Characterization of defects in plates by two-dimensional ultrasonic displacement maps: comparison between pulsed TV-holography measurements and finite element method predictions

Abstract

Pulsed TV-holography (PTVH) can be used for obtaining two-dimensional maps of instantaneous out-of-plane displacements in plates. In particular, scattering patterns generated by the interaction of elastic waves with defects can be measured with PTVH and employed for non-destructive inspection and damage detection in plate structures. For quantitative characterization of damage (position, dimensions, orientation, etc.) on this basis, modeling of elastic wave scattering is usually performed in terms of full-vector three-dimensional formulations based on elasticity theory. In this work, a finite element method (FEM) applied to a two-dimensional scalar model based on Helmholtz equation is employed for obtaining a quantitative description of the scattering patterns, avoiding the aforementioned more complex and rigorous standard approach. Simulated scattering patterns are obtained with the scalar FEM assuming harmonic regime and free-stress boundary conditions. The corresponding experimental interaction of narrowband Rayleigh-Lamb waves with artificial defects in plates are measured using our specifically developed PTVH system. In our case, the raw optical phase-difference values are processed by employing a specially developed procedure, based on a two step spatial Fourier transform method, to derive a high quality two-dimensional acoustic field map from which an important part of the noise component has been filtered out. A comparison between filtered experimental maps and FEM simulated maps is developed, considering defects with different sizes in relation to the acoustic wavelength.

Quantitative analysis of the agreement between scalar finite element simulation and pulsed TV-holography detection of the scattering of Rayleigh-Lamb waves in plates

“…The visual comparison of the images for the whole set (figure 5) confirms the reasonable agreement between experimental and numerical total fields, both in amplitude, phase and real part, except perhaps for the amplitude in the backscattering zone as we have claimed previously 6,7 . This conclusion was checked now in more detail by considering first the local total error distribution (figure 6).…”

“…can be extracted by analyzing the features of the associated scattering pattern. We have also shown that the direct problem of the scattering of Rayleigh-Lamb waves by through-thickness defects in plates can be solved by using numerical methods combined with a simplified 2-D scalar model, rendering numerical scattering patterns that by visual comparison show a reasonable agreement with the experiment, both in harmonic and transient regimes, except for the amplitude in the backscattering zone [6][7][8][9] .…”

“…In order to develop a quantitative comparison between experimental and numerical fields over a given region, beyond the previously developed visual comparison of images and profiles for the harmonic case 6,7 , we have used the general definitions and strategy for the comparison of real fields outlined in appendix A which allows to check their agreement both locally (pixel-wise), using the absolute local error distribution, and globally, using as the essential figure of merit a sort of averaged relative error 10 .…”

“…Despite the a priori applicability of this simplified 2-D scalar model has been discussed previously 6,7,10 , we recall the fact that it is valid for regions located a few wavelengths away from the hole, where contributions of the evanescent modes are not relevant. An exact description of the scattering process requires both propagating and evanescent Lamb and SH modes for taking into account modal conversion effects at the cylinder border and to fulfill the stress-free boundary conditions (see f.i.…”