A contact mechanics based model for partially-closed randomly distributed surface microcracks and their effect on acoustic nonlinearity in Rayleigh surface waves

Abstract

This research investigates the modeling of randomly distributed surface-breaking microcracks and the dependency of higher harmonic generation in Rayleigh surface waves on microcrack density. The microcrack model is based on micromechanical considerations of rough surface contact. An effective stress-strain relationship is derived to describe the nonlinear behavior of a single microcrack and implemented into a finite-element model via a hyperelastic constitutive law. Finite-element simulations of nonlinear wave propagation in a solid with distributed surface microcracks are performed for a range of microcrack densities. The evolution of fundamental and second harmonic amplitudes along the propagation distance is studied and the acoustic nonlinearity parameter is calculated. The results show that the nonlinearity parameter increases with crack density. While, for small crack densities (dilute concentration of microcracks) a proportionality between crack density and acoustic nonlinearity is observed, this is not valid for higher crack densities, as the microcracks start to interact.