Fracture mechanics of an arbitrary position crack emanating from a nano-hole in one-dimensional hexagonal piezoelectric quasicrystals

The mode III fracture behavior of an arbitrary position crack emanating from a nano-hole in one-dimensional hexagonal piezoelectric quasicrystals is studied. Based on the Gurtin-Murdoch surface theory and the boundary value problems theory, the expressions of the electro-elastic fields and the generalized field intensity factor at the crack tip are obtained. The presented solution can degenerate into existing results. The influences of the hole size, crack location, crack-hole interaction, applied electro-elastic loads and quasicrystal coupling coefficient on the generalized field intensity factor are discussed. The generalized field intensity factor has significant size effects when the surface effect is considered. The influence of the surface effect on the generalized field intensity factor depends on the crack location. The larger the relative size of the crack is, the greater the surface effect is. The effects of applied electro-elastic loads and quasicrystal coupling coefficient on each generalized field intensity factor are quite different.