Non-Uniformly Loaded Row of Moving, Antiplane Shear Cracks in One-Dimensional Piezoelectric Quasicrystals

Abstract

An antiplane shear deformation in one-dimensional piezoelectric quasicrystals created by a row of collinear cracks subject to non-uniform phonon, phason and electric displacement loads is analyzed using a generalized technique of dislocation layers. Closed-form expressions are derived for the components of the phonon and phason stress and electric displacement fields. Their variations with angle near a crack tip are demonstrated and the corresponding phonon and phason stress and electric displacement intensity factors are deduced. Previously constantly loaded rows of cracks in various media have been studied. But no explicit expressions for the field components at a general point nor their angular variations were presented for them; even in classical isotropic elastic solids. The material considered here is the currently most general that is amenable to such an investigation and some of the analogous results for non-quasicrystals or non-piezoelectric or purely elastic solids or stationary cracks that can be deduced as particular cases are outlined. Some illustrative numerical results are graphically presented.