中国物理B ›› 2001, Vol. 10 ›› Issue (8): 743-747.doi: 10.1088/1009-1963/10/8/315

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PLANE ELASTICITY PROBLEM OF TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS AND CRACK PROBLEM

范天佑1, 周旺民2   

  1. (1)Research Center of Materials Science, Beijing Institute of Technology, Beijing 100081, China; (2)Research Center of Materials Science, Beijing Institute of Technology, Beijing 100081, China; Central Iron and Steel Research Institute, Beijing 100081, China
  • 收稿日期:2000-10-18 修回日期:2001-03-19 出版日期:2001-08-15 发布日期:2005-06-12
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 19972011)

PLANE ELASTICITY PROBLEM OF TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS AND CRACK PROBLEM

Zhou Wang-min (周旺民)ab, Fan Tian-you (范天佑)a   

  1. a Research Center of Materials Science, Beijing Institute of Technology, Beijing 100081, China; b Central Iron and Steel Research Institute, Beijing 100081, China
  • Received:2000-10-18 Revised:2001-03-19 Online:2001-08-15 Published:2005-06-12
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 19972011)

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摘要： The plane elasticity theory of two-dimensional octagonal quasicrystals is developed in this paper. The plane elasticity problem of quasicrystals is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the exact analytic solution of a Mode I Griffith crack in the material is obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate can be calculated. The physical significance of the results relative to the phason and the difference between the mechanical behaviours of the crack problem in crystals and quasicrystals are figured out. These provide important information for studying the deformation and fracture of the new solid phase.

Abstract: The plane elasticity theory of two-dimensional octagonal quasicrystals is developed in this paper. The plane elasticity problem of quasicrystals is reduced to a single higher-order partial differential equation by introducing a displacement function. As an example, the exact analytic solution of a Mode I Griffith crack in the material is obtained by using the Fourier transform and dual integral equations theory, then the displacement and stress fields, stress intensity factor and strain energy release rate can be calculated. The physical significance of the results relative to the phason and the difference between the mechanical behaviours of the crack problem in crystals and quasicrystals are figured out. These provide important information for studying the deformation and fracture of the new solid phase.

Key words: plane elasticity, two-dimensional octagonal quasicrystals, crack, displacement function

中图分类号:  (Structural failure of materials)

  • 62.20.M-
02.30.Jr (Partial differential equations) 02.30.Uu (Integral transforms)