# Indentation Measurement in Thin Plates under Bending Using 3D Digital Image Correlation
## 3 Results and Discussion
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Thickness (mm)** & **2** & **3** & **4** & **5** & **6** \\ \hline
**Total applied energy (J)** & **0.80** & **2.06** & **4.21** & **5.53** & **7.31** \\ Total applied energy: contact (\%) & 4.80 & 8.32 & 12.09 & 14.49 & 16.50 \\ Total applied energy: bending (\%) & 95.20 & 91.26 & 86.40 & 83.84 & 81.60 \\ Total applied energy: system (\%) & 0.00 & 0.42 & 1.51 & 1.67 & 1.90 \\ \hline
**Recovered energy (elastic) (J)** & **0.38** & **0.80** & **1.50** & **1.90** & **2.42** \\ Elastic energy: contact (\%) & 3.12 & 5.26 & 7.99 & 10.94 & 13.48 \\ Elastic energy: bending (\%) & 96.88 & 94.74 & 89.33 & 86.84 & 83.50 \\ \hline
**Energy to generate permanent damage (plastic) (J)** & **0.42** & **1.26** & **2.71** & **3.63** & **4.89** \\ Energy to generate permanent damage: contact (\%) & 6.27 & 10.26 & 14.35 & 16.38 & 18.01 \\ Energy to generate permanent damage: bending (\%) & 93.83 & 89.06 & 84.78 & 82.28 & 80.61 \\ Energy to generate permanent damage: structure (\%) & 0.00 & 0.68 & 0.87 & 1.34 & 1.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Energy balance for contact experiments with different specimen thicknesses. Figure 11. Applied energy percentage due to contact and bending as a function of the specimen thickness. Splitting up the applied energies into elastic and plastic, Figure 12 shows the percentage of recovered elastic energy due to contact and bending as a function of the specimen thickness. Again, the results illustrate that thicker specimens show a lower elastic energy recovery due to bending, while thinner specimens experience a higher elastic energy recovery. For the case of contact damage, the percentage of recovered energy increases with the specimen thickness. Figure 12. Percentage of elastic recovered energy due to contact and bending as a function of the specimen thickness. Figure 13 shows the percentage of absorbed energy due to contact and bending. The results are represented as a function of the specimen thickness. They support the results shown in Figure 10, where both the three curves and thicknesses (2 mm, 4 mm and 6 mm) are linearly spaced. It means a linear influence of thickness on the total applied energy. The energy evolution involved in different contact experiments conducted on aluminum specimens is shown in Figures 11-13. It can be observed that the influence of bending drastically influences the energy absorption due to contact. An extreme case would be a half space where not bending occurred and all the percentage of the energy would be absorbed by contact damage. It is remarkable that, for 2 mm thick specimens, from the total applied energy, 4.8% is transformed to create contact damage; however, for thicker specimens this value is bigger, up to 16.5% for 6 mm thick specimens. These results are relevant for an accurate energy balance during experiments. The applied energy for bending deformation is decreasing for thicker specimens, being 81.6% of the applied energy for 6 mm thick specimens. During the unloading path, the recovered energy is evaluated, and therefore the absorbed energy is quantified. Thus, it is possible to distinguish  
Figure 11. Applied energy percentage due to contact and bending as a function of the specimen thickness. between absorbed energy due to permanent contact damage and bending deformation. For a 6 mm thick specimen, around 18% of the total applied energy was absorbed to generate permanent contact damage. However, for the case of 2 mm thick specimens, only 6.27% of the energy was absorbed. The loading frame behavior was assumed as elastic, although a small portion of energy was absorbed, it could be neglected. It could be associated to the applied preload which is introduced by screws when clamping the specimen. The results shown in Figures 7 and 8, and specifically the quasi-linearity in loading curve, reproduces the findings of other authors in metal specimens indented with spherical indenter. Data in Figures 11-13 could be fitted by third-order function.