The ultrasonic NDE technique to characterize the ultrasonic nonlinear response of the cyclically load 7075-T6 aluminum is described in this thesis. In order to estimate the nonlinear relation of the ultrasonic waves due to material fatigue damage or degradation, the spectral analysis techniques such as the power spectrum, bispectrum, and bicoherence spectrum are applied. The ultrasonic nonlinearity parameters by Cantrell and Jhang are introduced and presented as a function of the material fatigue growth, the number of fatigue cycles. This thesis presents the effectiveness of the bispectral analysis for evaluating the nonlinear aspects of the ultrasonic wave propagation. The results show that the nonlinearity parameters by Cantrell and Jhang are responsive to the output amplitude of the received signal and vary for the various materials, and independent of the input frequency and the ultrasonic wave propagation distance. By using the bispectral analysis tools, particularly the bicoherence spectrum, the increase of the coupling levels between the fundamental, its harmonic, and subharmonic frequency components is presented as the number of fatigue cycles is increased. This thesis suggests that the application of the bicoherence spectrum based on the nonlinear wave coupling relations be more effective for estimating the level of the material fatigue life. / Master of Science

This research investigates the modeling of randomly distributed surface-breaking microcracks and their effects on higher harmonic generation in Rayleigh surface waves. The modeling is based on micromechanical considerations of rough surface contact. The nonlinear behavior of a single microcrack is described by a hyperelastic effective stress-strain relationship. Finite element simulations of nonlinear wave propagation in a solid with distributed microcracks are performed. The evolution of fundamental and second harmonic amplitudes along the propagation distance is studied and the acoustic nonlinearity parameter is calculated. The results show that the nonlinearity parameter increases with crack density and root mean square roughness of the crack faces. While, for a dilute concentration of microcracks, the increase in acoustic nonlinearity is proportional to the crack density, this is not valid for higher crack densities, as the microcracks start to interact. Finally, it is shown that odd higher harmonic generation in Rayleigh surface waves due to sliding crack faces introduces a friction nonlinearity.

L'échographie est aujourd'hui une technique d'imagerie de diagnostic répandue. Si l'imagerie dite ‘classique' basée sur la réponse linéaire des tissus est couramment utilisée, l'imagerie harmonique, basée sur la réponse non linéaire des tissus, est maintenant aussi utilisée en routine clinique. L'estimation du paramètre de non linéarité d'un milieu par une technique ultrasonore amène de nouvelles perspectives en termes d'imagerie et de diagnostic. Cependant, la méthode de mesure du paramètre de non linéarité est limitée par deux facteurs, la présence du speckle et la concentration de l'énergie à une profondeur donnée (la zone focale). Cette thèse a pour objectifs de répondre aux deux limitations mentionnées précédemment en proposant de nouvelles méthodes de lissage de l'image pour réduire le speckle et d'améliorer l'estimation du paramètre de non linéarité en mode écho par de nouvelles méthodes d'émission. Dans un premier temps, il a été proposé d'utiliser une méthode de filtrage spatiale basée sur des filtres orthogonaux (filtres de Thomson) lors de la formation de voie en réception pour lisser le speckle. Ce filtrage spatiale intervient après la transmission d'ondes planes sous différents angles pour améliorer la résolution spatiale et le contraste tout en accélérant la cadence d'imagerie. Dans un deuxième temps, l'estimation du paramètre de non linéarité est faite avec une méthode comparative. Le champ de pression du second harmonique d'une zone de référence est comparé avec le champ de pression d'une zone dont le paramètre de non linéarité est inconnu. Cependant, dans le cas des images échographiques, le champ de pression du second harmonique n'est pas accessible. Nous faisons l'hypothèse que la pression acoustique locale est liée à l'intensité de l'image échographique si le speckle est réduit et lissé. La transmission d'ondes planes et l'application de filtres orthogonaux permet de mieux délimiter le paramètre de non linéarité par rapport à une transmission focalisée / Nowadays, ultrasound imaging is a common diagnostic tool thanks to its non-invasive behavior and relatively cheap equipment. Classic medical echographic imaging is based on the linear response of the biological tissue. However harmonic imaging, based on the harmonic frequencies generated by the nonlinear properties of the tissue, is more and more used for clinical application. The quantification of nonlinearity is based on the evaluation of the nonlinearity parameter which strongly influences the harmonics generation. The nonlinearity parameter estimation using an echographic approach would bring new modalities for imaging and diagnosis. However the echographic method for nonlinearity estimation is limited by two factors: the presence of speckles in the image and the focalization used during transmission, which concentrates the energy at one particular depth. The objectives of this thesis work are developing novel approaches to reduce the speckle noise using original smoothing techniques and improving the nonlinearity parameter estimation in echo mode using new transmission-reception strategies. Firstly, new speckle noise reduction approaches were investigated. The Thomson’s multitaper approach was proposed, consisting in using several different orthogonal apodizations during beamforming. This method was combined to a coherent plane-wave compounding transmission-reception strategy improving the spatial resolution and the contrast while improving the frame rate. In a second time, the nonlinearity parameter was estimated using a comparative method. The second-harmonic pressure field of a reference area was compared to the pressure field of an area where the nonlinearity parameter is unknown. However in echo-mode, the pressure field of the medium is unknown. It is assumed in this thesis work that the local pressure can be derived from envelope image local amplitude if the speckle noise is smoothed. The nonlinearity parameter estimation has been improved using plane-wave transmission and orthogonal apodizations compared to the use of a single focalization transmission / Oggigiorno, le tecniche di imaging ad ultrasuoni sono un comune strumento di diagnosi, grazie alla loro non invasività e alla relativa economicità dei sistemi. La risposta lineare dei tessuti biologici è la base per le tecniche di imaging ecografico tradizionali. La generazione di frequenze ad armoniche superiori da parte dei tessuti può essere sfruttata per sviluppare tecniche di imaging innovative (i.e., imaging armonico), che sono sempre più utilizzate per applicazioni cliniche. Tali tecniche sono basate sul metodo di valutazione del parametro di non linearità che influenza fortemente la generazione delle armoniche all’interno dei tessuti. I metodi per la stima dei suddetti parametri sfruttano solitamente un approccio ecografico tradizionale. Di conseguenza, gli effetti legati alla focalizzazione impiegata durante la trasmissione, che concentra l’energia ad una particolare profondità, e la presenza di speckle nell’immagine finale, rendono più incerta la stima del parametro di non linearità. In questa tesi sono proposti metodi innovativi finalizzati a due scopi: ridurre, nelle immagini, il rumore dovuto a speckle, tramite l’adozione di nuove tecniche di smoothing; migliorare la stima dei parametri di non linearità, tramite l’impiego di nuove strategie di beamforming in trasmissione e ricezione. Per ridurre il rumore dovuto a speckle, è stato proposto un approccio di filtraggio spaziale basato sull’impiego dei filtri di Thomson. Tale tecnica consiste nell’impiego di numerose apodizzazioni ortogonali fra di loro in fase di beamforming. Il metodo è stato in particolare combinato con la tecnica di imaging coherent plane-wave compounding, con lo scopo di migliorare la risoluzione spaziale e il contrasto e, al contempo, incrementare il frame rate. Il parametro di non linearità è stato misurato tramite un approccio comparativo. Il campo di pressione della seconda armonica in un’area di riferimento dell’immagine è stato confrontato con quello di un’area in cui il parametro di non linearità è ignoto. In questa tesi, grazie alla riduzione del rumore speckle, è stato possibile assumere che il campo di pressione

