Displacement discontinuity method for interfacial cracks in one-dimensional hexagonal quasi-crystal coating under thermal-mechanical loading

Abstract

This study derived Green’s functions of the concentrated interfacial displacement and temperature discontinuities. Green’s functions and the displacement and temperature discontinuity method were used to analyze interfacial cracks in a one-dimensional (1D) hexagonal quasi-crystal (QC) coating under thermal-mechanical loading. The boundary integral-differential equations were established for an interfacial crack, the fundamental solutions were obtained for uniformly distributed temperature, and the displacement discontinuities were applied over a line element. The near-crack-tip oscillatory singularity of stresses was eliminated by introducing the Gaussian distribution function to approximate the delta function. After this treatment, the expressions of the stress and heat flux intensity factors without oscillatory singularity, and the energy release rate (ERR) at the crack tips were obtained. The displacement and temperature discontinuity boundary element method for numerical simulation is proposed, and the influence of relevant factors is briefly discussed.

Keywords:

• Displacement and temperature discontinuity
• energy release rate
• interfacial crack
• one-dimensional hexagonal quasi-crystalline coating
• stress intensity factors
• thermal-mechanical loads

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China under Grant [Nos. 11572289, 1171407, 11702252, and 11902293] and the China Postdoctoral Science Foundation under Grant [No. 2019M652563].