Interfacial fracture analysis for a two-dimensional decagonal quasi-crystal coating layer structure

Abstract

The interface crack problems in the two-dimensional (2D) decagonal quasi-crystal (QC) coating are theoretically and numerically investigated with a displacement discontinuity method. The 2D general solution is obtained based on the potential theory. An analogy method is proposed based on the relationship between the general solutions for 2D decagonal and one-dimensional (1D) hexagonal QCs. According to the analogy method, the fundamental solutions of concentrated point phonon displacement discontinuities are obtained on the interface. By using the superposition principle, the hypersingular boundary integral-differential equations in terms of displacement discontinuities are determined for a line interface crack. Further, Green’s functions are found for uniform displacement discontinuities on a line element. The oscillatory singularity near a crack tip is eliminated by adopting the Gaussian distribution to approximate the delta function. The stress intensity factors (SIFs) with ordinary singularity and the energy release rate (ERR) are derived. Finally, a boundary element method is put forward to investigate the effects of different factors on the fracture.