Surface effect on two nanocracks emanating from an electrically semi-permeable regular 2n-polygon nanohole in one-dimensional hexagonal piezoelectric quasicrystals under anti-plane shear

In this paper, the conformal mapping from a regular 2n-polygon hole with two collinear asymmetric cracks into a circle is constructed. Based on the Gurtin-Murdoch surface/interface model and complex potential theory, two collinear asymmetric nanocracks emanating from an electrically semi-permeable regular 2n-polygon nanohole embedded in an infinite one-dimensional hexagonal piezoelectric quasicrystals with surface effect are investigated. The size-dependent stress intensity factors of phonon field and phason field, electric displacement intensity factor at the nanocrack tip are derived for electrically semi-permeable boundary condition. Numerical examples are illustrated to show that the size of the hole, mechanical load, electric load, cracks relative size change with stress intensity factor of phonon field and electric displacement intensity factor. Also analyzed the change of the electric displacement intensity factor with different electric permeability at the nanocrack tip and the dimensionless intensity factor with n.