Analysis of interface cracks in one-dimensional hexagonal quasi-crystal coating under in-plane loads

The displacement discontinuity (DD) method is proposed to analyze interface cracks in one-dimensional hexagonal quasi-crystal (QC) coating under in-plane loads. According to the general solutions and Fourier transform, fundamental solutions are derived for unit-point DDs at interface, with explicit expressions of displacements and stresses. The DD hyper-singular boundary integral-differential equations in terms of DDs are established across interface cracks. The fundamental solutions for uniformly distributed DDs are obtained over a constant line element. To eliminate the near-crack-tip oscillatory singularity, the delta function in fundamental solutions is approximated by the Gaussian distribution function. The expressions of stress intensity factors without oscillatory singularity and energy release rate are presented in terms of DDs. Finally, the DD boundary element method with checking accuracy is proposed for numerical simulation, and the influence of coating thickness, material combination, crack length and crack distance on the fracture behavior is comprehensively studied.

Automated summary

The displacement discontinuity method is proposed to analyze interface cracks in one-dimensional hexagonal quasi-crystal coatings under in-plane loads. Fundamental solutions and hyper-singular boundary integral-differential equations for unit-point and uniformly distributed DDs are derived. Stress intensity factors and energy release rate are presented without oscillatory singularity. The DD boundary element method is proposed for numerical simulation and the influence of various factors on fracture behavior is comprehensively studied.