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| The anti-plane Shear problems of a lip-shaped orifice with two unsymmetrical edge rips in one-dimensional hexagonal quasicrystals piezoelectric materials |
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Abstract The fracture problem of nonlinear cracks in one-dimensional hexagonal quasicrystal piezoelectric materials under anti-plane load is studied by using the complex variable function method and Stroh algorithm. The defect mechanics model of the secondary asymmetric cracks at the lip is first constructed, and the conformal transformation formula from the infinite region containing the secondary asymmetric cracks at the lip to the outer region of the unit circle is derived, the analytical expressions of the field intensity factor and the energy release rate at the crack tip are obtained. The numerical examples reveal the influence of the defect size, especially the lip height and the crack length, on the field intensity factor and the energy release rate. The results show that increasing the length of both sides of the crack will promote the crack expansion, and increasing the lip height will inhibit the crack growth. Finally, under given conditions, these analytical results can be simplified to the solutions of other defect models, for example, the solution of lip secondary single crack and lip secondary double symmetric crack can also be degenerated into the solution of classical Griffith crack and lip secondary crack. The above results are consistent with the conclusion of theoretical analysis
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Received: 19 June 2023
Published: 28 February 2024
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2024, Vol. 45 
