# Delamination Assessment in Composite Laminates through Local Impulse Excitation Technique (IET)
## 4 Sensitivity Analysis to Delamination  
To exploit the validated FE model of the local-IET test, a sensitivity analysis of the technique to detect delamination was addressed for an industrial composite material, indicated by _Leonardo S.p.A_. The material is made of unidirectional fiber laminae disposed with a quasi-stacking sequence for a total thickness of 3 mm. The analysis was conducted with the 150 \(\times\) 150 mm clamping device, which was retained to provide an effective constraint for the investigated material. After exploiting the validated FE model, the predicted first and second resonant frequencies obtained were 672 Hz and 1130 Hz. For the sensitivity analysis, different combinations of the position of the delamination, position of the impulse and size of the delamination were simulated in order to identify the best combination of impulse and delamination positions and to characterize the sensitivity to the delamination size. Given the symmetry of the model, the impulse position and delamination position were varied along a line passing through the center and parallel to one of the boundaries of the device. The impulse positions were 10 mm, 25 mm and 37 mm from the center of the device. The delamination was considered in the center and at 10 mm, 25 mm and 37 mm from the center of the device. It is worth noting that for the retained clamping device, the maximum modal displacement of the second mode occurred at 37 mm from the center. As such, it was expected that similar results would be obtained for the delamination positions farther than 37 mm from the center of the device. A rounded circular shape with a diameter varying between 5 mm and 50 mm, with intermediate values of 10 mm, 15 mm, 25 mm and 35 mm, is assumed for delamination. It is worth highlighting that, although delamination can have elliptical or non-rounded shapes [34,35], the rounded circular shape can be considered the smallest circle that can be inscribed within the elliptical or non-rounded delamination. Accordingly, through the rounded circular shape, we determined the lower bound of the sensitivity of the local-IET in the presence of delamination. For each position of the excitation impulse, a simulation with the undamaged plate was performed. As in the eight-layer glass fiber, the delamination was positioned in the neutral plane of the laminate. For each simulation, in order to speed up the analysis without decreasing accuracy, the FRF was computed with a step size of 5 mm. The corresponding \(\beta\) factor and the ratio \(\frac{\beta_{lam}}{\beta_{malma}}\) were computed for each point, and the maximum value of the \(\frac{\beta_{lam}}{\beta_{malma}}\) ratio was used to assess the technique sensitivity. As in the region proximal to the boundaries, the modal displacement was almost null, thus challenging the accuracy of the experimental  
Figure 10: Comparison of experimental and numerical results: \(\beta\) factor for undamaged and delaminated plate and \(\frac{\beta_{lam}}{\beta_{malma}}\) ratio between damaged and undamaged \(\beta\) factors. acquisitions, and the identification of the maximum value of the \(\frac{\beta_{lam}}{\beta_{multam}}\) ratio was restricted to the sub-domain with dimensions of 120 \(\times\) 120 mm. Figure 11 reports the trend of the maximum values of the \(\frac{\beta_{lam}}{\beta_{multam}}\) ratio as a function of the delamination size. The different markers refer to the location of the impulse, while the different colors refer to the position of the delamination within the device, reported within square brackets. According to Figure 11, as the delamination size increases, the ratio \(\frac{\beta_{lam}}{\beta_{multam}}\) increases, as shown with the dotted lines. In this regard, the local-IET has a good sensitivity in the presence of delamination, as an increment of 5% of the \(\frac{\beta_{lam}}{\beta_{multam}}\) ratio is observed for a delamination size of 15 mm, which is only 1/10 of the device dimensions.