Abstract:Abstract: Based on the anti-plane equations of piezoelectricity of one-dimensional hexagonal quasicrystals,the electric yielding zone of the anti-plane mode Ⅲ crack problem is analysed in this paper. The expression of the electric yielding zone is obtained by using the strip model and assuming the shear stress is a constant in the electric yielding zone.This method eliminates the singularity of the electric field and the stress field at the crack tip.The conclution is in accord with the reality and it will provide a theoretical foundation for the fracture analysis of the piezoelectricity of one-dimensional hexagonal quasicrystals.