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基于分布位错方法对纤维增强复合材料的横观裂纹问题研究

王皓,  江晓禹

王皓, 江晓禹. 基于分布位错方法对纤维增强复合材料的横观裂纹问题研究[J]. 应用数学和力学, 2026, 47(9): 1132-1143. doi: 10.21656/1000-0887.460153
引用本文: 王皓, 江晓禹. 基于分布位错方法对纤维增强复合材料的横观裂纹问题研究[J]. 应用数学和力学, 2026, 47(9): 1132-1143. doi: 10.21656/1000-0887.460153
Wang Hao, Jiang Xiaoyu. Research on Transverse Crack Problems in Fiber-Reinforced Composites With the Distributed Dislocation Method[J]. Applied Mathematics and Mechanics, 2026, 47(9): 1132-1143. doi: 10.21656/1000-0887.460153
Citation: Wang Hao, Jiang Xiaoyu. Research on Transverse Crack Problems in Fiber-Reinforced Composites With the Distributed Dislocation Method[J]. Applied Mathematics and Mechanics, 2026, 47(9): 1132-1143. doi: 10.21656/1000-0887.460153

基于分布位错方法对纤维增强复合材料的横观裂纹问题研究

doi: 10.21656/1000-0887.460153
基金项目: 

国家自然科学基金(12393782)

详细信息
    作者简介:

    王皓(2001—),男,硕士生(E-mail: 13274225158@163.com);江晓禹(1965—),男,教授,博士,博士生导师(通信作者. E-mail: xiaoyujiang8@sina.com).

    通讯作者:

    江晓禹(1965—),男,教授,博士,博士生导师(通信作者. E-mail: xiaoyujiang8@sina.com).

  • 中图分类号: O346

Research on Transverse Crack Problems in Fiber-Reinforced Composites With the Distributed Dislocation Method

Funds: 

The National Science Foundation of China(12393782)

