Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 32 ›› Issue (8): 973-980.doi: https://doi.org/10.1007/s10483-011-1473-x

• Articles • 上一篇    下一篇

Green’s function for T-stress of semi-infinite plane crack

崔庆元1 杨卫2 仲政1   

  1. 1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P. R. China;
    2. Office of the Presidents, Zhejiang University, Hangzhou 310058, P. R. China
  • 出版日期:2011-08-20 发布日期:2011-08-20

Green’s function for T-stress of semi-infinite plane crack

 CUI Qiang-Yuan1, YANG Wei2, ZHONG Zheng1   

  1. 1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai 200092, P. R. China;
    2. Office of the Presidents, Zhejiang University, Hangzhou 310058, P. R. China
  • Online:2011-08-20 Published:2011-08-20

摘要: Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switchinduced T-stress in a ferroelectric double cantilever beam (DCB) test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.

Abstract: Green’s function for the T-stress near a crack tip is addressed with an analytic function method for a semi-infinite crack lying in an elastical, isotropic, and infinite plate. The cracked plate is loaded by a single inclined concentrated force at an interior point. The complex potentials are obtained based on a superposition principle, which provide the solutions to the plane problems of elasticity. The regular parts of the potentials are extracted in an asymptotic analysis. Based on the regular parts, Green’s function for the T-stress is obtained in a straightforward manner. Furthermore, Green’s functions are derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method. Then, Green’s function is used to predict the domain-switchinduced T-stress in a ferroelectric double cantilever beam (DCB) test. The T-stress induced by the electromechanical loading is used to judge the stable and unstable crack growth behaviors observed in the test. The prediction results generally agree with the experimental data.

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