Quantitative evaluation of the fatigue limit of a metal with an arbitrary crack under a stress controlled condition – Stress Ratio R=−1

The static crack problem of a functionally graded coating-substrate structure with an internal or edge crack perpendicular to the interface is investigated under an in-plane load. The structure is made up of a functionally graded coating with an internal or edge crack and a homogeneous substrate of finite thickness. The material properties are assumed to vary continuously from the coating to the substrate. By use of Fourier transform method, the mixed boundary value problem is reduced to a singular integral equation which can be solved numerically. During the analysis, a higher-order term is obtained in the asymptotic analysis of the singular kernel to improve the convergence efficiency of numerical integrals. The influences of material constants and the geometry parameters on the stress intensity factors (SIFs) are studied. In Part II of this paper, the transient response of the structure subjected to an in-plane impact is investigated.