Study on the surface effect and microscopic mechanism of a lip‐shaped orifice with two asymmetric edge cracks in one‐dimensional hexagonal piezoelectric quasicrystals

Abstract Based on the principles of continuum mechanics and the Gurtin‐Murdoch (GM) surface/interface theoretical model, the mechanical behavior characteristics of a nanoscale lip‐shaped orifice with two asymmetric nano‐cracks in one‐dimensional (1D) hexagonal piezoelectric quasicrystals (PEQCs) is studied, taking into account surface effects. By employing conformal mapping techniques, the electro‐elastic field distribution is obtained. Under partially electrically permeable boundary conditions, the precise analytical solutions are derived for the intensity factors of electro‐elastic fields and the energy release rate (ERR) at the crack tips. The obtained solutions can be reduced to existing results to verify the effectiveness of the method. Meanwhile, the effects of surface effects on stress intensity factors (SIFs), electric displacement factor (EDIF), and ERR are analyzed in detail through numerical examples, and the physical mechanism is also explained. The results indicate that the electro‐elastic field intensity factors exhibit significant size dependence. The surface effect usually acts as a “shield” and attenuates the intensity of the crack tip field. Appropriately increasing the electrical conductivity can effectively inhibit crack propagation. The findings of this study provide invaluable theoretical guidance for the design of smart devices in micro‐electromechanical systems and nano‐electromechanical systems.