# Detection and Quantification of Damage in Metallic Structures by Laser-Generated Ultrasonics
## 1 Introduction  
During the life cycle of a metallic structure, the appearance of damage is inevitable due to the structure's complex working environments [1; 2; 3]. For example, the working environment of engine blades is very severe. These blades suffer from shock, friction and high temperatures as well as heating and cooling cycles. Therefore, it is very easy to produce cracks in the engine blades [1]. According to the statistics on predecessors, the failures in metallic structures caused by fatigue cracks account for more than 90% [4]. Each year, the breakdown and disorderly closedown of equipment caused by fatigue cracks cause owners to expend large amounts of time and money, and sometimes failures even threaten the operators' safety and lives [5; 6]. These safety and economic considerations have spurred research within the field of NDT of metallic structures in the past few years. Among various structural damage detection techniques, such as infrared testing [7], eddy current testing [8; 9], magnetic particle testing [10], and ultrasound testing [11; 12], the ultrasound testing technique has been widely used due to its relatively high spatial resolution, portable operation, high performance ratio, and high effectiveness in damage detection. By recording the ultrasonic waves propagating through a structure, macroscopic damage such as cracks, inclusions, and notches can be detected by using this method [5]. Influenced by the linear interaction between propagating waves and damage, the ultrasonic waves experience reflection, diffraction, and mode conversion. By extracting metrics from the response waves, the damage can be defined. Notably, most damage detection techniques use linear metrics extracted from response waves to detect damage, namely, the damage is assumed only to affect the structure in a linear way. However, according to [PERSON]'s study [12], damage evolution is a nonlinear process that initiates certain nonlinear properties in the structure. When dealing with nonlinear damage, linear ultrasonic waves may lose their effectiveness and reliability. Recent studies have shown that nonlinear ultrasonic waves are usually more sensitive to small cracks than classical linear ones. In the nonlinear ultrasonic techniques, a fatigue crack plays the role of a nonlinear radiation source [13]. It will distort the original propagating ultrasonic waves and generate different waves with new frequency components as shown in Figure 1. This makes the new nonlinear component a damage-sensitive feature for damage detection. [PERSON] et al. [14] investigated the application of the nonlinear vibro-acoustic modulation technique for the assessment of fatigue cracks in steel beams and nickel-based alloy plates. In their experiments, the specimens were subjected to both a low ultrasound frequency and a low structural vibration frequency. The ratio of the average first sideband amplitude over the ultrasonics carrier was proposed as a nonlinear feature to assess the cracks. [PERSON] et al. [13] also investigated the application of the vibro-acoustic modulation technique for the detection of cracks in steel pipes. They delimited the Modulation Index as a crack-sensitive feature. The influence of the frequency and amplitude of vibration on the sideband amplitudes was experimentally investigated. [PERSON] et al. [15] conducted nonlinear modulation measurement for non-destructive testing of the cracks in aluminum plates and scaled steel shafts. The nonlinear spectral coefficient was used to isolate the nonlinear modulation components from noisy environments and show a higher sensitivity to fatigue cracks than the traditional nonlinear coefficient. [PERSON] et al. [16] investigated the application of the linear surface acoustic waves and the nonlinear surface acoustic waves in non-destructive testing of surface cracks. They demonstrated that the nonlinear surface acoustic waves could be more effective to crack detection. [PERSON] et al.