# Assessment of the Length and Depth of Delamination-Type Defects Using Ultrasonic Guided Waves
## 4 Verification of Proposed Delamination Depth and Length Estimation Technique
### Verification with 3D Model  
In order to verify the applicability of the method for the real measurement, the 3D case was investigated. The reason for that is that in the case of 2D modeling of guided waves, the diffraction  
Figure 14: The vertical component of the particle velocity at nodal point \(r_{2}\) for sample No. 1 (**a**) and sample No. 2 (**b**) showing the converted and direct A\({}_{0}\) modes along with estimated delay values. does not affect the signals, in contrary to the 3D case when diffraction takes place, and signals can be overlapped with boundary reflections. There are many signal processing methods which work perfectly in the case of 1D or 2D models; however, they still fail when they are applied for real structures or 3D models. So, the verification of the method for a 3D case is very important for the assessment of the potential of the method for in situ applications. For this purpose, a 3D GFRP numerical model with the dimensions of 600 mm \(\times\) 300 mm \(\times\) 4 mm was employed with a square (90 mm \(\times\) 90 mm) delamination-type defect, located at 1.6 mm below the top surface. The defect was centered both according to the \(x\) and \(z\) axes (Figure 15). The structure was meshed by using SOLID64 elements which had eight nodes each with three degrees of freedom. The properties of the GFRP structure were the same as it was described in the previous sections. The spatial size of the element was set to 0.8 mm, which corresponds to 16 nodes per wavelength for A\({}_{0}\) mode at 90 kHz central frequency. In total, four 3D models were created, each with a different excitation frequency which was varying from 90 kHz to 150 kHz with an increment of 20 kHz. The excitation zone was a square with dimensions of 10 mm by 10 mm. It was centered according to the \(x\) axis and had an offset of 200 mm from the origin of the \(z\) axis. The excitation signal in all the cases was a Gaussian envelope tone burst of three cycles in order to correspond to the previous experiments. A\({}_{0}\) mode was introduced by applying the normal out-of-plane nodal displacements to the top surface of the sample at a predefined area of 10 mm\({}^{2}\). The integration step in the time domain was 0.625 \(\upmu\)s, which is 1/18 of the period at 90 kHz central frequency. The sketch of the numerical model used in this study is presented in Figure 15.  
The magnitude variation of A\({}_{0}\) mode was estimated at various excitation frequencies (\(f_{1}\) = 90 kHz, \(f_{2}\) = 110 kHz, \(f_{3}\) = 130 kHz, \(f_{4}\) = 150 kHz) and compared to the database of predictions at different defect depths (\(h_{11}\) = 0.4 mm, \(h_{12}\) = 0.8 mm, \(h_{13}\) = 1.2 mm, \(h_{14}\) = 1.6 mm) and lengths (\(l_{1}\), \(l_{2}\),... \(l_{n}\)). The comparison between the measured magnitude variation from the 3D model and the prediction at the defect size of 90 mm is presented in Figure 16. As it can be observed, the approximated curve which goes through the measured magnitude values (the solid line) is close to the prediction at depth \(h_{14}\) (the dash double-dot line). This depth of the damage corresponds to the actual depth used in the model. To measure the match between the measurement and the reference dependency, the parameter \(h_{\text{opt}}\) described by Equation (4) was used. The results are summarized in Table 2.  
Figure 15: Sketch of 3D GFRP numerical model which was used for the verification of the damage size and the depth estimation technique. The results presented in Table 2 show that the correct damage depth estimation was observed by using the parameter \(h_{\text{opt}}\). For the damage length estimation, the delay between direct and converted A\({}_{0}\) modes was estimated at a frequency of \(f_{4}\) = 150 kHz. The measured delay was equal to \(\Delta t_{\text{A0}}\) = 38.1 \(\upmu\)s. It was compared to the estimated delay at a defect depth of \(h_{14}\) = 1.4 mm. It can be observed that the estimated delay values correspond to the defect length of 84.1 mm.