Linearized forward and inverse problems of the resonant ultrasound spectroscopy for the evaluation of thin surface layers

Abstract

In this paper, linearized approximations of both the forward and the inverse problems of resonant ultrasound spectroscopy for the determination of mechanical properties of thin surface layers are presented. The linear relations between the frequency shifts induced by the deposition of the layer and the in-plane elastic coefficients of the layer are derived and inverted, the applicability range of the obtained linear model is discussed by a comparison with nonlinear models and finite element method (FEM), and an algorithm for the estimation of experimental errors in the inversely determined elastic coefficients is described. In the final part of the paper, the linearized inverse procedure is applied to evaluate elastic coefficients of a 310 nm thick diamond-like carbon layer deposited on a silicon substrate.

Forward and inverse problems for surface acoustic waves in anisotropic media: A Ritz–Rayleigh method based approach

“…The reason is that for such a case the Ritz-Rayleigh method leads to an eigensystem very similar to (11) and derivable from it by using a perturbation theory, as shown for RUS in [27].…”

Sensitivity of the resonant ultrasound spectroscopy to weak gradients of elastic properties

“…[15][16][17] As shown in Ref. 17 by a similar perturbation approach, the presence of such layer induces, in an approximation of the first order, significant shifts of the resonant frequencies.…”

Application of resonant ultrasound spectroscopy to determine elastic constants of plasma-sprayed coatings with high internal friction

“…In [28], the shifts of the frequencies induced by the presence of the layer were studied by various numerical models. It was shown that for thin layers the shifts are linearly proportional to the thickness of the layer and that this approximation can be used with acceptable accuracy up to ratios log[(a − a 0 )/a 0 ] b − 1.5.…”

“…consisting of in-plane tension/compressions and in-plane shears only. The two-dimensional elasticity of a thin layer under the plane-stress condition can, in general, characterized by a two-dimensional 4th order tensor q IJKL such that [28]:…”

“…This modified approach originates from classical RUS method for evaluation of thin layers [26,28], which is based on the comparison of the resonant spectra of the same substrate sample before and after deposition of the layer. The shifts of the peaks then carry information on the in-plane elasticity of the layer.…”