An insight into nonlinearity of guided ultrasonic waves in fatigued materials based on a nonlinear local interaction simulation approach : theory, modelling and experimental validation

PolyU Library Call No.: [THS] LG51 .H577P ME 2017 Radeckixxxiii, 281 pages :illustrationsThe non-destructive evaluation (NDE) techniques making use of guided ultrasonic waves (GUWs) have been well developed for years. In particular, the Rayleigh-Lamb waves (RLWs), as a representative type of the GUWs are extensively used in NDE, as well as structural health monitoring (SHM). However, most of the existing approaches have been developed based on the use of linear features of the RLW, for example the change of the amplitude or the time-of-flight. Although those approaches are normally effective to inspect damage in large-scale structures, from infrastructure to mechanical systems, where the tolerance for the damage size is above few millimetres, they may not be enough for undersized damage. To circumvent such a deficiency, the analysis of the nonlinear features of RLWs was introduced, which can be induced to the wave through different sources, such as fatigue cracks, de-bonding at adhesive joints, plastic zone in materials, or the medium itself owing to material nonlinearity. The influence of these nonlinear sources on the representation of the wave signal in frequency domain can be observed by exploiting such features as the mixed frequency responses (e.g. nonlinear wave modulation spectroscopy), shift of resonance frequency (e.g. nonlinear resonant ultrasound spectroscopy), dual frequency mixing, high-or sub-harmonics generation as reviewed in [72]. The high-order harmonics generation is a nonlinear feature of the particular interest. It is the energy transfer of the incident wave from the fundamental frequency w0 to its high-order harmonics (2w0, 3w0 and so on). The aim of the current work is to achieve an insight into the high-order harmonic generation due to the presence of the different sources of nonlinearities in an examined structure, and particularly the "breathing" type damage (such as fatigue crack). The waves concerned are generated by coupled PZT elements. The available theoretical knowledge in numerical and experimental nature is reviewed to understand the behaviour of the generated high-order harmonic, precisely, the second order harmonic, due to the presence of the nonlinear material and "breathing" damage. By extending the nonlinear Local Interaction Simulation Approach (LISA) in conjunction with the use of the Spring Model (SM), a dedicated modelling and numerical simulation approach is developed to advance the insight into the generation and accumulation of nonlinearity of guided waves propagating in fatigued materials. The accuracy of the calculated numerical simulation, while considering the synchronism condition is examined. Moreover, the waves excited in the low-and high-frequency regions of the Lamb wave dispersion curves are analysed. Various cases are examined depending on the few characteristics, such as the type of the excitation used, the size and the placement of the damage. The presented results exhibit interesting features, which give different view on the modelling of the high-order harmonic generation in the contrast to the available literature. The results from the performed experiment are shown as a validation of the developed model.The first part of the work is focused on the review of the available analytical solutions of the high-order harmonic generation and propagation in the elastic, isotropic and homogenous structure. For the purpose of comparison, the numerical method-Local Interaction Simulation Approach (LISA) - is expanded by the hyper-elastic material definition in the two-dimensional matter. The cumulative synchronism condition of the high-order symmetric mode was considered, which states that if between two considered modes the phase velocity matching and the non-zero power flux conditions are satisfied, the linearly increasing pattern of the second harmonic with the propagation is observed. The increasing pattern of the second harmonic was observed. However, the trend was in the slight contradiction to the analytical prediction. Instead of the linear increase with the propagation distance, the slight flattening was observed, suggesting that the obtained behaviour is for the case of the approximate phase velocity matching, not exact. Such observation has its roots in the definition of the numerical simulation and it is discussed in the work. The second part of this work is focused on the nonlinearity induced by "breathing" fatigue crack. The conjunction of the nonlinear LISA method with the SM approach was used in order to analyse the influence on the generated second harmonics, and also, the interaction of second harmonic modes generated from different sources of nonlinear behaviour. It was observed, that depending of which excitation types is chosen, the resultant second harmonic magnitude may have different trends upon the propagation distance. Final part of the work contains the results from the experiment performed to validate the developed numerical simulation model. The consistent results were obtained, which give a great potential for further development in the areas of numerical simulations and nonlinear damage detection applications. The conclusions drawn from this study are: 1. The cumulative synchronous pair can be also found among the basic Lamb wave modes; 2. The difference of the second harmonics magnitude behaviour on the propagation distance, when considering various excitation types, is more visible for the high frequency Lamb wave mode pair than for the low frequency mode pair; 3. High influence of the defined numerical parameters and beam thickness on the propagating second harmonic, generated from the high-order symmetric Lamb wave mode pair, is observed; 4. The relative acoustic nonlinear parameter ß' exhibits more appropriate features of defining the damage severity in the structure than analysing the second harmonic magnitude alone; and 5. It is shown through experimental and numerical investigation that the nonlinear material does not have a major influence on the generated second harmonic due to the "breathing" crack phenomenon, for the certain amplitudes of excitation.Department of Mechanical EngineeringPh.D., Department of Mechanical Engineering, The Hong Kong Polytechnic University, 2017Doctorat