Scattering of plane waves from an interface crack between the 1D hexagonal quasicrystals coating and the elastic substrate

Abstract

Interface cracks are an important structural defect across various engineering domains. Based on Bak’s model, this paper explores the scattering problem of an interface crack between a 1D hexagonal quasicrystals (QCs) coating and an elastic substrate under harmonic plane waves. The Fourier transform method has been used to obtain the Cauchy singular integral equations (CSIEs) of the second kind in which the unknown variables are the dislocation density functions. The Jacobi polynomials have been used to reduce the CSIE into a system of linear algebraic equations. By taking the limit of the stress field near the crack tip, dynamic stress intensity factors (DSIFs) and crack opening displacements (CODs) are obtained. Finally, numerical results investigate the DSIFs for various wave types, material combinations, crack sizes, incident angles, and coupling coefficients of the phonon-phason field. The research findings provide valuable insights into using integral equation methods to address practical engineering issues related to crack detection and prediction.