This study investigates wave propagation in an elastic half-space with quadratic nonlinearity due to a line load on the surface. The consideration of this problem is one of the well known Lamb problems. Even since Lamb's original solution, numerous investigators have obtained solutions to many different variants of the Lamb problem. However, most of the solutions existing in the current literature are limited to wave propagation in a linear elastic half-space. In this work, the Lamb problem in an elastic half-space with quadratic nonlinearity is considered. For this, the problem is first formulated as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. The accuracy of the numerical method is first studied by comparing the numerical solution with the analytical solution for a half-space with linear response (the original Lamb's problem). The numerical results for the half-space with quadratic nonlinearity are than studied using signal-processing tools such as the fast Fourier transform (FFT) in order to analyze and interpret any nonlinear effects. This in particular gives the possibility to evaluate the excitation of higher order harmonics whose amplitude is used to infer material properties. To quantify and compare the nonlinearity of different materials, two parameters are introduced; these parameters are similar to the acoustical nonlinearity parameter for plane waves.

Although several studies have proven the accuracy of using a non-contact, air-coupled receiver in nonlinear ultrasonic (NLU) Rayleigh wave measurements, inconsistent results have been observed when working with narrow specimens. The objectives of this research are first, to develop a 3D numerical finite element (FE) model which predicts nonlinear ultrasonic measurements and second, to apply the validated model on the narrow waveguide to determine causes of the previously observed experimental issues. The commercial FE-solver ABAQUS is used to perform these simulations. Constitutive law and excitation source properties are adjusted to match experiments conducted, considering inherent effects of the non-contact detection, such as frequency dependent pressure wave attenuation and signal averaging. Comparison of “infinite” and narrow width simulations outlines various influences which impair the nonlinear Rayleigh wave measurements. When the wave expansion is restricted, amplitudes of the fundamental and second harmonic components decrease more significantly and the Rayleigh wavefronts show an oscillating interaction with the boundary. Because of the air-coupled receiver’s finite width, it is sensitive to these edge effects which alter the observed signal. Thus, the narrow specimen adversely affects key factors needed for consistent measurement of material nonlinearity with an air-coupled, non-contact receiver.

This research investigates wave propagation in an elastic half-space with a quadratic nonlinearity in its stress-strain relationship. Different boundary conditions on the surface are considered that result in both one- and two-dimensional wave propagation problems. The goal of the research is to examine the generation of second-order frequency effects and static effects which may be used to determine the nonlinearity present in the material. This is accomplished by extracting the amplitudes of those effects in the frequency domain and analyzing their dependency on the third-order elastic constants (TOEC). For the one-dimensional problems, both analytical approximate solutions as well as numerical simulations are presented. For the two-dimensional problems, numerical solutions are presented whose dependency on the material's nonlinearity is compared to the one-dimensional problems. The numerical solutions are obtained by first formulating the problem as a hyperbolic system of conservation laws, which is then solved numerically using a semi-discrete central scheme. The numerical method is implemented using the package CentPack. In the one-dimensional cases, it is shown that the analytical and numerical solutions are in good agreement with each other, as well as how different boundary conditions may be used to measure the TOEC. In the two-dimensional cases, it is shown that there exist comparable dependencies of the second-order frequency effects and static effects on the TOEC. Finally, it is analytically and numerically investigated how multiple reflections in a plate can be used to simplify measurements of the material nonlinearity in an experiment.