Scattering of harmonic antiplane shear waves by an arc-shaped interfacial crack in functionally graded annular bi-material guide rail

Abstract

The dynamic behavior of an arc-shaped interfacial crack in an orthotropic functionally graded annular bi-material structure is investigated. In order for the analysis to be executable, the material properties are assumed to vary with the power function of the radial coordinates. By applying the separation variable method, the boundary value problem of the partial differential equation describing the fracture problem of this article can be transformed into a Cauchy kernel singular integral equation with the unknown jump of displacements across the crack surfaces. The obtained integral equation is solved numerically by Lobatto–Chebyshev collocation method to show the effects of the geometric and physical parameters upon the dynamic stress field near the crack tips.

Communicated by Kuang-Hua Chang.

Keywords:

• Functionally graded materials
• annular structure
• bi-materials
• arc-shaped crack
• interfacial crack
• antiplane shear waves

Additional information

Funding

This work was supported by the Fund of National Natural Science Foundation of China [No. 11802225] and the Natural Science Basic Research Plan in Shaanxi Province of China [Program Nos. 2019JQ-261 and 2019JQ-609]. The author also thanks the anonymous reviewers for careful reading of the manuscript and for their recommendations.