Two collinear mode-III cracks in one-dimensional hexagonal piezoelectric quasicrystal strip

This paper studies two collinear permeable anti-plane shear or mode-III cracks of equal length lying at the mid-plane of a one-dimensional hexagonal piezoelectric quasicrystal strip. By using the integral transform technique, the associated mixed boundary value problem is reduced to triple integral equations, and then to a singular integral equation. By making transformation of variables, a standard singular integral equation with Cauchy kernel of the first kind is derived and exact closed-form solution is obtained. Explicit expressions for the electroelastic field including phonon and phason stresses, electric field and crack tearing displacements at crack faces are determined. The formulae for calculating field intensity factors and energy release rate at the inner and outer crack tips are given, respectively. Some special cases of the present results for the field intensity factors and the energy release rate are discussed. Effects of material properties and geometric size on fracture parameters are examined.