Elastic analysis of a mode II crack in a decagonal quasi-crystal
Li Xian-Fang (李显方)a, Fan Tian-You (范天佑)b
a College of Science, Hunan Normal University, Changsha, Hunan 410081, China; b Department of Applied Physics, Beijing Institute of Technology, Beijing 100081, China
Abstract The elastic analysis of a mode II Griffith crack penetrating through a decagonal quasi-crystal along the periodic axis is made within the context of the continuum theory. By using a general solution obtained previously, the problem in the case of uniform shear stress at infinity is solved, and the analytical expressions for the entire stress field disturbed by an internal crack are derived in an explicit form. The asymptotic fields of the displacement and stress around a crack tip in both phonon and phason fields indicate that the stresses near a crack tip exhibit the square-root singularity. The formula for evaluating the energy release rate is also given. If imposing that the phason field is absent, the well-known results of a mode II crack in a conventional material are recovered from the present results.
Received: 01 June 2001
Revised: 06 November 2001
Accepted manuscript online:
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