本論文總結了應用非破壞性檢測技術對於碳纖維增強複合材料的結構分析。由於碳纖維增強複合材料具備了較高的強度和較低的重量，因此該材料被廣泛應用於航天領域。但是，在製造複合材料過程中引入的一些缺陷會影響到複合材料部件的在實際應用中的表現。本論文的研究目的爲應用非破壞性檢測技術改善對航天複合材料部件的結構分析，以此來改進對缺陷在工業界內的檢測方法和提高對部件破壞行爲的分析手段。
本論文研發出一項創新的技術可以用來檢測碳纖維增強層壓板內的缺陷。這項技術的實現基於對含有面內波紋缺陷的共振行爲的研究。首先，振幅變動電子光斑影像干涉術和模態分析法結合起來獲取到了複合材料層壓板的振型。其次，在振型中可識別的節線區域的輪廓線被提取出來。提取輪廓線應用了專門爲此編寫的一套算法，該算法基於密度空間的聚類分析（Density-based spatial clustering of applications with noise）。傅裏葉描述子被用來分解提取到的輪廓線，以此來降低數據維度和進行數據對比。振型輪廓線的區別被用來識別缺陷是否存在於碳纖維層壓板內。這項對比節點區域輪廓線的技術可以極大地簡化條紋圖像的對比，來達到損傷檢測的目的。這項技術在驗證有限元模型的有效性方面同樣顯示出很大的潛力。
本論文也探討了應用有限元模型進行預測波紋缺陷導致的殘餘應變的研究。有限元模型預測的準確性可以通過與實驗數據進行對比得出。在此基礎上，本論文發明了一項創新的方法用來識別對超聲波C掃描數據進行處理的最佳算法。這些算法可以通過表徵超聲波C掃描數據獲得碳纖維的方向，以此來繪製出纖維取向圖。有限元模型的建立基於纖維取向圖，而纖維取向圖可以通過三種算法得到，分別是：拉冬變換（Radon transform）, 二維快速傅裏葉變換（2D fast Fourier transform），和索貝爾濾波器（Sobel filters）。試樣表面的殘餘應變可以通過對試樣在靜態下的面外位移的計算得到，面外位移可以通過數字影像相關法測量得到。模型預測得到的殘餘應變圖與實驗得到的殘餘應變圖可以被正交多項式分解成特徵向量來降低數據維度和進行量化對比。實驗數據與應用到優化參數的模型預測結果符合程度良好。通過對三種算法得到的有限元模型的預測表現進行對比，拉冬變換（Radon transform）表現最佳。
本論文研究了有缺陷的碳纖維層壓板在受力情況下的表現。四種不同程度的缺陷被引入到試樣中。通過四點彎折實驗，這些試樣被折斷。數字影像相關法（DIC）測量得到了在加載過程中試樣的上、下表面産生的逐漸變化的應變。對於含有少量缺陷的試樣，分層損傷是主要的破壞方式。對於含有大量缺陷的試樣，碳纖維的微屈曲先在缺陷區域發生，然後在受力面是壓應力的板層進行擴展，與此同時局部的分層損傷也會産生。有限元模型被用來預測斷裂行爲。內聚力模型被用來預測分層損傷，哈辛-羅特姆（Hashin-Rotem）斷裂準則應用到了UMAT（用戶自定義材料子程序）裡來模擬層內損傷。該模型有效地預測了含有不同程度缺陷的複合材料的斷裂行爲。這項關於分層損傷和微屈曲的研究對於了解含有面內波紋缺陷的複合材料的斷裂行爲至關重要。這些研究成果對於設計和維修含有面內波紋缺陷的複合材料部件來阻止上述斷裂行爲的産生也很重要。

