# A Nonlinear Method for Characterizing Discrete Defects in Thick Multilayer Composites
## 1 Introduction  
Carbon Fiber Reinforced Polymer (CFRP) is one of the most widely used multilayer composites in aerospace due to its specific features, such as high ratio of strength to weight, high modulus, and high fatigue resistance. Discrete defects, like larger voids, delaminations, and cracks can occur during manufacturing or service process, and they may result in a significant loss of mechanical properties [1]. Thus, early defect detection is essential to avoid serious problems that are caused by defects. Nondestructive testing (NDT) has been employed to characterize discrete defects in composite structures for many years [2; 3]. As an important NDT method, ultrasonic testing has been widely used in the evaluation of defects in CFRP. [PERSON] et al. [4] used the ultrasonic arrays technique to improve the characterization of side drilled holes in a 19 mm thick CFRP block, in which the holes were 1.5 mm in diameter and 16 mm in length and down to a depth of 16 mm. [PERSON] et al. [5] performed single-sided technique of contact pulse-echo inspection on CFRP specimen with thickness of 10 mm, to study the effect of crack in the middle of the specimen, while the length of the crack is approximately 25 mm. [PERSON] et al. [6] have successfully applied a two-dimensional fast Fourier transform (2D-FFT) method to B-scan images for detecting out of plane fiber waviness in structures that are as thick as 18 mm. Most researches of inspecting thick CFRP were focused on defects with large sizes, however defects, such as larger voids or micro-cracks, may be smaller than 1 mm. It is not yet able to specify limitations for discrete defects in thick section CFRP. More reliable and quantitative studies are required [3]. Unlike the signals of metallic materials, there are no clearly identifiable defect echoes in the signal of multilayer composites, since the fiber layer with a different direction may also cause a reflected ultrasonic echo [7]. Although ultrasonic inspection can be performed in a variety of physical configurations, for example, the ultrasonic array, pulse-echo inspection is most straightforward and practical among all of the ultrasonic techniques. The detection of discrete defects is mainly based on signal processing of the backscattered signal, which is between the front surface echo and the back wall echo in a typical ultrasonic signal, as shown in Figure 1. Due to the layered structure with a layer thickness that is close to the wavelength of the ultrasonic pulse, the backscattered signal will exhibit resonance noise that is continuously attenuated. [PERSON] [8] believes that the frequency continuity and amplitude degradation of backscattered signals will be destroyed for local defects, which can be detected by time-frequency analysis and time-energy analysis. This method is effective for thin CFRP. However, as the thickness of the material increases, defects may occur in the portion where the resonance noise has been attenuated, and the defect echoes are mixed with echoes that are caused by the material structure. The amplitude and energy of the backscattered signal are low, while the signal-to-noise ratio (SNR) of the defect is also low. Thus, the defect echo in the second half of the backscattered signal of the thick section CFRP cannot be well distinguished by traditional time-frequency analysis or time-energy analysis. In order to solve the problem of characterizing defects in composites, model driven methods, such as ultrasonic pulse-echo modeling and structural modelling of composites, have been researched. A generalized parametric ultrasonic echo model and algorithms for accurately estimating the parameters have been presented in literature [9]. In Part II of the study, the advantage of the model-based estimation method in ultrasonic applications has been explored [10]. Using model-based methods, the ultrasonic signal waveform consisting of multiple overlapping echoes from within thin multilayer structures has been successfully reconstructed [11].