016/0263-8223(95)00002-X
    [39] ALLIX O, CORIGLIANO A. Modeling and simulation of crack propagation in mixed-modes interlaminar fracture specimens[J]. International Journal of Fracture,1996,77(2):111-140. doi: 10.1007/BF00037233
    [40] CHAMPANEY L, VALOROSO N. Evaluation of interface models for the analysis of non-linear behaviour of adhesively bonded joints[C]. Proceedings of the European Conference on Computational Mechanics ECCM-2001, Cracow, 2001.
    [41] 卢子兴. 复合材料界面的内聚力模型及其应用[J]. 固体力学学报, 2015, 36(S1):85-94.

    LU Zixing. A simple review for cohesive zone models of composite interface and their applications[J]. Chinese Journal of Solid Mechanics,2015,36(S1):85-94(in Chinese).
    [42] RICHEFEU V, CHRYSOCHOOS A, HUON V, et al. Toward local identification of cohesive zone models using digital image correlation[J]. European Journal of Mechanics, A/Solids,2012,34(27):38-51.
    [43] J. REINOSO, M. PAGGI, A. BLAZQUEZ. A nonlinear finite thickness cohesive interface element for modelig delamination in fibre-reinforced composite laminates[J]. Compo-sites Part B: 2017, 40(5): 116-128.
    [44] HAN T S, URAL A, CHEN C S, et al. Delamination buckling and propagation analysis of honeycomb panels using a cohesive element approach[J]. International Journal of Fracture,2002,115(2):101-123. doi: 10.1023/A:1016333709040
    [45] RIDHA M, TAN V B C, TAY T E. Traction separation laws for progressive failure of bonded scarf repair of composite panel[J]. Composite Structures,2011,93(4):1239-1245. doi: 10.1016/j.compstruct.2010.10.015
    [46] 张鹏, 胡小飞, 姚伟岸. 内聚力模型裂纹问题分析的解析奇异单元[J]. 固体力学学报, 2017, 38(2):68-75.

    ZHANG Peng, HU Xiaofei, YAO Weian. An analytical singular element to study the cohesive zone model for cracks[J]. Chinese Journal of Solid Mechanics,2017,38(2):68-75(in Chinese).
    [47] 王振清, 雷红帅, 周博, 等. 基于内聚力模型的形状记忆合金短纤维增强树脂基复合材料的模拟分析[J]. 复合材料学报, 2012, 24(5):236-243.

    WANG Zhenqing, LEI Hongshuai, ZHOU Bo. Simulation and analysis on short-cut shape memory alloy reinforced epoxy composite based on cohesive zone model[J]. Acta Materiae Compositae Sinica,2012,24(5):236-243(in Chinese).
    [48] WAAS V D, HIDAYAT M I P, NOEROCHIM L. Finite element simulation of delamination in carbon fiber/epoxy laminate using cohesive zone model: Effect of meshing variation[J]. Materials Science Forum,2019,964(7):257-262.
    [49] SADIQ M A, ZAFAR N, BUTT H S U, et al. An efficient approach to the design of damage tolerant CFRP stiffened panels[C] 2017 14th International Bhurban Conference on Applied Sciences and Technology (IBCAST). IEEE, 2017: 58-65.
    [50] NIAN G, LI Q, XU Q, et al. A cohesive zone model incorporating a Coulomb friction law for fiber-reinforced compo-sites[J]. Composites Science and Technology,2018,34(157):195-201.
    [51] 关志东, 刘德博, 李星, 等. 基于界面单元的复合材料层间损伤分析方法[J]. 复合材料学报, 2012, 29(2):136-140.

    GAUN Zhidong, LIU Debo, LI Xing, et al. Composite interlaminar damage analysis based on cohesive element[J]. Composites Science and Technology,2012,29(2):136-140(in Chinese).
    [52] 尹涵彬. 薄膜/基底界面撕脱全过程力学行为的定量预测[D]. 北京: 中国科学院大学, 2018.

    YIN Hanbin. Quantitative prediction of mechanical behavior in the whole process of film/substrate interface avulsion[D]. Beijing: Chinese Academy of Sciences, 2018(in Chinese).
    [53] 孙中雷, 赵美英, 万小朋. 含分层复合材料层合板剪切稳定性数值模拟研究[J]. 机械强度, 2013, 35(5):641-645.

    SUN Zhonglei, ZHAO Meiying, WAN Xiaopeng. A numerical study on shear behavior of composite plate with a circular delamination[J]. Journal of Mechanical Strength,2013,35(5):641-645(in Chinese).
    [54] 尹世豪, 张建宇, 龚愉, 等. 新型三线性本构内聚力模型的界面参数研究[J]. 重庆大学学报, 2020, 43(2):1-8. doi: 10.11835/j.issn.1005-2909.2020.02.001

    YIN Shihao, ZHANG Jianyu, GONG Yu, et al. Studies on the interfacial parameters in a novel three-linear cohesive zone model[J]. Journal of Chongqing University,2020,43(2):1-8(in Chinese). doi: 10.11835/j.issn.1005-2909.2020.02.001
    [55] GUTKIN R, LAFFAN M L, PINHO S T, et al. Modeling the R-curve effect and its specimen-dependence[J]. International Journal of Solids and Structures,2011,48(11):1767-1777.
    [56] 段红燕, 王智明, 桑元成. III型裂纹裂尖应力场的内聚力模型[J]. 上海交通大学学报(自然版), 2017, 51(1):113-118.