This thesis summarises the research on the development of structural assessment of carbon fibre reinforced composites using non-destructive based techniques. Carbon fibre reinforced composites are widely used in the aerospace industry because of their high stiffness and low weight. However, the performance of composite parts is affected by defects induced during the manufacturing stage. The aim of this thesis is to improve the structural assessment of aerospace composites based on non-destructive measurements, such that defect identification in industry can be enhanced and better analysis of component failure can be achieved.
A novel technique for identifying defects in carbon fibre reinforced plates has been developed when investigating the resonance behaviour of defective composites with in-plane fibre waviness. Amplitude-fluctuation electronic speckle pattern interferometry combined with modal analysis were used to obtain the mode shapes of composite plates first. Then the contours of the nodal regions visible in the mode shapes were extracted using a specially developed algorithm based on density-based spatial clustering of applications with noise. Fourier descriptors were used to decompose the contours to reduce data dimensionality and make comparisons. The differences in contours can be used for identifying the presence of defects. This technique for nodal region comparison was found to greatly simplify the comparison of fringe patterns for the purpose of damage assessment and could potentially be used as part of validation procedures for finite element models.
This thesis also investigates the prediction of residual strains caused by fibre waviness using finite element models. Based on the prediction accuracy by comparing with experimental data, a novel method for identifying the most effective algorithm for characterising fibre orientation for the geometric ply map using ultrasonic C-scan data has been developed. Finite element models were generated based on the fibre-orientation data from three different algorithms: the Radon transform, 2D fast Fourier transform, and Sobel filter. Residual strains on the surface of the specimens were obtained from calculations based on the out-of-plane displacements measured using a digital image correlation system. The predicted and measured residual strain maps were decomposed into feature vectors using orthogonal polynomials to reduce data dimensionality and make quantitative comparisons. The measured residual strains and the predictions based on models using optimised parameters showed good agreement. The differences in performance were quantified based on the accuracy of the predicted residual strains, which showed that the Radon transform performed best.
The performance of defective composites under mechanical loadings were investigated. Four severities of in-plane waviness were induced in composite specimens. The specimens were loaded to failure using four-point bending tests, and progressive changes in strain in both the bottom and top ply of the specimen during the tests were obtained using digital image correlation (DIC). For specimens with lower level of waviness, delamination was the dominant failure mode. For specimens with higher level of waviness, micro-buckling of carbon fibres occurred first at the defective regions then propagated through the surface of the ply under compression, and local delaminations were also observed. Finite element analysis was used to predict the failure behaviour. A cohesive zone model was used to model the delaminations and Hashin-Rotem damage criterion was applied via a UMAT (User Material Subroutine) to model the intra lamina failure. The model was shown to be effective for predicting the failure of different severities of waviness. The investigation on the delaminations and micro buckling behaviour is crucial for understanding the failure mechanism of composites containing in-plane fibre waviness. The results should also be useful in designing and repairing composite components with in-plane fibre waviness to prevent potential occurrence of such damages.

Table of Contents
Abstract i
中文摘要（Abstract in Chinese） iii
Acknowledgements v
List of Figures ix
List of Tables xiv
1. Introduction 1
1.1. Background 1
1.2. Aim and Objectives 3
2. Literature Review 4
2.1. Formation of fibre waviness and its effect 4
2.2. Characterisation techniques for defects in composites 8
2.3. Non-contact measurement techniques 12
2.4. Fracture and failure analysis for composites 17
2.4.1. Failure modes 17
2.4.2 Failure criteria for composites 20
2.5. Shape descriptors and image decomposition 23
2.6. Knowledge Gaps 26
3. Experimental techniques 28
3.1. Pulse-echo ultrasonic inspection 28
3.2. Digital Image Correlation 29
3.3. Amplitude fluctuation electronic speckle pattern interferometry 30
4. Identification of defects in composite laminates by comparison of mode shapes from electronic speckle pattern interferometry 32
4.1. Introduction 32
4.2. Experimental Methods 33
4.2.1. Specimen preparation 33
4.2.2. Modal analysis by impact excitation 34
4.2.3. Modal analysis by shaker excitation combined with AF-ESPI technique 35
4.3. Results 36
4.4. Discussion 49
4.5. Summary 52
5. Prediction of residual strains due to in-plane fibre waviness 53
5.1. Introduction 53
5.2. Experimental Methods 54
5.2.1. Specimen preparation 54
5.2.2. Digital image correlation characterisation 55
5.2.3. Ultrasonic Inspection 56
5.3. Characterisation of fibre orientation and finite element analysis 57
5.3.1. Radon transformation-based algorithm 58
5.3.2. 2D fast Fourier transformation-based algorithm 58
5.3.3. Sobel filter-based algorithm 59
5.3.4. Finite Element Analysis 60
5.4. Results 63
5.5. Discussion 72
5.5.1. Comparison of the RT, FFT and the SF based algorithms 72
5.5.2. Validation of the models 74
5.6. Summary 76
6. Failure analysis for defective specimen with in-plane fibre waviness under four-point bending test 78
6.1. Introduction 78
6.2. Experimental methods 79
6.2.1. Specimen preparation 79
6.2.2. Ultrasonic Characterisation 79
6.2.3. Digital Image Analysis 79
6.3. Finite element analysis 81
6.3.1. Simulation of the test 81
6.3.2. Simulation of the defect 87
6.3.3. Simulation of the cohesive layers 88
6.4 Results 91
6.4.1 Bending test on specimens with fibre waviness 91
6.4.2 Delamination and micro-buckling analysis using DIC 93
6.4.3 Characterisation of the damage 97
6.4.4 Finite element analysis 100
6.5 Discussion 104
6.6 Summary 108
7. Discussion 110
7.1 Quantifying the severity of defects in CFRP composites 110
7.2 Improvement of utilisation of ultrasound data 112
7.3 Enhancement of failure assessment 113
7.4 Future work 114
8. Conclusions 117
References 120

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