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

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

doi: 10.3879/j.issn.1000-0887.2011.08.002
  • Received Date: 2010-07-21
  • Rev Recd Date: 2011-05-16
  • Publish Date: 2011-08-15
  • Green's function for the T-stress near a crack tip was addressed by an analytic function method for a semi-infinite crack lying in an elastical,isotropic,and infinite plate.The cracked plate was loaded by single inclined concentrated force at interior point.The complex potentials were obtained by a superpo sition principle,which provide the solutions to the plane problems of elasticity.The regular parts of the potentials were extracted by an asymptotic analysis.Based on the regular parts,Green's function for the T-stress was obtained in a straight-forward manner.Furthermore,Green's functions were derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimpo sing method.Then Green's function was used to predict the do ain-switch-induced T-stress in a ferroelectric double cantilever beam(DCB)test.The T-stress induced by the electro mechanical loading was used to judge the stable and unstable crack growth behaviors observed in the test.The prediction results roughly agree with the experimental data.
  • loading
  • [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.
    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))
    Westergaard H M. Bearing pressures and cracks[J]. Journal of Applied Mechanics—Transactions of the ASME, 1939, 6: 49-53.
    Sih G C. On the Westergaard method of crack analysis[J]. International Journal of Fracture Mechanics, 1966, 2(4): 628-631.
    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
    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
    Cotterell B, Rice J R. Slightly curved or kinked cracks[J]. International Journal of Fracture, 1980, 16(2): 155-169. doi: 10.1007/BF00012619
    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
    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.
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    Fett T. A Compendium of T-Stress Solutions[M]. FZKA-6057. Wissenschaftliche Berichte, Karlsruhe: Farschungszentrum Karlsruhe GmbH, 1998.
    Tada H, Paris P C, Irwin G R. The Stress Analysis of Cracks Handbook[M]. 3rd ed. New York: ASM International, 2000.
    Murakami Y. Stress Intensity Factors Handbook[M]. Oxford: Pergamon Press, 1987.
    Muskhelishvili N. Some Basic Problems of the Mathematical Theory of Elasticity[M]. Groningen: Noordhoff, 1954.
    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.
    Sih G C. Application of Muskhelishvili’s method to fracture mechanics[J]. Transactions, the Chinese Association for Advanced Studies, 1962, 25: 25-35.
    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
    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
    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
  • 加载中


    通讯作者: 陈斌,
    • 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 (1777) PDF downloads(883) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint