Approximate Phase Velocity Matching Based S0 Mode Nonlinear Lamb Waves for Characterizing and Evaluating Microstructural Damages in Plate-like Structures

S0模態相速度近似匹配的板狀結構微損傷非線性蘭姆波表徵與評估

Student thesis: Doctoral Thesis

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Award date24 Jul 2017

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Abstract

Plate-like structures have been widely used in many safety-critical engineering equipment in aviation, spaceflight and navigation fields. There is an urgent need using NDT (non-destructive testing) methods for the evaluation and characterization of early material degradations and microstructural damages. Among various NDT methods, the method of nonlinear ultrasonic Lamb waves has emerged to be a promising and attractive inspection approach for characterizing microstructural changes, as it possesses the early damage detection capability of nonlinear ultrasound with the efficient large-scale inspection ability of Lamb waves. However, the traditional used PVM-NLW (Phase Velocity Matching based Nonlinear Lamb Waves) method has certain limitations, such as not suitable for inspecting large-scale structures, unable to characterize internal micro-scale damages and high signal complexity. Therefore, a new method for efficiently characterize and evaluate internal micro-scale damages in a large-scale plate is demanding.

By using the almost non-dispersive nature of S0 mode at low frequencies, APVM-S0-NLW (Approximate Phase Velocity Matching based S0 mode Nonlinear Lamb Waves) is proposed to overcome the drawbacks of PVM-NLW. Two parameters are proposed to reflect the cumulative effect of APVM-S0-NLW method. They are MCPD (Maximum Cumulative Propagation Distance) and MLCPD (Maximum Linear Cumulative Propagation Distance). The effectiveness of the method is verified by both numerical and experimental studies. The results show that the proposed APVM-S0-NLW has addressed the shortcomings of the traditional PVM-NLW. The proposed method is preferable in real applications as the signal complexity and the requirements for the experimental equipment can be significantly reduced. It provides a new method for effectively evaluating microstructural damages in large-scale structures.

Although APVM-S0-NLW overcomes the limitations of PVM-NLW, it results in two disadvantages simultaneously. First, the excited fundamental frequency can only lie in a narrow range within which the dispersion curve of phase velocity is almost flat. Second, low fundamental frequency reduces the sensitivity. In this thesis, we propose to use SC-S0-NLW (Static Component of S0 mode Nonlinear Lamb Waves) to improve these two weaknesses. The result shows that SC-S0-NLW has improved the weakness of APVM-S0-NLW. Furthermore, it provides another alternative for characterizing micro-scale damages in structures.

Micro-scale damage induced nonlinearity is derived by using one-dimensional model. It is improper and difficult to be integrated into the existent formulations to analytically and numerically predict second harmonic amplitude of nonlinear Lamb waves. This issue was resolved by assuming that the third order elastic constants, A, B, and C are a function of microstructure. In this way, the strain energy function can be expressed as a function of microstructure. This provides theoretical basis for the characterization of distributed microstructural damages in an inspected structure.

Compared to globally distributed microstructural damages, little attention has been paid to characterize the locally distributed microscale damages which are located at certain region but not in the entire material. Reflection and transmission characteristics of a locally distributed microstructural damage are analyzed. Based on these characteristics, locally distributed micro-scale damages are characterized. The effects of the length, width, location and constant volume with varying length and width of localized degradation area on the relative nonlinear parameter are studied. The results show that the method using APVM-S0-NLW is capable of characterizing locally distributed degradation located at any location of a plate.

The surface-breathing crack implemented by the “birth and death” model in the previous studies cannot reflect the actual situation of a crack interacting with ultrasonic waves. A more realistic micro crack model is built and performed in Abaqus software. The micro crack is modelled as oval shape with its two surfaces applied contact and frictionless property. Second harmonic components in the reflected and transmitted waves generated due to the interactions between S0 mode Lamb waves and the micro crack are analyzed. Dependence of the relative nonlinear parameter on the length and width of a micro crack is investigated. The results show that APVM-S0-NLW is suitable for detecting and characterizing micro cracks, especially the ones buried in the interior of an inspected structure.

At last, APVM-S0-NLW and SC-S0-NLW are applied to characterize the evolution of fatigue damage in aluminium plates. The normalized relative nonlinear parameter as well as the normalized relative static nonlinear parameter with the fatigue time are obtained. The relationships help to evaluate fatigue levels of a structure. These two parameters also provided valuable information for identifying the existence of a micro crack. These results verifies that APVM-S0-NLW and SC-S0-NLW are suitable to provide early warning on early microstructural damages occurred in the inspected plates or plate-like structures.