XING Shuaibing, WANG Qiangsheng, SHENG Yue, JIANG Xiaoyu. Effects of Circular Inhomogeneity on Crack Propagation[J]. Applied Mathematics and Mechanics, 2019, 40(2): 189-199. doi: 10.21656/1000-0887.390136
Citation: XING Shuaibing, WANG Qiangsheng, SHENG Yue, JIANG Xiaoyu. Effects of Circular Inhomogeneity on Crack Propagation[J]. Applied Mathematics and Mechanics, 2019, 40(2): 189-199. doi: 10.21656/1000-0887.390136

Effects of Circular Inhomogeneity on Crack Propagation

doi: 10.21656/1000-0887.390136
Funds:  The National Natural Science Foundation of China(11472230)
  • Received Date: 2018-05-02
  • Rev Recd Date: 2018-05-17
  • Publish Date: 2019-02-01
  • The solution of an infinite plane containing a crack and an arbitrarily oriented inhomogeneity under uniaxial tensile load was presented based on the distributed dislocation technique. The stress field and the strain energy density were obtained. The crack propagation direction was predicted according to the minimum strain energy density criterion. The results show that, the soft inhomogeneity has an amplifying effect on the stress intensity factor, the strain energy density and the stress field near the crack tip, while the hard inhomogeneity has a shielding effect. The effect of the inhomogeneity on the crack propagation direction increases with the decreasing distance, the increasing absolute value of lg(μ21), and the increasing inhomogeneity radius. The inhomogeneity has a little effect on the crack propagation direction for -30°<θ<30°.The soft inhomogeneity has an attracting effect, while the hard inhomogeneity has a repulsing effect on the crack propagation for -90°<θ<-30°and 30°<θ<90°.
  • loading
  • [1]
    HAN J J, DHANASEKAR M. Modelling cracks in arbitrarily shaped finite bodies by distribution of dislocation[J]. International Journal of Solids & Structures,2004,41(2): 399-411.
    [2]
    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 circluar hole with edge cracks under shear load[J]. Applied Mathematics and Mechanics,2016,37(7): 740-747.(in Chinese))
    [3]
    LI Z, CHEN Q. Crack-inclusion interaction for mode I crack analyzed by Eshelby equivalent inclusion method[J]. International Journal of Fracture,2004,118(1): 29-40.
    [4]
    张明焕, 汤任基, 裂纹与弹性夹杂的相互影响[J]. 应用数学和力学, 1995,16(4): 289-300.(ZHANG Minghuan, TANG Renji. Interaction between crack and elastic inclusion[J]. Applied Mathematics and Mechanics,1995,16(4): 289-300.(in Chinese))
    [5]
    杨立宏. 裂纹与任意形状夹杂相互作用的近似解法[D]. 博士学位论文. 上海: 上海交通大学, 2005.(YANG Lihong. Approximate solution of interaction between crack and inclusion of arbitrary shape[D]. PhD Thesis. Shanghai: Shanghai Jiao Tong University, 2005.(in Chinese))
    [6]
    MOGILEVSKAYA S G, CROUCH S L, BALLARINI R, et al. Interaction between a crack and a circular inhomogeneity with interface stiffness and tension[J]. International Journal of Fracture,2009,159: 191-207.
    [7]
    周荣欣. 裂纹与夹杂之间的构型力及Ⅱ型裂纹裂尖塑性区的屏蔽效应[D]. 硕士学位论文. 上海: 上海交通大学, 2012.(ZHOU Rongxin. The configuration force between crack and inclusion & the shielding effects of plastic zone at mode II crack-tip[D]. Master Thesis. Shanghai: Shanghai Jiao Tong University, 2012.(in Chinese))
    [8]
    YANG R, XU P, YUE Z, et al. Dynamic fracture analysis of crack-defect interaction for mode I running crack using digital dynamic caustics method[J]. Engineering Fracture Mechanics,2016,161: 63-75.
