In-plane stress analysis of cracked layers under harmonic loads

Abstract

Stress analysis is carried out in an isotropic layer weakened by multiple cracks under time-harmonic loading. The viscous damping is used to model energy dissipation in the material. The analysis is based on the stress fields caused by climb and glide of an edge dislocation in the layer. The solution for dislocation is obtained by means of the integral transform method. Furthermore, stress analysis in the intact layer under self-equilibrating harmonic point loads is carried out. These solutions are employed to derive a set of Cauchy singular integral equations for analyzing cracks parallel/perpendicular to the layer boundary. The numerical solution of these equations yields dislocation densities on a crack surface which are used to determine dynamic stress intensity factors over a range of frequency. The natural frequencies of layers with horizontal cracks are obtained and the interaction of multiple cracks is studied.