中国物理B ›› 2007, Vol. 16 ›› Issue (4): 1111-1118.doi: 10.1088/1009-1963/16/4/042

• CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES • 上一篇    下一篇

Elastic analysis of a mode II crack in an icosahedral quasicrystal

祝爱玉1, 范天佑2   

  1. (1)Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, China; (2)Department of Physics, School of Science, Beijing Institute of Technology, Beijing 100081, China
  • 收稿日期:2006-09-12 修回日期:2006-10-16 出版日期:2007-04-20 发布日期:2007-04-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10372016).

Elastic analysis of a mode II crack in an icosahedral quasicrystal

Zhu Ai-Yu(祝爱玉)a)† and Fan Tian-You(范天佑)b)   

  1. a Department of Mathematics, School of Science, Beijing Institute of Technology, Beijing 100081, China; b Department of Physics, School of Science, Beijing Institute of Technology, Beijing 100081, China
  • Received:2006-09-12 Revised:2006-10-16 Online:2007-04-20 Published:2007-04-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10372016).

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摘要： Based on the displacement potential functions, the elastic analysis of a mode II crack in an icosahedral quasicrystal is performed by using the Fourier transform and dual integral equation theory. By the solution, the analytic expressions for the displacement field and stress field are obtained. The asymptotic behaviours of the phonon and phason stress fields around the crack tip indicate that the stresses near the crack tip exhibit a square root singularity. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are evaluated in an explicit version.

Abstract: Based on the displacement potential functions, the elastic analysis of a mode II crack in an icosahedral quasicrystal is performed by using the Fourier transform and dual integral equation theory. By the solution, the analytic expressions for the displacement field and stress field are obtained. The asymptotic behaviours of the phonon and phason stress fields around the crack tip indicate that the stresses near the crack tip exhibit a square root singularity. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are evaluated in an explicit version.

Key words: icosahedral quasicrystal, elasticity, crack, energy release rate

中图分类号:  (Quasicrystals)

  • 61.44.Br
62.20.M- (Structural failure of materials) 62.20.D- (Elasticity) 63.20.-e (Phonons in crystal lattices)