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半无限平面裂纹构型横向应力的Green函数

崔元庆 杨卫 仲政

崔元庆, 杨卫, 仲政. 半无限平面裂纹构型横向应力的Green函数[J]. 应用数学和力学, 2011, 32(8): 912-919. doi: 10.3879/j.issn.1000-0887.2011.08.002
引用本文: 崔元庆, 杨卫, 仲政. 半无限平面裂纹构型横向应力的Green函数[J]. 应用数学和力学, 2011, 32(8): 912-919. doi: 10.3879/j.issn.1000-0887.2011.08.002
CUI Yuan-qing, YANG Wei, ZHONG Zheng. Green’s Function for T-Stress of a Semi-Infinite Plane Crack[J]. Applied Mathematics and Mechanics, 2011, 32(8): 912-919. doi: 10.3879/j.issn.1000-0887.2011.08.002
Citation: CUI Yuan-qing, YANG Wei, ZHONG Zheng. Green’s Function for T-Stress of a Semi-Infinite Plane Crack[J]. Applied Mathematics and Mechanics, 2011, 32(8): 912-919. doi: 10.3879/j.issn.1000-0887.2011.08.002

半无限平面裂纹构型横向应力的Green函数

doi: 10.3879/j.issn.1000-0887.2011.08.002
基金项目: 国家自然科学基金资助项目(10702071;11090334);中国博士后科学基金资助项目(201003281);上海博士后科学基金资助项目(10R21415800);上海市重点学科计划资助项目(B302);中德科学中心项目“Crack Growth in Ferroelectrics Driven by Cyclic Electric Loading”资助
详细信息
    作者简介:

    崔元庆(1973- ),男,陕西富平人,副教授,博士(联系人.Tel:+86-21-65982591;E-mail:cuiyuanqing@gmail.com).

