# Guided Wave-Based Monitoring of Evolution of Fatigue Damage in Glass Fiber/Epoxy Composites
## 1 Introduction  
Nowadays, composites are widely used in engineering structures due to their advantages of light weight, high specific stiffness and strength. However, in the long run, fatigue damage initiated with matrix cracks may inevitably accumulate in composite structures under cyclic loads. If this kind of fatigue damage cannot be detected in time, it may continue to grow with new emerging damage patterns such as delamination and fiber breakages, leading to catastrophic failure of the structures [1; 2]. Thus it is very important and crucial to develop structural health monitoring (SHM) techniques to detect the fatigue damage inside composite structures and, if possible, to continuously monitor its evolution [3; 4; 5; 6; 7; 8; 9; 10; 11]. During the past two decades, a lot of techniques and methods as well as sensor networks have been proposed to detect and identify damage in composites [12; 13; 14; 15; 16; 17]. Among them, the guided wave-based approach is considered as one of the most promising techniques. Using advanced signal processing techniques, damage could be detected and identified by extracting characteristic information contained in transient guided waves. A wide range of theoretical and experimental studies have been performed to demonstrate the effectiveness of damage detection and identification using guided waves [18; 19; 20; 21; 22; 23; 24; 25; 26; 27]. However, most of these methods focus on impact damage which is localized damage phenomenon instead of extended damage such as those caused by cyclic fatigue loads [28; 29]. Usually, in the initial stage, fatigue damage in composites mainly contains accumulated micro matrix cracks, resulting in a gradual stiffness degradation [1; 2]. Thus, for monitoring fatigue damage in composites, it is a straightforward way to monitor the degradation of stiffness to reflect the internal damage. For example, [PERSON] et al. studied the change of velocities and amplitudes of guided waves in thermal-mechanical aged composites. They found that the velocities of symmetric S0 Lamb waves reduced with the reduction of the in-plane stiffness, demonstrating that the accumulated fatigue damage in composites can be characterized by measuring the velocities of the waves [28]. [PERSON] et al. employed noncontact technique to excite and receive guided waves in composite under different fatigue loading conditions, and studied the relationship between the change of wave velocities of antisymmetric A0 Lamb waves and the stiffness degradation [29]. Further, to quantitatively indicate the internal fatigue damage, studies have been performed to identify the elastic properties of composites under different fatigue states by using guided waves and try to relate the reduction of elastic properties with internal matrix cracks with micromechanics models. For example, [PERSON] et al. used semianalytical finite element (SAFE) method to model the dispersion curves of guided waves in an anisotropic composite plate, and combined the experimentally obtained dispersion curves from time-frequency analysis to identify the elastic parameters [30]. [PERSON] et al. used a laser-ultrasonic system to measure the phase velocity of ultrasonic guided waves in composites, and then employed genetic algorithm combined with the measured phase velocity to invert the elastic modulus [31]. [PERSON] et al. selected phase velocity of the S0 mode Lamb wave in the low frequency region to characterize the fatigue damage in a composite laminate under cyclic loads in different fatigue stages. They also used the phase velocity and damage model to predict the evolution of fatigue damage [32]. In contrast to the aforementioned velocity-based characterization methods, researchers also used signal features to characterize fatigue damage in composites with guided waves [33; 34; 35; 36]. By extracting the damage-sensitive feature from the received guided waves, the fatigue damage can be classified and identified. For example, [PERSON] et al. used guided waves for in situ fatigue life prognosis for composite laminates.