GUO Jun-hong, LIU Ping, LU Zi-xing, QIN Tai-yan. Anti-Plane Analysis of a Semi-Infinite Crack in a Piezoelectric Strip[J]. Applied Mathematics and Mechanics, 2011, 32(1): 72-78. doi: 10.3879/j.issn.1000-0887.2011.01.008
Citation: GUO Jun-hong, LIU Ping, LU Zi-xing, QIN Tai-yan. Anti-Plane Analysis of a Semi-Infinite Crack in a Piezoelectric Strip[J]. Applied Mathematics and Mechanics, 2011, 32(1): 72-78. doi: 10.3879/j.issn.1000-0887.2011.01.008

Anti-Plane Analysis of a Semi-Infinite Crack in a Piezoelectric Strip

doi: 10.3879/j.issn.1000-0887.2011.01.008
  • Received Date: 2010-09-06
  • Rev Recd Date: 2010-11-17
  • Publish Date: 2011-01-15
  • Using the complex variable function method and the technique of conformal mapping,the fracture problem of a semi-infinite crack in a piezoelectric strip was studied under the anti-plane shear stress and in-plane electric load.The analytical solutions of the field intensity factors and the mechanical strain energy release rate were presented with the assumption that the surface of the crack was electrically impermeable.When the height of the strip tends to infinity,the analytical solutions of an infinitely large piezoe-lectric solid with a semi-infinite crack were obtained.Moreover,the present results can be reduced to the well-known solutions for a purely elastic material in the absence of electric loading.In addition,numerical examples were conducted to analyze the influences of loaded crack length,the height of the strip and applied mechanical/electric loads on the mechanical strain energy release rate.
  • loading
  • [1]
    方岱宁, 刘金喜. 压电与铁电体的断裂力学[M]. 北京:清华大学出版社, 2008.(FANG Dai-ning, LIU Jin-xi. Fracture Mechanics of Piezoelectric and Ferroelectric Solids[M]. Beijing: Tsinghua University Press, 2008. (in Chinese))
    [2]
    ZHANG Tong-yi, ZHAO Ming-hao, TONG Ping. Fracture of piezoelectric ceramics[J]. Advanced Applied Mechanics, 2002, 38: 147-289. doi: 10.1016/S0065-2156(02)80104-1
    [3]
    ZHANG Tong-yi, GAO Cun-fa. Fracture behaviors of piezoelectric materials[J]. Theoretical and Applied Fracture Mechanics, 2004, 41(1/3): 339-379. doi: 10.1016/j.tafmec.2003.11.019
    [4]
    Kuna M. Fracture mechanics of piezoelectric materials-where are we right now?[J]. Engineering Fracture Mechanics, 2010, 77(2): 309-326. doi: 10.1016/j.engfracmech.2009.03.016
    [5]
    WANG Yong-jian, GAO Cun-fa. The mode III cracks originating from the edge of a circular hole in a piezoelectric solid[J]. International Journal of Solids and Structures, 2008, 45(16): 4590-4599. doi: 10.1016/j.ijsolstr.2008.04.001
    [6]
    GUO Jun-hong, LU Zi-xing, HAN Hai-tao, YANG Zhen-yu. Exact solutions for anti-plane problem of two asymmetrical edge cracks emanating from an elliptical hole in a piezoelectric material[J]. International Journal of Solids and Structures, 2009, 46(21): 3799-3809. doi: 10.1016/j.ijsolstr.2009.07.002
    [7]
    GUO Jun-hong, LU Zi-xing, HAN Hai-tao, YANG Zhen-yu. The behavior of two non-symmetrical permeable cracks emanating from an elliptical hole in a piezoelectric solid[J]. European Journal of Mechanics A/Solids, 2010, 29(4): 654-663. doi: 10.1016/j.euromechsol.2010.01.001
    [8]
    GUO Jun-hong, LU Zi-xing, FENG Xiang. The fracture behavior of multiple cracks emanating from a circular hole in piezoelectric materials[J]. Acta Mechanica, 2010, doi: 10.1007/s 00707-010-0327-4.
    [9]
    Razzaq A A, Hussain R, Gao C F, Yu J H. Two-dimensional analysis of a semi-infinite crack in piezoelectric media[J]. Mechanics Research Communications, 1998, 25(6): 695-700. doi: 10.1016/S0093-6413(98)00089-5
    [10]
    LI Xian-fang, FAN Tian-you. Semi-infinite anti-plane crack in a piezoelectric material[J]. International Journal of Fracture, 2000, 102(3): 53-60. doi: 10.1023/A:1007617023726
    [11]
    LI Xian-fang. Transient response of a piezoelectric material with a semi-infinite mode-Ⅲ crack under impact loads[J]. International Journal of Fracture, 2001, 111(2): 119-130. doi: 10.1023/A:1012208524059
    [12]
    Li S, Mataga P A. Dynamic crack propagation in piezoelectric materials—part Ⅰ: Electrode solution[J]. Journal of Mechanics and Physics Solids, 1996, 44(11): 1799-1830. doi: 10.1016/0022-5096(96)00055-5
    [13]
    Li S, Mataga P A. Dynamic crack propagation in piezoelectric materials—part Ⅱ: Vacuum solution[J]. Journal of Mechanics and Physics Solids, 1996, 44(11): 1831-1866. doi: 10.1016/0022-5096(96)00056-7
    [14]
    刘淑红, 郭增强, 邹振祝. 含半无限长裂纹压电材料的Ⅲ型强度因子[J]. 中国安全科学学报, 2003, 13(9): 62-64.(LIU Shu-hong, GUO Zeng-qiang, ZOU Zhen-zhu. Mode-Ⅲ intensity factors of semi-infinite crack in a piezoelectric material[J]. China Safety Science Journal, 2003, 13(9): 62-64.(in Chinese))
    [15]
    FAN Tian-you. Exact solutions of semi-infinite crack in a strip[J]. Chinese Physics Letters, 1990, 44(11): 402-405.
    [16]
    Park S B, Sun C T. Fracture criteria for piezoelectric ceramics[J]. Journal of the American Ceramic Society, 1995, 78(6): 1475-1480. doi: 10.1111/j.1151-2916.1995.tb08840.x
  • 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 (1463) PDF downloads(756) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return