Anti-plane fracture analysis of 1D hexagonal piezoelectric quasicrystals with the effects of damage due to materials degradation

Most fracture mechanics analysis is based on the assumptions of prefabricated crack and ideal undamaged body. In practical, a cracked structure contains microstructural defects so that the material damage is considered to exist in the body rather than an ideal defect-free body. In this paper, it is the first time to take the material damage into account to the constitutive equation of quasicrystals, and the anti-plane fracture analysis of the onedimensional hexagonal piezoelectric quasicrystals is carried out to obtain the more actual solutions. The continuum damage mechanics theory is used to define the damage variable and evolution law of the micro-voids' growth in the quasicrystals. Semi-qualitative analysis of damage effects on the stress intensity factors are conducted, in which the stress intensity factors and J-integral are solved by using the boundary element method. In a case study, the fields of stress and displacement along the crack or distributed on the plate are obtained. The comparisons between the presented numerical results and the analytical results have good agreement, which verifies the accuracy of the presented solutions. The numerical results suggest that fracture failure analysis for quasicrystals engineering applications should consider the effective (actual) stress intensity factors calculated by the effective stress instead of nominal stress intensity factors.