A comparison of three approaches for the inversion of ultrasonic rayleigh wave data into residual stress profiles

In various industries the surfaces of highly-loaded materials and components are specially treated to increase their resistivity to wear, corrosion and stresses. By shotpeening, laser shock-peening, heat-treatment or other methods residual stresses are deliberately generated. In order to characterize these in the near-surface areas, ultrasonic (Rayleigh) surface waves can be applied. In this contribution, we study the possibility of retrieving the near-surface residual stress state of a material from synthetic Rayleigh wave data. Several formulations that have been proposed in the past in various contexts are compared. It is shown that this particular problem may reveal in relevant materials undesired behaviors for some methods that could be reliably applied to infer other properties. The instabilities of a method based on a Taylor expansion are explained by highlighting singularities in the series of coefficients. At the same time, it is shown that a method based on a piecewise linear expansion regularized through a Singular Value Decomposition (SVD) can successfully provide performances which only weakly depend on the material. Orders of magnitudes are given for residual stress profiles generated by shot-peening. Systematic errors and sensitivities to noise are compared on a limited frequency range, with a focus on lower and intermediate frequencies.