Research into ultrasonic NDE techniques for the inspection of multilayered structures relies strongly on the use of modeling tools which calculate dispersion curves and reflection and transmission spectra. These predictions are essential to enable the best inspection strategies to be identified and their sensitivities to be evaluated. General purpose multilayer modeling tools may be developed from a number of matrix formulations which have evolved in the latter half of this century and there is now a formidable number of publications on the subject. This paper presents a review of the main developments of the matrix techniques, and their use in response and modal models, with emphasis on ultrasonics applications. >

Matrix techniques for modeling ultrasonic waves in multilayered media

Structural health monitoring techniques for aircraft composite structures

The idea of the log spectrum or cepstral averaging has been useful in many applications such as audio processing, speech processing, speech recognition, and echo detection for the estimation and compensation of convolutional distortions. To suggest what prompted the invention of the term cepstrum, this article narrates the historical and mathematical background that led to its discovery. The computations of earlier simple echo representations have shown that the spectrum representation domain results does not belong in the frequency or time domain. Bogert et al. (1963) chose to refer to it as quefrency domain and later termed the spectrum of the log of a time waveform as the cepstrum. The article also recounts the analysis of Al Oppenheim in relation to the cepstrum. It was in his theory for nonlinear signal processing, referred to as homomorphic systems, that the realization of the characteristic system of homomorphic convolution was reminiscent of the cepstrum. To retain both the relationship to the work of Bogart et al. and the distinction, the term power cepstrum was eventually applied to the nonlinear mapping in homomorphic deconvolution . While most of the terms in the glossary have faded into the background, the term cepstrum has survived and has become part of the digital signal processing lexicon.

From frequency to quefrency: a history of the cepstrum

Lamb waves can propagate over long distances which means that they are attractive for the quick, long range inspection of large structures, and they can also be useful for localized inspection, particularly in thin structures. This paper discusses the selection of the appropriate mode and frequency range for different inspection requirements and reviews the possible methods of excitation, response measurement and signal processing. It is usually desirable to transmit a single, non-dispersive mode, and excitation methods to achieve this are discussed. A variety of signal processing techniques from simple time domain to relatively complex two-dimensional Fourier analysis are available. Time domain processing can often be applied satisfactorily in low frequency-thickness regions where only two modes can propagate, but tends to be unreliable above the cut-off frequency of the a 1 mode. As an example of the design of a Lamb wave testing regime, a set of tests on a butt-welded steel plate with simulated weld defects of different depths is described. It is shown that by operating below the a 1 cut-off frequency with judicious selection of testing technique, the presence of defects can be detected reliably from changes in the shape of the received waveform.

Optimization of Lamb wave inspection techniques

Guided acoustic and ultrasonic waves have been utilized in various manners for non-destructive evaluation and testing. If a guided wave mode is dispersive, a pulse of energy will spread out in space and time as it propagates. For a long-range guided wave inspection application, this constrains the choice of operating point to regions on the dispersion curves where dispersion effects are small. A signal processing technique is presented that enables this constraint on operating point to be relaxed. The technique makes use of a priori knowledge of the dispersion characteristics of a guided wave mode to map signals from the time to distance domains. In the mapping process, dispersed signals are compressed to their original shape. The theoretical basis of the technique is described and an efficient numerical implementation is presented. The robustness of the technique to inaccuracies in the dispersion data is also addressed. The application of the technique to experimental data is shown and the resulting improvement in spatial resolution is demonstrated. The implications of using dispersion compensation in practical systems are briefly discussed.

A rapid signal processing technique to remove the effect of dispersion from guided wave signals

Amplitude spectrum method for the measurement of phase velocity

The detection of thin embedded layers using normal incidence ultrasound

A signal regeneration technique for long-range propagation of dispersive Lamb waves

The use of ultrasonic reflection coefficient measurements at both normal and oblique incidence for the detection and characterization of oxide layers at the adhesive-adherend interface in adhesive joints has been investigated. Tests have been carried out on aluminium alloy-oxide-epoxy specimens with a minimal (< 0.1 $\mu $m) thickness oxide layer, 43 and 15 $\mu $m thick sulphuric acid anodized oxide oxide layers and an industry standard, 3.5 $\mu $m thick chromic acid anodized oxide layer. A superpure aluminium-90 $\mu $m thick oxalic acid anodized layer-water system has also been investigated. The results indicate that the cell wall density of the sulphuric acid anodized oxide layer is only 1990 kg m$^{-3}$, compared to 2850 kg m$^{-3}$ for the oxalic acid anodized layer. The cell wall density and Young's modulus are obtained from normal incidence measurements. Predictions of the oblique incidence reflection coefficients using the effective elastic constants of the oxide layer obtained from a standard porosity model assuming these cell wall properties and the porosity measured from TEM images showed good agreement with the measurements made on both the sulphuric acid anodized and oxalic acid anodized specimens, only small adjustments to the properties being required to obtain a very good fit. The frequency range over which it is necessary to take measurements increases as the thickness of the oxide layer decreases. Maximum frequencies of 15 MHz for the oblique incidence measurements and 70 MHz for the normal incidence measurement were adequate to obtain values of $\rho $, C$\_{11}$ and C$\_{33}$ for a 43 $\mu $m thick sulphuric acid anodized layer to an estimated accuracy of $\pm $10% and to set a lower bound on C$_{55}$. In order for a 3.5$\mu $m thick oxide layer with similar properties to be detectable at normal incidence, the frequency would have to be increased to over 200 MHz, while the frequency of the oblique incidence measurements would have to be raised to about 25 MHz if a 5% change could reliably be detected, or 50 MHz if a 10% change is necessary in order to ensure detection.

The characterization of oxide layers in adhesive joints using ultrasonic reflection measurements

The detection of a weak adhesive/adherend interface in an adhesive joint is one of the major current challenges in NDE; the lack of a satisfactory non destructive test for this region is retarding the exploitation of the advantages of adhesive bonding in safety critical areas. It is the interface layer which is affected by the common problem of slight contamination due to, for example, grease on the adherend surfaces prior to bonding. The interface is particularly important in aluminium-aluminium joints in which an inappropriate interface structure can cause greatly enhanced susceptibility to environmental attack [1]. Inspection of the interface layer is difficult because it is frequently only of the order of lμm thick, compared with an adhesive layer thickness of the order of 100 μm.

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=2694&context=qnde

Tom Pialucha

Papers

Amplitude spectrum method for the measurement of phase velocity

The detection of thin embedded layers using normal incidence ultrasound

A signal regeneration technique for long-range propagation of dispersive Lamb waves

The characterization of oxide layers in adhesive joints using ultrasonic reflection measurements

The Reflection of Ultrasound from Interface Layers in Adhesive Joints