  • 摘要: 在单轴拉伸载荷作用下,对于无限大平面内的纤维增强复合材料的基体裂纹与界面裂纹的相互作用问题,使用分布位错法进行研究,裂纹面用连续分布位错替代,将纤维增强复合材料模型转换为二维平面中含有圆形夹杂问题.根据叠加原理,将问题分为两个子问题,得到了基体裂纹尖端与界面裂纹的应力强度因子、应力场、界面处最大拉应力、基体裂纹与界面裂纹尖端的能量释放率.利用裂纹尖端最大能量释放率比值来判断裂纹扩展方向.结果表明,当夹杂位于基体裂纹尖端指向区域,夹杂对裂纹扩展起屏蔽作用,在其他区域,对基体裂纹扩展起增强作用.根据界面处最大拉应力判断,初步解释了界面裂纹产生的原因.当基体裂纹尖端指向界面裂纹尖端时,基体裂纹与界面裂纹会促进相互之间的扩展,两者距离越近,界面裂纹越容易扩展.
  • Tamate O. The effect of a circular inclusion on the stresses around a line crack in a sheet under tension[J].International Journal of Fracture Mechanics,1968,4(3): 257-266.
    [2]鲁兴学. 基于相场法碳纤维增强复合材料细观尺度裂纹扩展研究[D]. 郑州: 郑州大学, 2020. (Lu Xingxue. Mesoscale investigation of crack propagation in carbon fiber reinforced polymer based on the phase field method[D]. Zhengzhou: Zhengzhou University, 2020. (in Chinese))
    [3]段士杰, 刘淑红. 剪切荷载作用下圆孔孔边裂纹的解[J]. 应用数学和力学, 2016,37(7): 740-747. (Duan Shijie, Liu Shuhong. Solutions for a circular hole with edge cracks under shear load[J].Applied Mathematics and Mechanics,2016,37(7): 740-747. (in Chinese))
    [4]Theotokoglou E N, Theotokoglou E E. The interface crack along a circular inclusion interacting with a crack in the infinite matrix[J].International Journal of Fracture,2002,116(1): 5088337.
    [5]Toya M. A crack along the interface of a rigid circular inclusion embedded in an elastic solid[J].International Journal of Fracture,1973,9(4): 463-470.
    [6]郭树起. 应用边界积分法求圆形夹杂问题的解析解[J]. 力学学报, 2020,52(1): 73-81. (Guo Shuqi. Exact solution of circular inclusion problems by a boundary integral method[J].Chinese Journal of Theoretical and Applied Mechanics,2020,52(1): 73-81. (in Chinese))
    [7]Najmeddine A, Gupta S, Moini R. Coupled large deformation phase-field and cohesive zone model for crack propagation in hard-soft multi-materials[J].Journal of the Mechanics and Physics of Solids,2025,196: 106016.
    [8]吴祖荣, 董庆兵, 熊广. 含夹杂和裂纹的平面内应力干涉半解析模型[J]. 固体力学学报, 2024,45(4): 441-455. (Wu Zurong, Dong Qingbing, Xiong Guang. A semi-analytical model of stress interaction with inclusions and cracks in an infinite plane[J].Chinese Journal of Solid Mechanics,2024,45(4): 441-455. (in Chinese))
    [9]官高菲, 李彤, 聂雪阳, 等. 二维准晶双材料界面断裂分析的相场法[J]. 应用数学和力学, 2024,45(11): 1440-1454. (Guan Gaofei, Li Tong, Nie Xueyang, et al. A phase-field model for interfacial fracture in 2D quasicrystal bimaterials[J].Applied Mathematics and Mechanics,2024,45(11): 1440-1454. (in Chinese))
    [10]郭钊, 任晓丹, 和东宏. 裂纹-夹杂问题分析的本征计算模型及其数值模拟[J]. 应用数学和力学, 2025,46(3): 371-381. (Guo Zhao, Ren Xiaodan, He Donghong. Numerical modeling for the analysis of crack-inclusion problems by the eigen iterative computational model[J].Applied Mathematics and Mechanics,2025,46(3): 371-381. (in Chinese))
    [11]Dundurs J, Mura T. Interaction between an edge dislocation and a circular inclusion[J].Journal of the Mechanics and Physics of Solids,1964,12(3): 177-189.
    [12]Tao Y S, Fang Q H, Zeng X, et al. Influence of dislocation on interaction between a crack and a circular inhomogeneity[J].International Journal of Mechanical Sciences,2014,80: 47-53.
    [13]Erdogan F, Gupta G D, Ratwani M. Interaction between a circular inclusion and an arbitrarily oriented crack[J].Journal of Applied Mechanics,1974,41(4): 1007-1013.
    [14]Kelly P, Hills D A, Nowell D. Curved interface cracks between elastically dissimilar media, with application to the analysis of circular inclusions[J].International Journal of Mechanical Sciences,1994,36(3): 173-181.
    [15]邢帅兵, 王强胜, 生月, 等. 圆形杂质对裂纹扩展的影响[J]. 应用数学和力学, 2019,40(2): 189-199. (Xing Shuaibing, Wang Qiangsheng, Sheng Yue, et al. Effects of circular inhomogeneity on crack propagation[J].Applied Mathematics and Mechanics,2019,40(2): 189-199. (in Chinese))
    [16]Zhang Y M, Zhang W G, Fan M, et al. Stress investigation on a cracked craze interacting with a nearby circular inclusion in polymer composites[J].Acta Mechanica,2017,228(4): 1213-1228.
    [17]Hills D A, Kelly P A, Dai D N, et al. Solution of crack problems: the distributed dislocation technique[J].Journal of Applied Mechanics,1998,65(2): 548.
    [18]李孝滔. 材料缺陷对裂纹扩展行为的影响[D]. 成都: 西南交通大学, 2020. (Li Xiaotao. Effect of defects in materials on the behavors of crack growth[D]. Chengdu: Southwest Jiaotong University, 2020. (in Chinese))
    [19]Muskhelishvili N I, Radok J R M.Some Basic Problems of the Mathematical Theory of Elasticity[M]. Groningen: Noordhoff, 1953.
    [20]Dundurs J. Effect of elastic constants on stress in a composite under plane deformation[J].Journal of Composite Materials,1967,1(3): 310-322.
    [21]Erdogan F, Gupta G D, Cook T S.Methods of Analysis and Solutions of Crack Problems[M]. Dordrecht: Springer, 1973: 368-425.
    [22]Kaya A C, Erdogan F. On the solution of integral equations with strongly singular kernels[J].Quarterly of Applied Mathematics,1987,45(1): 105-122.
    [23]高闯. 两相材料界面两侧倾斜裂纹的相互影响及在界面接触后的扩展分析[D]. 上海: 上海交通大学, 2000. (Gao Chuang. Interaction between inclined cracks on both sides of an interface in two-phase materials and propagation analysis after interface contact[D]. Shanghai: Shanghai Jiao Tong University, 2000. (in Chinese))
    [24]Nuismer R J. An energy release rate criterion for mixed mode fracture[J].International Journal of Fracture,1975,11(2): 245-250.
    [25]Rana A K, Paul S K, Dey P P. Stress field in an isotropic elastic solid containing a circular hard or soft inclusion under uniaxial tensile stress[J].Materials Today: Proceedings,2019,11: 657-666.
    [26]Dabrowski M, Schmid D W. A rigid circular inclusion in an anisotropic host subject to simple shear[J].Journal of Structural Geology,2011,33(7): 1169-1177.
    [27]张立峰, 王盛, 乔伟林, 等. 单向碳纤维复合材料界面力学性能测试研究[J]. 机械科学与技术, 2019,38(8): 1296-1300. (Zhang Lifeng, Wang Sheng, Qiao Weilin, et al. Experimental study on interface mechanical properties of unidirectional carbon fiber composites[J].Mechanical Science and Technology for Aerospace Engineering,2019,38(8): 1296-1300. (in Chinese))
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出版历程
  • 收稿日期:  2025-08-27
  • 修回日期:  2026-07-08
  • 网络出版日期:  2026-09-24
  • 刊出日期:  2026-09-01

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