Anti-Plane Analysis of a Semi-Infinite Crack in a Piezoelectric Strip
-
摘要: 利用保角变换和复变函数方法,研究了裂纹面上受反平面剪应力和面内电载荷共同作用下的有限高狭长压电体中半无限裂纹的断裂问题,给出了电不可通边界条件下裂纹尖端场强度因子和机械应变能释放率的解析解.当狭长体高度趋于无限大时,可得到无限大压电体中半无限裂纹的解析解.若不考虑电场作用,所得解可退化为纯弹性材料的已知结果.此外,通过数值算例,分析了裂纹面上受载长度、狭长体高度以及机电载荷对机械应变能释放率的影响规律.Abstract: 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.
-
[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
点击查看大图
计量
- 文章访问数: 1473
- HTML全文浏览量: 103
- PDF下载量: 756
- 被引次数: 0