# Assessment of the Length and Depth of Delamination-Type Defects Using Ultrasonic Guided Waves
## 2 Method for Assessment of Delamination Parameters  
### Interaction of A\({}_{0}\) Mode with Delamination-Type Defect  
Let us analyze a composite plate with length l and thickness h which is shown in Figure 1. It will be investigated with the 2D approach, which means that the plate is infinite along the \(y\) axis. Let us consider that the delamination-type defect is present in the structure, which is \(l_{1}\) long and situated at distances of \(l_{0}\) and \(l_{2}\) from the source (excitation) and monitoring (reception) points, respectively, at a depth of \(h_{1}\) with respect to the top surface. The delamination is parallel to the surface of the sample (Figure 1). The fundamental A\({}_{0}\) mode has been selected in this paper. As multiple guided wave modes are being generated simultaneously, different strategies exist to excite isolated modes, such as angle beam excitation [27], element width selection [28], inter-element spacing or interdigital transducers [29; 30], in-phase and out-of-phase excitation [31], etc. In this research the fundamental dispersion zone has been selected and the excitation frequencies were limited from 50 kHz up to 200 kHz. At such frequencies, the wavelengths of A\({}_{0}\) mode varies from 17.2 mm (at 50 kHz), to 5.6 mm (at 200 kHz) at 4 mm GFRP plate (\(E_{\text{x}}\) = 10 GPa, \(E_{\text{z}}\) = 35.7 GPa; \(\upsilon_{\text{xz}}\) = 0.325, \(\upsilon_{\text{zx}}\) = 0.091, \(\upsilon_{\text{yz}}\) = 0.35; \(G_{\text{xz}}\) = 2.8 GPa; \(\rho\) = 1800 kg/m\({}^{3}\)). This shows that both A\({}_{0}\), S\({}_{0}\) and higher order A\({}_{1}\) and S\({}_{1}\) modes can exist at such a constant wavelength (see Figure 2a). However, using a Plexiglas wedge (2700 m/s) as a coupling medium and normal incidence angles, the fundamental A\({}_{0}\) mode is being generated most effectively (see Figure 2b), and sophisticated mode isolation techniques were not applied. The signal of A\({}_{0}\) mode excited at the source point and measured at the monitoring point after propagation through the delaminated area will be the subject of all the upcoming investigations. Upon the interaction of A\({}_{0}\) mode with the delamination-type defect, the reflection, transmission and mode conversion occur at each end of the damage. In such a way, at the leading edge of the damage, the incident A\({}_{0}\) mode reflects back, and in the forward direction it splits into wave packets which accordingly propagate on the sub-laminates above and below the defect. Moreover, mode conversion occurs at the leading edge; therefore, part of the energy transforms into S\({}_{0}\) mode as well (see Figure 3a). Similarly, at the trailing edge of the damage, both A\({}_{0}\) and S\({}_{0}\) modes are reflecting back, propagating forward and converting to each other (see Figure 3b). This representation does not take into account the scattering coefficients of each reflected/converted mode. Figure 1: Schematic diagram of considered example of a composite plate with delamination-type damage. Figure 2: Phase velocity dispersion curves of 4 mm glass fibre reinforced plastic (GFRP) plate (**a**) and excitation angle versus frequency using Plexiglas as coupling medium (**b**). In this research, only the forward scattered wave-packets of A\({}_{0}\) mode will be considered; they are squared red in Figure 3b. Mathematically, the spectrum of the signal of A\({}_{0}\) mode \(U_{\text{IA0}}(f)\) which arrives first to the monitoring (reception) point can be expressed as:  
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