Dynamic propagation of a Dugdale-model interfacial crack in two dissimilar one-dimensional hexagonal piezoelectric quasicrystals

A moving Dugdale-type interfacial crack between two dissimilar\one-dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs) is considered. By considering the coupling effects of the phonon field, phason field, and electric field, the dynamic behavior of the interfacial crack under anti-plane mechanical loading and in-plane electrical loading is investigated. The mixed boundary value problem is transformed into dual integral equations by using the Fourier transform. The explicit expressions for the yield zone sizes and the crack sliding displacement are derived separately for both the phonon field and phason field. The results show that the electric field load exerts a significant regulatory effect on the interfacial cracks in 1D hexagonal PQCs. Both the yield zone sizes and crack sliding displacement have a functional correlation with external loads and are strongly regulated by the electric field. An increase in the Mach number exacerbates the material mismatch effect, resulting in different amplitudes of crack sliding displacement on the upper and lower crack surfaces. \noindent\textbf{Key words:} 1D hexagonal PQCs; Moving Dugdale interfacial crack; Dual integral equations; The yield zone; Crack sliding displacement.