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Abstract The material properties of the quasicrystals are greatly affected by the defects attribute to the high brittleness. It is necessary to understand fracture behavior of quasicrystals in order to develop the application of the materials. In this paper, the fracture mechanical of one-dimensional hexagonal quasicrystals with periodic Type III multiple cracks emanating from a nanoscale hole is investigated theoretically. Based on the complex elasticity theory and the Gurtin-Murdoch surface elasticity theory, the stress fields of a nano-hole with periodic multiple cracks considering surface effect are obtained by using the theory of boundary value problems of analytic function and the conformal transformation technique. The analytical expressions of stress intensity factors and energy release rate of the phonon field and the phase field at crack tip under the same conditions are further derived. The effects of the aperture size, the number of periodic cracks, the crack-length/aperture ratio, the phonon field-phase field coupling coefficient and the applied loads on the dimensionless stress intensity factors and dimensionless energy release rate are discussed. The results show that the coupling coefficient, the applied loads and the aperture size have no influence on the dimensionless stress intensity factors without considering the surface effect. The larger the aperture size, the more significant the size dependence on the dimensionless stress intensity factors and the dimensionless energy release rate becomes when considering the surface effect. There is an obvious coupling effect between the phonon field and the phase field. The influences of the number of periodic cracks on the dimensionless stress intensity factors and energy release rate are restricted by the size of defects. The effects of the phonon field loads and the phase field loads on the dimensionless stress intensity factors and energy release rate are different. This work reveals the specific influence of surface effect on the fracture behavior of multi-cracks at the hole edge, and has important academic significance in the development of quasicrystal fracture mechanics.
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Received: 30 April 2024
Published: 11 October 2024
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2024, Vol. 45 
