Effective spring boundary conditions for modelling wave propagation through a damaged interface between dissimilar orthotropic media

Abstract

In-plane elastic wave propagation through a damaged interface between dissimilar orthotropic media is investigated. The damage is modelled as a randomly distributed array of micro-cracks, and this is converted into the effective spring boundary conditions stated at the imperfect interface. Wave propagation through the interfaces with perfect contact and imperfect contact described by the spring boundary conditions and a distribution of micro-cracks is considered. Asymptotic solution for plane wave scattering by a single interface crack is obtained in an explicit form and compared with the numerical solution for a small ratio of crack length to wavelength. Based on the asymptotic solution, explicit analytical formulae for effective spring stiffnesses are derived in terms of the elasticity tensor of contacting orthotropic media, the crack density and the micro-crack length. Several examples of spring stiffnesses for a variety of typical laminated composites are presented. The resulting relations can be employed for estimating the severity of interfacial damages considering the stiffnesses of the interface, which can be estimated using ultrasonic methods.