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Abstract Like the classical materials, there are a variety of defects such as cracks and dislocations in quasicrystalline materials. Based on the fundamental equations of piezoelectricity of quasicrystalline material, by means of the analytic function theory and the complex variable method, the interactions among multi-defects in the piezoelectric material of one-dimensional hexagonal quasicrystals are studied. First, the models of fracture mechanics of the interactions among n parallel dislocations and a semi-infinite crack in the material are established, and the interaction forces and the equivalent action point of the n parallel dislocations are obtained, which are the versions of the well-known Peach-Koehler formula in the piezoelectric material of one-dimensional hexagonal quasicrystals with n parallel dislocations. Second, the analytic solutions of electric-elastic fields of the interactions among n parallel dislocations and a semi-infinite crack in the piezoelectric material of one-dimensional hexagonal quasicrystals are derived. Finally, some numerical examples show that the stress and electric displacement of crack surface vary with the position of dislocation and the size of Burgers vector. These results offer the basis of theory to discuss the dislocation emission from a crack tip, screening for dislocation and crack shielding in the piezoelectric material of one-dimensional hexagonal quasicrystals. As the development of the corresponding parts of classical elasticity, these are all firstly given in the present paper. When the electric fields or phason fields disappear, the results of this paper degenerate into those of the classical one.
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Received: 09 March 2016
Published: 20 April 2017
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2017, Vol. 38 
