Stress distribution determination in isotropic materials via inversion of ultrasonic Rayleigh wave dispersion data

Abstract

The possibility of using measurements of the dispersion of Rayleigh (surface) waves propagating on pre-stressed, initially isotropic materials to determine the surface stress and gradients in such materials is analytically investigated. Using a first-order perturbation formula for the description of the acoustoelastic effect on Rayleigh waves, it is shown that knowledge of the frequency dependence of the change in phase (or phase velocity) of the Rayleigh wave after propagating a certain distance can, in theory, be used to determine the stress level at the surface of the medium as well as its derivatives up to a given order. Basic questions concerning the uniqueness of the inversion are addressed, and a formal method of inverting inhomogeneous bi-axial stress distributions is presented. The effect of the range of frequencies included in the measurements is discussed and illustrated with a numerical example.