Fundamental solutions and analysis of an interfacial crack in a one-dimensional hexagonal quasicrystal bi-material

Abstract

Using the Stroh formalism, Green’s functions are obtained for phonon and phason dislocations and opening displacements on the interface of a one-dimensional hexagonal quasicrystal bi-material. The integro-differential equations governing the interfacial crack are then established, and the singularities of the phonon and phason displacements at the crack tip on the interface are analyzed. To eliminate the oscillating singularities, we represent the delta function in terms of the Gaussian distribution function in the Green’s functions and the integro-differential equations, which helps reduce these equations to the standard integral equations. Finally, a boundary element numerical approach is also proposed to solve the integral equation for the crack opening displacements, the asymptotic expressions of the extended intensity factors, and the energy release rate in terms of the crack opening displacements near the crack tip. In numerical examples, the effect of the Gaussian parameter on the numerical results is discussed, COMSOL software is used to validate the analytical solution, and the influence of the different phonon and phason loadings on the interfacial crack behaviors is further investigated.

Three-dimensional thermo-electro-elastic field in one-dimensional hexagonal piezoelectric quasi-crystal weakened by an elliptical crack

“…Many classical methods in elasticity theory were extended to analyze crack problems in QCs, such as the integral transformation method [6, 7], Stroh formalism [8, 9], the potential theory method [10–13], the displacement discontinuity method [14–18], the dislocation layer method [19, 20], and the weight function method [21]. By using these methods, some classical crack problems, including those for line cracks [8, 14], half-infinite cracks [12, 13], penny-shaped cracks [10–13], elliptical cracks [22], and interface cracks [9, 15, 16, 23], were considered, and the corresponding analytical or semi-analytical solutions were obtained.…”

Mechanism and prediction models for interfacial shear separation of claddings excited by Love waves

“…3,4 On the other hand, researchers have been plagued by coating peeling at certain frequency bands of the vibration. 5,6 Therefore, interface shear separation mechanism and prediction of cladding structures excited by horizontal shear waves should be studied in depth.…”