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
a Research Center of Materials Science, Beijing Institute of Technology, Beijing 100081, China; b Central Iron and Steel Research Institute, Beijing 100081, China
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.
Received: 18 October 2000
Revised: 19 March 2001
Accepted manuscript online:
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 19972011)
Cite this article:
Zhou Wang-min (周旺民), Fan Tian-you (范天佑) PLANE ELASTICITY PROBLEM OF TWO-DIMENSIONAL OCTAGONAL QUASICRYSTALS AND CRACK PROBLEM 2001 Chinese Physics 10 743
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