Approximate dispersion formulae for Rayleigh-like waves in a layered medium

Abstract

In a layered medium, the measurement of the velocity and attenuation coefficient of Rayleigh waves (RW) as a function of the frequency can be related to the characteristics (e.g. elastic constants, porosity, grain size and roughness) of the substrate and of the layer materials. Because of the large number of parameters describing this relationship, the inverse problem must be solved numerically. Besides being time consuming, these methods do not explicitly show the influence of each parameter on the general behaviour of the wave. The problem of the propagation of elastic waves in an isotropic layered medium is briefly reviewed: the dispersion relationship leading to the characteristics of Rayleigh-like waves is stated. The analytical expression of the Rayleigh wave velocity and attenuation coefficient as a function of the system parameters is then established using a Taylor expansion of the previous relationship assuming that the substrate and layer materials have close elastic constants. An illustration of the use of such formulae in an industrial context is proposed. The elastic constants of vacuum plasma-sprayed metallic coatings (NiCoCrAlY) deposited on an Ni-based alloy substrate are deduced from the measurement of the RW velocity and attenuation coefficient as a function of the frequency using the approximate formulae. The computer time of the best-fitting is reduced to 50 ms instead of the 2 min reported in the literature. These materials are used for the manufacture of gas turbine blades for electricity production.