| Author: | Xu, Lei |
| Title: | Quantitative characterization of three-dimensional fatigue cracks using nonlinear ultrasonic waves : a framework from analytical modeling to noncontact implementation |
| Advisors: | Su, Zhongqing (ME) |
| Degree: | Ph.D. |
| Year: | 2022 |
| Subject: | Ultrasonic waves Materials -- Fatigue -- Testing Fracture mechanics Structural health monitoring Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Mechanical Engineering |
| Pages: | xxiv, 192 pages : color illustrations |
| Language: | English |
| Abstract: | Beyond the detectability of ordinary nondestructive evaluation (NDE) and structural health monitoring (SHM) methods, microscopic damage, as typified by embryonic fatigue cracks with their characteristic dimensions being remarkably smaller than the wavelength of a probing ultrasonic wave, is often overridden by damage detection approaches using ultrasonic waves. This remarkably jeopardizes the integrity of engineering structures under cyclic loads, under which hairline fatigue damage is initiated. Nonlinear guided ultrasonic wave (GUW)-based methods have demonstrated their capability of evaluating undersized fatigue cracks (with dimensions smaller than 1/10 of the probing wavelength), most of which, however, are developed based on the hypothesis that a fatigue crack, at its embryonic stage, can be simplified as a two-dimensional (2D) scenario which penetrates the entire thickness of the waveguide. Nonetheless, real-world fatigue cracks (e.g., surface cracks and corner cracks), particular at their initial stages, are three-dimensional (3D) and in a non-penetrating manner. As the non-penetrating stage constitutes the majority of the entire fatigue life of a crack, such simplification makes the characterization results debatable. On the other hand, most approaches exploring the nonlinear features of GUWs for damage identification and evaluation are of a nature of numerical simulation and experimental observation. There is obvious insufficiency of analytical interrogation to shed light on underlying physical aspects of nonlinearity in GUWs induced by microscopic structural damage and embryonic fatigue cracks in particular. Motivated by this, a SHM framework making use of the second harmonic generation of GUWs is developed in this PhD study, aimed at quantitative characterization and continuous monitoring of 3D, non-penetrating fatigue cracks. To start with, a dedicated elastodynamic reciprocity-driven model is elaborated to interpret the second harmonic generation of Lamb waves induced by the 'breathing' behavior of a crack from an analytical perspective. The model yields a closed-form solution to the modulation mechanism of a 'breathing' fatigue crack on Lamb wave propagation. On this basis, the magnitude of crack-induced second harmonic can be determined. By virtue of the model, a nonlinear damage indicator, governed by the quantified second harmonic generation by the crack, is defined and proven proportional against crack surface area. With the indicator, crack severity can be calibrated in a quantitative manner. Finite element (FE) simulation is performed to verify the analytical model and demonstrate its accuracy when used for characterizing damage onset. Experimental validation is conducted to verify the proportional trend of the defined damage indicator with respect to crack severity. Different from 2D, through-thickness cracks that only grow in the direction of crack length, a 3D, non-penetrating crack progresses in both the length and depth under a cyclic fatigue load, until its depth penetrates the entire thickness of the waveguide. To quantitatively characterize and continuously monitor a non-penetrating fatigue crack, from its initiation, through progressive growth to formation of a macroscopic crack, the developed framework embraces two steps, in which the nonlinear ultrasonic testing and prediction of crack growth based on fracture mechanics are respectively performed. In the first step, the proposed elastodynamic reciprocity-driven analytical model is employed to interrogate the generation of second harmonic of Lamb waves under the nonlinear modulation of 'breathing' behavior of a non-penetrating fatigue crack. By making use of the defined nonlinear damage indicator, the surface area of the non-penetrating fatigue crack can be estimated quantitatively. In the second step, a 3D fatigue crack growth model, originated from the fatigue crack growth theory, predicts the shape evolution and the continuous growth of the identified crack in the length and depth along the crack front. The two-step framework is validated using FE simulation, followed with experiment, in both of which the initiation and progressive growth of a real corner fatigue crack emanating from a fastener hole is monitored, with continuous prediction of the corner crack growth in length and depth. Experimental results have demonstrated the accuracy and precision of the developed modeling framework for quantitatively characterizing embryonic fatigue cracks. In a high frequency-thickness product scenario which results from a large thickness of the waveguide or a high frequency of the incident guided wave (i.e., laser-generated ultrasonics), the guided waves propagate in the form of Rayleigh surface waves. With the wave energy dominance near the wave guide surface, Rayleigh wave is an excellent candidate for detecting and characterizing damage near surface. Nevertheless, theoretical interpretation on underlying physics of Rayleigh wave scattering by a defect remain a daunting task, owing to the difficulty in analytically modeling the stress and displacement fields of a Rayleigh wave in the vicinity of a defect, in an explicit and accurate manner. In this backdrop, the elastodynamic reciprocity-driven model, along with a virtual wave approach, has been extended to depict the linear scattering of Rayleigh waves by a fully open surface crack and the nonlinear scattering by a crack with 'breathing' and rubbing behaviors. For a fully open surface crack, an analytical solution to the magnitude of scattered wave is obtained and the scattering effect is found to be dependent on the frequency of incident waves. For a 'breathing' surface/sub-surface crack, the generated second harmonics are modeled analytically, and the harmonic magnitudes are quantified, leading to an analytical solution to nonlinear Rayleigh wavefield in the crack vicinity. Proof-of-concept FE simulation and experiment are performed, respectively, to validate the analytical model and the solution. Results have confirmed the validity of the analytical modeling and solution for quantitative characterizing embryonic material defects that are on or near structural surfaces. Noncontact implementation of the developed framework is conducted via a laser ultrasonic technique (LUT). The pulsed laser is focused as a line wave source to generate wideband Rayleigh waves which are captured before and after the interaction with a surface crack. By performing frequency analysis, the spectra of the undistorted wave and transmitted wave are obtained, based on which a spectral damage indicator is defined to assess the scattering effect of the surface crack at different frequencies. The frequency-dependent scattering of Rayleigh waves by a surface crack, predicted by analytical modeling and confirmed by FE simulation, is also observed in experiment, which demonstrates the validity of the noncontact implementation of the framework for quantitative evaluation of surface cracks. In conclusion, this PhD study starts from analytical modeling for elucidating the second harmonic generation of Lamb waves by a fatigue crack, combines numerical and experimental investigation to identify microscopic damage, establishes a SHM framework for quantitative characterization and continuous monitoring of 3D fatigue cracks and conducts the noncontact implementation of the framework. By making use of defect-induced nonlinear attributes of GUWs, the 3D, non-penetrating fatigue crack, a prevailing embryonic damage in engineering structures, is identified and characterized quantitatively with the developed framework. This study is expected to provide a solution for early awareness and quantitative evaluation of embryonic fatigue cracks, with potential to greatly improve the accuracy and advance the practical employment of existing SHM approaches. |
| Rights: | All rights reserved |
| Access: | open access |
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