    DUAN Hongyan, WANG Zhiming, SHAN Yuancheng. Cohesive zone modeling for model III crack based on near tip stress field[J]. Journal of Shanghai Jiao Tong University (Nature Edition),2017,51(1):113-118(in Chinese).
    [57] 刘斌, 徐绯, 菊池正纪, 等. 斜胶接CFRP的冲击损伤容限研究[J]. 固体火箭技术, 2015, 38(6):870-876.

    LIU Bin, XU Fei, KIKUCHI Masanori, et al. Study on impact damage tolerance of scarf bonded CFRP[J]. Journal of Solid Rocket Technology,2015,38(6):870-876(in Chinese).
    [58] 朱炜垚, 许希武. 复合材料层合板低速冲击损伤的有限元模拟[J]. 复合材料学报, 2010, 27(6):200-207.

    ZHU Weiyao, XU Xiwu. Finite element simulation of low velocity impact damage on composite laminates[J]. Acta Materiae Compositae Sinica,2010,27(6):200-207(in Chinese).
    [59] FAGGIANI A, FALZON B G. Predicting low-velocity impact damage on a stiffened composite panel[J]. Compo-sites: Part A, 2010, 41(6): 737-749.
    [60] 于飞. 弹塑性断裂过程与复合材料层板低速冲击损伤的数值模拟[D]. 南京: 南京航空航天大学, 2012.

    YU Fei. Numerical study on elastoplastic fracture process and low-velocity impact damage of laminated composites[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2012(in Chinese).
    [61] LI S, THOULESS M D, WAAS A M, et al. Mixed-mode cohesive-zone models for fracture of an adhesively bonded polymer-matrix composite[J]. Engineering Fracture Mechanics,2006,73(1):64-78. doi: 10.1016/j.engfracmech.2005.07.004
    [62] LI S, THOULESS M D, WAAS A M, et al. Use of a cohesive-zone model to analyze the fracture of a fiber-reinforced polymer-matrix composite[J]. Composites Science & Technology,2005,65(3-4):537-549.
    [63] BORG R, NILSSON L, SIMONSSON K. Simulating DCB, ENF and MMB experiments using shell elements and a cohesive zone model[J]. Composites Science and Technology,2004,64(2):269-278. doi: 10.1016/S0266-3538(03)00255-0
    [64] BORG R, NILSSON L, SIMONSSON K. Modeling of delamination using a discretized cohesive zone and damage formulation[J]. Composites Science and Technology,2002,62(10):1299-1314.
    [65] RICE J R, BELTZ G E. The activation-energy for dislocation nucleation at a crack[J]. Journal of the Mechanics and Physics of Solids, 1994, 42(6): 333-360.
    [66] TURON A, DÁVILA C G, CAMANHO P P, et al. An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models[J]. Engineering Fracture Mechanics,2007,74(10):1665-1682. doi: 10.1016/j.engfracmech.2006.08.025
    [67] 郭历伦, 陈忠富, 罗景润, 等. 扩展有限方法即应用综述[J]. 力学季刊, 2011, 32(4):144-157.

    GUO Lilun, CHEN Zhongfu, LUO Jingrun, et al. A review of the extended finite element method and its applications[J]. Chinese Quarterly of Mechanics,2011,32(4):144-157(in Chinese).
    [68] 丁晶. 扩展有限元在断裂力学中的应用[D]. 南京: 河海大学, 2007.

    DING Jing. Application of the extend finite element method to fracture mechanics[D]. Nanjing: Hohai University, 2007(in Chinese).
    [69] 王哲成, 张云, 于军, 等. 基于扩展有限元的应力强度因子计算精度研究[J]. 南京大学学报, 2019, 55(3):361-369.

    WANG Zhecheng, ZHANG Yun, YU Jun, et al. Calculation of stress intensity factor based on the extended finite element method[J]. Journal of Nanjing University,2019,55(3):361-369(in Chinese).
    [70] BELYTSCHKO T, CHEN H, XU J, et al. Dynamic crack propagation based on loss if hyperbolicity and a new discontinuous enrichment[J]. International Journal for Numerical Methods in Engineerinf,2003,58(12):1873-1905. doi: 10.1002/nme.941
    [71] FRIES T P. A corrected XFEM approximation with out problems in blending elements[J]. International Journal for Numerical Methods in Engineering,2008,75(5):503-532. doi: 10.1002/nme.2259
    [72] MOES N, CLOIREC M, CARTRAUD P, et al. A computational approach to handle complex microstructure geometries[J]. Computer Methods in Applied Mechanics & Engineering,2003,192(28):3163-3177.
    [73] 林铁军, 练章华, 曾晓健, 等. 应用XFEM模拟研究钻杆裂纹扩展过程[J]. 重庆大学学报, 2010, 33(7):123-128.

