# Assessment of the Length and Depth of Delamination-Type Defects Using Ultrasonic Guided Waves
## 5 Conclusions  
A model-based method to estimate the absolute depth and length of delamination was proposed which is based on the magnitude variation pattern and the time-of-flight measurement of A\({}_{0}\) mode at different excitation frequencies.  
A reference dependency estimation technique was developed which allows predicting the magnitude variation patterns of A\({}_{0}\) mode at different depths and lengths of a delamination-type defect. It was shown that, in comparison with the experimental measurements, the reference dependencies can be used to extract the absolute depth of the delamination. The proposed delamination depth estimation technique exploits the phase velocity dependency of A\({}_{0}\) mode on the thickness of the sub-laminate, thus, different magnitude variation patterns at different excitation frequencies are observed. As a result, the proposed method provides improved depth estimation accuracy even in the presence of significant dispersion. Furthermore, finite element verification demonstrated that the defect depth can be estimated with a high accuracy even in those cases when the thickness of the sub-laminate that is created by the presence of the defect is relatively thin in comparison with the wavelength of A\({}_{0}\) mode. The performance of the proposed method was demonstrated and verified in detecting and describing delamination-type defects of various lengths and depths.  
It was demonstrated that the length of delamination at a fixed depth can be reliably estimated from the delay time between the converted and direct A\({}_{0}\) modes by exploiting the conversion of the incident A\({}_{0}\) mode to S\({}_{0}\) mode within the defect. The proposed approach uses previously obtained information about the depth of the defect, which allows for the determination of the phase velocities of A\({}_{0}\) and S\({}_{0}\) modes in the upper and lower sub-laminates. The results of our numerical validation demonstrated that the size of the defect can be reconstructed with an error of approximately 6%.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \(h_{11}\) = 0.4 mm, & \(h_{12}\) = 0.8 mm, & \(h_{13}\) = 1.2 mm, & \(h_{14}\) = 1.4 mm, \\  & \(h_{21}\) = 3.6 mm & \(h_{22}\) = 3.2 mm & \(h_{23}\) = 2.8 mm & \(h_{24}\) = 2.6 mm \\ \hline \(h_{\text{opt}}\) & 0.068 & 0.034 & 0.023 & 0.019 \\ \hline \hline \end{tabular}
\end{table}
Table 2: \(h_{\text{opt}}\) values used as a criterion to estimate the depth of delamination in 3D model.  
Figure 16: Comparison between simulated magnitude variation of A\({}_{0}\) mode (the magenta solid line) and the predicted variations and different depths and damage length of 90 mm.  
The main value of the proposed technique lies in multi-frequency excitation, which leads to different magnitude patterns of \(A_{0}\) mode for delamination depth assessment and more accurate velocity values for defect length estimation. Hence, such a technique can be used even in the presence of the dispersion of \(A_{0}\) mode and provide information about the absolute depth and length of the damage by employing a few time traces measured at slightly different frequencies.  
V.S.: Conceptualization, Methodology, Software, Validation, Investigation, Writing--Original Draft, Visualization, Supervision. L.M.: Conceptualization, Methodology, Writing--Review and Editing, Supervision. R.R.: Validation, Formal analysis, Investigation, Data Curation, Writing--Original Draft, Visualization. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.