Non-destructive Detection of a Circular Cavity in a Finite Functionally Graded Material Layer Using Anti-plane Shear Waves

Abstract

A semi-analytical method is proposed to investigate the non-destructive detection of a circular cavity buried in a functionally graded material layer bonded to homogeneous materials, and the multiple scattering effect of shear waves is described accurately. The image method is used to satisfy the traction free boundary condition at the edge of the functionally graded material layer. The analytical solutions of wave fields are expressed by employing wave function expansion method, and the expanded mode coefficients are determined by satisfying the boundary conditions at the edge and around the cavity. The analytical and numerical solutions of dynamic stress concentration factors around the cavity are presented. The effects of the position of the cavity in the material layer, the incident wave number, and the properties of the two phases of materials on the dynamic stress concentration factors are analyzed. Analyses show that when the buried depth of the cavity and the thickness of the layer are relatively small, the properties of the two phases of materials have great effect on the distribution of dynamic stress around the cavity. In the region of higher frequency, the effects of the position of the cavity and the properties of the two phases of materials on the maximum dynamic stress are greater.