Analytical solutions of periodic mode-III cracks emanating from a nano-hole in one-dimensional hexagonal piezoelectric quasicrystals

In this paper, the fracture mechanics of one-dimensional hexagonal piezoelectric quasicrystals (1D-HPQCs) with periodic mode-III multiple cracks emanating from a nanoscale hole is investigated theoretically. The surface effects of nano-defects (hole and periodic cracks) are considered according to the Gurtin-Mordoch surface elasticity theory. The electroelastic fields in closed form under electrically permeable/impermeable conditions are obtained using boundary value problems of analytic function theory and the conformal transformation technique. Analytical expressions for the electroelastic field stress intensity factors (SIFs) and the energy release rate (ERR) at the crack tip are derived. The effects of geometrical parameters, material properties, and applied loads on dimensionless electroelastic field SIFs and dimensionless/normalized ERR are explored. The dimensionless electroelastic field and dimensionless ERR exhibit significant size-dependent effects. The effects of crack number on dimensionless electroelastic field SIFs and dimensionless ERR are restricted by defect size. The applied electroelastic field loads exert varying effects on dimensionless electroelastic field SIFs and dimensionless/normalized ERR.