The nondestructive determination of material property gradients using ultrasonic surface wave dispersion was studied, and an approach which balances the requirements of inverse solution existence and uniqueness was found. The method uses homogeneous layers to approximate, in a piecewise sense, how the properties of a material system vary with depth. In the forward problem, formally exact dispersion curves can be defined for any arrangement of homogeneous layers. Inverse solutions are obtained by adjusting the model layer thicknesses and positions until the differences between measured dispersion data and forward model predictions are minimized. To increase solution stability the inversion employs a damped, least squares algorithm. Although the approach is general, a specific example of predicting steel hardness gradients was solved.;To establish correlations between measured ultrasonic parameters and the mechanical gradient we sought to predict, an experimentally determined model basis was established. This allowed us to maximize our use of a priori knowledge while limiting the set of possible solutions. Parametric studies showed that an accurate hardness gradient predictions required precise dispersion measurements. To accomplish this goal, a dual beam interferometer was built with an innovative low frequency vibration controller that measured surface acoustic wave displacement at two probe points.;Cross correlation of collected displacement data revealed dispersion curves which could not be attributed to experimental error, sample morphology or material properties. Based on sensitivity analysis and relevant wave mechanics phenomena, the unexpected dispersion results were explained via multimode superposition. To experimentally support this contention, two dimensional analyses were employed to extract phase velocity values using, the 2-D Fourier transform, and a 2-D separable spectral estimator based on Fourier transformation and autoregressive moving average modeling. The 2-D separable estimator was capable of resolving the fundamental Rayleigh-like wave velocity with greater accuracy than the 2-D FFT approach.;Insights from the 2-D computations were combined with a modified phase slope algorithm to extract the fundamental surface wave dispersion data of an unknown hardened steel sample. Given these intermediate results, the inverse formalism predicted a hardness gradient that matched well with the sample's destructively measured profile.
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