Axial shear fracture of a transversely isotropic piezoelectric quasicrystal cylinder: Which field (phonon or phason) has more contribution?

Quasicrystals are a kind of new materials that exhibit a number of unique mechanical behaviors such as the coexistence of the phonon and phason fields. However, they are brittle and susceptible to the failure of fracture. As is known, both phonon and phason fields may contribute to fracture, but which one has more contribution? This is an open question that is of both scientific and engineering significance. The main purpose of the present paper is to answer this question. For this purpose, the axial shear fracture analysis is performed for a cylindrical composite that is made of 1D piezoelectric quasicrystals. Because of material symmetry (i.e. transverse isotropy), the problem is formulated in the cross section of the cylinder by using the polar coordinate system. The solution of the governing equation is expressed as an infinite series and the generalized dislocations are introduced to derive the singular integral equation, which is numerically solved. The computation is first verified by considering an existing example. Parametric studies then reveal that the fracture is dominated by the phason field when the phonon-phason loading ratio is below a critical point, but it is governed by the phonon field instead if the critical point is passed. In addition, the position of the critical point may be shifted by changing the values of a part of material properties only.