    LIN Tiejun, LIAN Zhanghua, ZENG Xiaojian, et al. Simulation on crack growth of drill pipe with XFEM[J]. Journal of Chongqing University,2010,33(7):123-128(in Chinese).
    [74] OSHER S, SETHIAN J. Fronts propagating with curvature dependent speed: Algorithms based on Hamilton Jacobi formulations[J]. Journal of Computational Physics,1988,79(1):12-49. doi: 10.1016/0021-9991(88)90002-2
    [75] GROGAN D M, BRDALGH C, LEEN S B. A combined XFEM and cohesive zone model for composite laminate microcracking and permeability[J]. Composite Structures,2015,120(7):246-261.
    [76] GROGAN D M, BRDALGH C, MCGARRY J P, et al. Damage and permeability in tape-laid thermoplastic composite cryogenic tanks[J]. Composites Part A: Applied Science and Manufacturing,2015,78(4):390-402.
    [77] NAGASHIMA T, SUEMASU H. XFEM analysis of a thin-walled composite shell structure with a delamination[J]. Computers & Structures, 2010, 88(9): 549-557.
    [78] CURIEL SOSA J, KARAPURATH N. Delamination modelling of GLARE using the extended finite element method[J]. Composites Science and Technology, 2012, 72(7): 788-791.
    [79] JIN C F, ZHU Q Z, SHAO J F. A numerical analysis of interface damage effect on mechanical properties of composite materials[J]. Mechanics Research Communications,2014,62(4):18-24.
    [80] ZHAO L B, ZHI J, ZHANG J Y, at al. XFEM simulation of delamination in composite laminates[J]. Composites Part A: Applied Science and Manufacturing,2016,80(7):61-71.
    [81] ZHAO L B, ZHI J, ZHANG J Y, at al. XFEM based model for simulating zigzag delamination growth in laminated composites under mode I loading[J]. Composite Structures,2017,160(7):1155-1162.
    [82] 段青枫. 基于LaRC05和XFEM的复材构件失效行为数值研究[D]. 武汉: 武汉理工大学, 2019.

    DUAN Qingfeng. Numerical study on failure behavior of composite structure components based on LaRC05 and XFEM[D]. Wuhan: Wuhan University of Technology, 2019(in Chinese).
    [83] 周立明, 孟广伟, 李峰, 等. 含裂纹复合材料的Cell-based光滑扩展有限元法[J]. 东北大学学报: 自然科学版, 2016, 8(37):1127-1132.

    ZHOU Liming, MENG Guangwei, LI Feng, et al. Cell-based smoothed extended finite element method for composite materials with cracks[J]. Journal of Northeastern University: Natural Science,2016,8(37):1127-1132(in Chinese).
    [84] CHANG Y E, SHI J, GARY J. An extended finite element study on the effect of reinforcing particles on the crack propagation behavior in a metal matrix composite[J]. International Journal of Fatigue, 2012, 44(1): 151-156.
    [85] 杨宇宙, 钱林方, 徐亚栋, 等. 复合材料身管的疲劳裂纹扩展分析[J]. 弹道学报, 2013, 25(2):100-105. doi: 10.3969/j.issn.1004-499X.2013.02.020

    YANG Yuzhou, QIAN Linfang, XU Yadong, et al. Analysis of fatigue crack growth of composite barrel[J]. Journal of Ballistics,2013,25(2):100-105(in Chinese). doi: 10.3969/j.issn.1004-499X.2013.02.020
    [86] 王志勇, 马力, 吴林志, 等. 基于扩展有限元法的颗粒增强复合材料静态及动态断裂行为研究[J]. 固体力学学报, 2011, 32(6):566-573.

    WANG Zhiyong, MA Li, WU Linzhi, et al. Investigation of static and dynamic fracture behavior of particle-reinforced composite materials by the extended finite element method[J]. Chinese Journal of Solid Mechanics,2011,32(6):566-573(in Chinese).
    [87] 屈琼. 基于实验的复合材料层合板的界面损伤分析及界面力学性能研究[D]. 福州: 福州大学, 2010.

    QU Qiong. Experiment-based analysis of interfacial damage in laminates and study on interfacial mechanical properties[D]. Fuzhou: Fuzhou University, 2010(in Chinese).
    [88] 胡振东, 黄海, 贾光辉. 超高速撞击条件下铝合金材料参数识别方法[J]. 北京航空航天大学学报, 2008, 34(9):99-102.

    HU Zhendong, HUANG Hai, JIA Guanghui. Identification method for the material parameters of alloy under the condition of hypervelocity impact[J]. Journal of Beijing University of Aeronautics and Astronautics,2008,34(9):99-102(in Chinese).
    [89] BOLZON G, GHILOTTI D, MAIER G. Strength of periodic elastic-brittle composites evaluated through homogenization and parameter identification[J]. European Journal of Mechanics A/Soilds, 2002, 21(7): 355-378.
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出版历程
  • 收稿日期:  2020-09-03
  • 录用日期:  2020-10-22
  • 网络出版日期:  2021-03-02
  • 刊出日期:  2021-04-08

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