Study on the surface effect and microscopic mechanism of four cracks emanating from a nanoscale lip-shaped orifice in one-dimensional hexagonal piezoelectric quasicrystals

Based on the complex potential theory and the Gurtin-Murdoch surface/interface elasticity theory, the crack propagation behavior and microfracture mechanism of a nanoscale lip-shaped orifice with four nano-cracks in an infinite one-dimensional (1D) hexagonal piezoelectric quasicrystal (PEQC) material with surface effect are investigated, which is subjected to far-field anti-plane mechanical loads and in-plane electrical loads. By using the analytic function conformal mapping technique, the analytical solutions of the electro-elastic field intensity factors and the energy release rate (ERR) at the crack tip are obtained for partially electrically permeable boundary conditions. The obtained solutions can be reduced to the existing results. Then numerical examples are used to analyze the effects of the geometrical parameters of defects, the crack length, mechanic loadings, electric loading, dielectric constant, and phonon-phason coupling coefficient on the mechanical behavior. The results show that the surface effect has a greater effect on the stress intensity factor than the electric field intensity factor at the nanometer scale. An increase in the length of the lip orifice and the length of the transverse crack at the orifice’s edge tends to accelerate crack growth. Conversely, an increase in the ratio of lip orifice height to crack length can delay crack growth. The research provides novel ideas and methodologies for studying the mechanical and electrical properties of materials at the nanoscale.