An interface crack in 1d piezoelectric quasicrystal under antiplane mechanical loading and electric field

TL;DR

This paper develops an analytical framework for understanding the behavior of a mode III interface crack in 1D piezoelectric quasicrystals under combined mechanical and electric loading, providing exact solutions and numerical visualizations.

Contribution

It introduces an exact analytical solution for interface cracks in 1D piezoelectric quasicrystals considering complex electromechanical interactions and different boundary conditions.

Findings

Exact solutions for stress and electric fields are derived.

Numerical simulations illustrate field distributions under various loadings.

Formulas for stress intensity factors are provided.

Abstract

The present study provides the consideration of a mode III interface crack in one-dimentional (1D) piezoelectric quasicrystal under antiplane phonon and phason loading and inplane electric field. Due to complex function approach all required electromechanical parameters are presented through vector-functions analytic in the whole complex plane except the crack region. The cases of electrically impermeable (insulated) and electrically limited permeable conditions on the crack faces are considered. In the first case a vector Hilbert problem in the complex plane is formulated and solved exactly and in the second one the quadratic equation with respect to the electric flux through the crack region is obtained additionally. Its solution permits to find phonon and phason stresses, displacement jumps (sliding) and also electric characteristics along the material interface. Analytical formulas are also obtained for the corresponding stress intensity factors related to each field. The numerical computations for three selected variants of the loading conditions was conducted and the resulting field distributions are visualised on the crack continuation beyond the crack and also inside of the crack region.