ELASTIC ANALYSIS OF A GRIFFITH CRACK IN ICOSAHEDRAL QUASICRYSTAL Al-Pd-Mn QUASICRYSTAL

Abstract

The elastic analysis of a Griffith crack in an icosahedral quasicrystal is performed using the general solution and systematic Fourier transform-dual integral equations method, the analytic expressions for the displacement and stress fields are obtained. The asymptotic behavior of the stress field around the crack tip indicates that the stress near the crack tip exhibits the square root singularity. The singularity in the phason stress field arising from those of the phonon and phonon–phason coupling is also discussed. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are determined.