  • 中图分类号: O174.5;O343

Green’s Function for T-Stress of a Semi-Infinite Plane Crack

  • 摘要: 针对各向同性弹性无限大板中半无限裂纹,用解析函数方法求解了裂尖处横向应力的Green函数.加载情况为一任意集中力作用于任意一内点处.用叠加法求解了复势,它给出该平面问题的弹性解.通过渐近分析抽取复势的非奇异部分.基于该非奇异部分,用一种直接方法求解了横向应力的Green函数.进一步,用叠加法得到了一对对称和反对称集中力加载时的Green函数.然后,用得到的Green函数来预测铁电材料双悬臂梁试验中畴变引起的横向应力.用力电联合加载引起的横向应力来判断试验中所观察到的稳定和不稳定裂纹扩展行为.预测结果和试验数据基本吻合.
  • [1] Williams M L. On the stress distribution at the base of a stationary crack[J]. Journal of Applied Mechanics—Transactions of the ASME, 1957, 24: 111-114.
    [2] 杨卫.宏微观断裂力学[M]. 北京:国防工业出版社, 1995.(YANG Wei. Macroscopic and Microscopic Fracture Mechanics[M]. Beijing: National Defence Press, 1995.(in Chinese))
    [3] Westergaard H M. Bearing pressures and cracks[J]. Journal of Applied Mechanics—Transactions of the ASME, 1939, 6: 49-53.
    [4] Sih G C. On the Westergaard method of crack analysis[J]. International Journal of Fracture Mechanics, 1966, 2(4): 628-631.
    [5] Larsson S G, Carlsson A J. Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials[J]. Journal of the Mechanics and Physics of Solids, 1973, 21(4): 263-277. doi: 10.1016/0022-5096(73)90024-0
    [6] Rice J R. Limitations to the small scale yielding approximation for crack tip plasticity[J].Journal of the Mechanics and Physics of Solids, 1974, 22(1): 17-26. doi: 10.1016/0022-5096(74)90010-6
    [7] Cotterell B, Rice J R. Slightly curved or kinked cracks[J]. International Journal of Fracture, 1980, 16(2): 155-169. doi: 10.1007/BF00012619
    [8] Tvergaard V. Effect of T-stress on crack growth under mixed mode Ⅰ-Ⅲ loading[J]. International Journal of Solids and Structures, 2008, 45(18/19): 5181-5188. doi: 10.1016/j.ijsolstr.2008.05.014
    [9] Li X F, Tang B Q, Peng X L, Huang Y. Influence of elastic T-stress on the growth direction of two parallel cracks[J]. Structural Engineering and Mechanics, 2010, 34(3): 377-390.
    [10] Leevers P S, Radon J C. Inherent stress biaxiality in various fracture specimen geometries[J]. International Journal of Fracture, 1982, 19(4): 311-325. doi: 10.1007/BF00012486
    [11] Kfouri A P. Some evaluations of the elastic T-term using Eshelby’s method[J]. International Journal of Fracture, 1986, 30(4): 301-315. doi: 10.1007/BF00019710
    [12] Sham T L. The determination of the elastic T-term using higher order weight functions[J].International Journal of Fracture, 1991, 48(2): 81-102. doi: 10.1007/BF00018392
    [13] Wang X. Elastic T-stress solutions for semi-elliptical surface cracks in finite thickness plates[J]. Engineering Fracture Mechanics, 2003, 70(6): 731-756. doi: 10.1016/S0013-7944(02)00081-4
    [14] Broberg K. A note on T-stress determination using dislocation arrays[J]. International Journal of Fracture, 2005, 131(1): 1-14. doi: 10.1007/s10704-004-3637-5
    [15] Li X. T-stress near the tips of a cruciform crack with unequal arms[J]. Engineering Fracture Mechanics, 2006, 73(6): 671-683. doi: 10.1016/j.engfracmech.2005.11.002
    [16] Fett T, Rizzi G, Bahr H A, Bahr U, Pham V B, Balke H. Analytical solutions for stress intensity factor, T-stress and weight function for the edge-cracked half-space[J].International Journal of Fracture, 2007, 146(3): 189-195. doi: 10.1007/s10704-007-9152-8
    [17] Lewis T, Wang X. The T-stress solutions for through-wall circumferential cracks in cylinders subjected to general loading conditions[J]. Engineering Fracture Mechanics, 2008, 75(10):3206-3225. doi: 10.1016/j.engfracmech.2007.12.001
    [18] Chen Y Z. Closed form solutions of T-stress in plane elasticity crack problems[J]. International Journal of Solids and Structures, 2000, 37(11): 1629-1637. doi: 10.1016/S0020-7683(98)00312-6
    [19] Chen Y Z, Wang Z X, Lin X Y. Evaluation of the T-stress for interacting cracks[J].Computational Materials Science, 2009, 45(2): 349-357. doi: 10.1016/j.commatsci.2008.10.006
    [20] Chen Y Z, Lin X Y. Evaluation of the T-stress in branch crack problem[J]. International Journal of Fracture, 2010, 161(2): 175-185. doi: 10.1007/s10704-010-9451-3
    [21] Sherry A H, France C C, Goldthorpe M R. Compendium of T-stress solutions for two and three dimensional cracked geometries[J]. Fatigue and Fracture of Engineering Materials and Structures, 1995, 18(1): 141-155. doi: 10.1111/j.1460-2695.1995.tb00148.x
    [22] Fett T. A Compendium of T-Stress Solutions[M]. FZKA-6057. Wissenschaftliche Berichte, Karlsruhe: Farschungszentrum Karlsruhe GmbH, 1998.
    [23] Tada H, Paris P C, Irwin G R. The Stress Analysis of Cracks Handbook[M]. 3rd ed. New York: ASM International, 2000.
    [24] Murakami Y. Stress Intensity Factors Handbook[M]. Oxford: Pergamon Press, 1987.
    [25] Muskhelishvili N. Some Basic Problems of the Mathematical Theory of Elasticity[M]. Groningen: Noordhoff, 1954.
    [26] Erdogan F. On the stress distribution in plates with collinear cuts under arbitrary loads[C]Rosenberg R M, Barton M V, Bisplinghoff R L.Proceedings of the Fourth US National Congress of Applied Mechanics.Oxford: Pergamon Press, 1962, 547-553.
    [27] Sih G C. Application of Muskhelishvili’s method to fracture mechanics[J]. Transactions, the Chinese Association for Advanced Studies, 1962, 25: 25-35.
    [28] Westram I, Ricoeur A, Emrich A, Rdel J, Kuna M. Fatigue crack growth law for ferroelectrics under cyclic electrical and combined electromechanical loading[J]. Journal of the European Ceramic Society, 2007, 27(6): 2485-2494. doi: 10.1016/j.jeurceramsoc.2006.09.010
    [29] Cui Y Q, Yang W. Electromechanical cracking in ferroelectrics driven by large scale domain switching[J]. Science China Physics, Mechanics and Astronomy, 2011, 54(5): 957-965. doi: 10.1007/s11433-011-4308-y
    [30] Cui Y Q, Zhong Z. Large scale domain switching around the tip of an impermeable stationary crack in ferroelectric ceramics driven by near-coercive electric field[J]. Science China Physics, Mechanics and Astronomy, 2011, 54(1): 121-126. doi: 10.1007/s11433-010-4176-x
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出版历程
  • 收稿日期:  2010-07-21
  • 修回日期:  2011-05-16
  • 刊出日期:  2011-08-15

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