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

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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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Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, P. R. China

    Yuan-qing Cui  (崔元庆) & Zheng Zhong  (仲 政)

  2. Office of the Presidents, Zhejiang University, Hangzhou, 310058, P. R. China

    Wei Yang  (杨 卫)

Authors
  1. Yuan-qing Cui  (崔元庆)
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  2. Wei Yang  (杨 卫)
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  3. Zheng Zhong  (仲 政)
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Correspondence to Yuan-qing Cui  (崔元庆).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 10702071 and 11090334), the China Postdoctoral Science Foundation (No. 201003281), the Shanghai Postdoctoral Scientific Program (No. 10R21415800), and the Shanghai Leading Academic Discipline Project (No. B302)

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Cui, Yq., Yang, W. & Zhong, Z. Green’s function for T-stress of semi-infinite plane crack. Appl. Math. Mech.-Engl. Ed. 32, 973–980 (2011). https://doi.org/10.1007/s10483-011-1473-x

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  • DOI: https://doi.org/10.1007/s10483-011-1473-x

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