# Assessment of the Length and Depth of Delamination-Type Defects Using Ultrasonic Guided Waves
## 1 Introduction  
Delamination is one of the most common defects found in fiber-reinforced composite laminates due to their weak transverse tensile and inter-laminar shear strengths [1]. Such defects may be caused by an impact and tend to develop internally between the neighboring fiber layers of the laminate. This results in loss of the strength of the structure without any visual evidence. As a result, sophisticated non-destructive testing and signal processing techniques are of great significance for the structural integrity assessment of fiber reinforced laminates. Ultrasonic guided wave structural health monitoring (SHM) emerged as one of the most powerful tools which uses a network of embedded sensors to detect and continuously track the development of such defects in various industrial fields [2]. SHM systems usually employ ultrasonic guided waves which propagate in elongated thin-walled structures, possess low attenuation and are sensitive to the integral elastic properties of the material; thus, they can be used to infer large structures with only a few coupled transducers. Numerous researches have targeted non-linear, multimodal behavior, scattering and energy leakage of guided waves for the detection and sizing of delamination-type defects [3; 4; 5; 6; 7]. By interaction of guided waves with delamination, waves are scattered and converted to other modes [8]. The mechanism of wave scattering depends on the type of the guided wave mode as wellas on the depth and size of the defect. Various investigations have demonstrated that A\({}_{0}\) and S\({}_{0}\) modes of guided waves propagate in the two regions divided by the delamination individually and then interact with each other after exiting the defect [9; 10]. The anti-symmetric modes are found to be more suitable for the assessment of delaminations as they show higher sensitivity to delamination located at different through-thickness positions compared to the symmetric mode [11]. A few studies on A\({}_{0}\) mode interaction with asymmetrical and symmetrical delaminations in laminated composites were presented by [PERSON] et al. [12; 13]. It was found that, in the case of symmetrical delamination, incident A\({}_{0}\) mode and converted A\({}_{0}\) (A\({}_{0}\)\(\cdot\)S\({}_{0}\)\(\cdot\)A\({}_{0}\)) mode propagate after the exit of delamination. In the case of an asymmetrical defect, an additional S\({}_{0}\) mode (A\({}_{0}\)\(\cdot\)S\({}_{0}\)\(\cdot\)S\({}_{0}\)) appears upon the interaction with the defect. The authors also proposed the method for the assessment of the delamination size based on the time-of-flight measurement of A\({}_{0}\) mode [14]. However, such a method appeared to be valid at low dispersion regions of A\({}_{0}\) mode as the velocities in the upper and lower sub-laminate layer of the defect were assumed to be equal to the velocity in the entire structure. In case of sub-surface delaminations, the velocities in sub-laminates can be essentially different, which leads to high errors. Lamb wave scattering and conversion at the leading and trailing edge of delamination is another topic which has been extensively studied by numerous research groups. For example, [PERSON] et al. [15] estimated frequency-dependent scattering coefficients for fundamental Lamb wave modes separately at the leading and trailing edges of delamination. [PERSON] et al. [16] developed a technique to locate the delamination-type defects by using two embedded transducers and an S\({}_{0}\) mode by measuring signals reflected from the tip of the defect. A study on S\({}_{0}\) mode interaction with the delamination-type defect was presented, which showed that, at each end of delamination, the transmitted and reflected A\({}_{0}\)/S\({}_{0}\) modes are being generated with each mode having different reflection and transmission coefficients depending on the local bending stiffness of the structure. An extensive study on Lamb wave mode conversion in a 2D plate containing a finite length delamination parallel with the surface was presented by [PERSON] and [PERSON] [17].