    [9]
    XIAO Z M, BAI J, MAEDA R. Electro-elastic stress analysis on piezoelectric inhomogeneity-crack interaction[J]. International Journal of Solids & Structures,2001,38(8): 1369-1394.
    [10]
    PENG B, LI Z, FENG M. The mode I crack-inclusion interaction in orthotropic medium[J]. Engineering Fracture Mechanics,2015,136: 185-194.
    [11]
    CHEN Y Z. Solution for a crack embedded in thermal dissimilar elliptic inclusion[J]. Engineering Fracture Mechanics,2016,160: 15-21.
    [12]
    DUNDURS J, MURA T. Interaction between an edge dislocation and a circular inclusion[J]. Journal of the Mechanics & Physics of Solids,1964,12(3): 177-189.
    [13]
    WANG X, SCHIAVONE P. Interaction between an edge dislocation and a circular inhomogeneity with a mixed-type imperfect interface[J]. Archive of Applied Mechanics,2017,87(1): 87-98.
    [14]
    WANG C C, ZHAO Y X, ZHANG Y B, et al. The interaction between an edge dislocation and a semi-infinite long crack penetrating a circular inhomogeneity[J]. Theoretical & Applied Fracture Mechanics,2015,76: 91-99.
    [15]
    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.
    [16]
    陈勇, 宋迎东, 高德平. 圆形夹杂前端直裂纹的应力强度因子研究[C]//中国航空学会发动机结构强度振动学术讨论会. 威海, 2002.(CHEN Yong, SONG Yingdong, GAO Deping. Study on stress intensity factor of straight crack in front end of circular inclusion[C]//Symposium on Strength Vibration Of Engine Structure of China Aeronautics Society . Weihai, 2002.(in Chinese))
    [17]
    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.
    [18]
    ZHANG J, QU Z, HUANG Q, et al. Interaction between cracks and a circular inclusion in a finite plate with the distributed dislocation method[J]. Archive of Applied Mechanics,2013,83(6): 861-873.
    [19]
    ERDOGAN F, GUPTA G D, RATWANI M. Interaction between a circular inclusion and an arbitrarily oriented crack[J]. Journal of Applied Mechanics,1975,41(4): 1287-1297.
    [20]
    ERDOGAN F, SIH G C. On the crack extension in plates under plane loading and transverse shear[J]. Journal of Basic Engineering,1963,85(4): 519-525.
    [21]
    PALANISWAMY K, KNAUSS W G. Propagation of a crack under general, in-plane tension[J]. International Journal of Fracture Mechanics,1972,8(1): 114-117.
    [22]
    NUISMER R J. An energy release rate criterion for mixed mode fracture[J]. International Journal of Fracture,1975,11(2): 245-250.
    [23]
    LI C. Vector ctd criterion applied to mixed mode fatigue crack growth[J]. Fatigue & Fracture of Engineering Materials & Structures,1989,12(1): 59-65.
    [24]
    SIH G C. Strain-energy-density factor applied to mixed mode crack problems[J]. International Journal of Fracture,1974,10(3): 305-321.
    [25]
    HILLS D A, KELLY P A, DAI D N, et al. Solution of crack problems: the distributed dislocation technique[J]. Journal of Applied Mechanics,1996,65(2): 548.
    [26]
    ERDOGAN F, GUPTA G D, COOK T S. Numerical solution of singular integral equations[M]//Methods of Analysis and Solutions of Crack Problems . Netherlands: Springer, 1973: 368-425.
    [27]
    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.
    [28]
    MIRANDA A C O, MEGGIOLARO M A, CASTRO J T P, et al. Fatigue life and crack path predictions in generic 2D structural components[J]. Engineering Fracture Mechanics,2003,70(10): 1259-1279.
    [29]
    CHUDNOVSKY A, CHAOUI K, MOET A. Curvilinear crack layer propagation[J]. Journal of Materials Science Letters,1987,6(9): 1033-1038.
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (1065) PDF downloads(457) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return