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A Mode- II Griffith Crack in Decagonal Quasicrystals

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Abstract

By using the method of stress functions, the problem of mode- II Griffith crack in decagonal quasicrystals was solved. First, the crack problem of two-dimensional quasi-crystals was decomposed into a plane strain state problem superposed on anti-plane state problem and secondly, by introducing stress functions, the 18 basic elasticity equations on coupling phonon-phason field of decagonal quasicrystals were reduced to a single higher-order partial differential equations. The solution of this equation under mixed boundary conditions of mode- II Griffith crack was obtained in terms of Fourier transform and dual integral equations methods. All components of stresses and displacements can be expressed by elemental functions and the stress intensity factor and the strain energy release rate were determined.

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References

  1. HU Chen-zhen, YANG Wen-ge, WANG Ren-hui, et al. The symmetry and physical properties of quasicrystals[J]. Progress in Physics,1997,17(4):345-375. (in Chinese)

    Google Scholar 

  2. DING Di-hua, YANG Wen-ge, HU Cheng-zheng, et al. Generalized elasticity theory of quasicrystals[J]. Phys Rev B,1993,48(10):7003-7010.

    Google Scholar 

  3. FAN Tian-you. Foundation of Fracture Mechanics[M]. Nanjing: Jiangsu Science and Technology Press,1978.(in Chinese)

    Google Scholar 

  4. FAN Tian-you, GUO Yu-cui. Mathematical methods for a class of mixed boundary-value problems of planar penpagonal quasicrystal and some solutions[J]. Science in China(A),1997,27(6):553-565.

    Google Scholar 

  5. GUO Yu-cui, FAN Tian-you. Stress intensity factor of pentagonal quasicrystals[J]. Journal of Beijing University of Post and Telecommunications,1998,21(4):62-65. (in Chinese)

    Google Scholar 

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Authors and Affiliations

  1. Basic Science Department, Beijing University of Post and Telecommunications, Beijing, 100088, P R China

    Yu-cui Guo

  2. Research Center of Material Science, Beijing Institute of Technology, Beijing, 100081, P R China

    Tian-you Fan

Authors
  1. Yu-cui Guo
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  2. Tian-you Fan
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Guo, Yc., Fan, Ty. A Mode- II Griffith Crack in Decagonal Quasicrystals. Applied Mathematics and Mechanics 22, 1311–1317 (2001). https://doi.org/10.1023/A:1016382308840

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  • DOI: https://doi.org/10.1023/A:1016382308840

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