# Indentation Measurement in Thin Plates under Bending Using 3D Digital Image Correlation
## 3 Results and Discussion  
In this section, the experimental results from the analysis of the contact and bending deformation of the specimen using 3D-DIC during the tests will be analyzed and discussed. To establish the contact model, images from both cameras were captured during the test at each displacement step and post-processed using the 3D-DIC technique. The facet size was set to 25 \(\times\) 25 pixels with an overlap of 2 pixels. As an example, Figure 6 shows the measured out-of-plane displacements in a 2 mm thick specimen for different cylinder displacements. They show the cylinder displacement of 0 mm, 0.72 mm, 1.57 mm and 2 mm, which corresponds to 0 mm, \(-\)0.05 mm, \(-\)0.096 mm and \(-\)0.111 mm indentation and loads of 0 N, 320 N, 611 N, and 731 N, respectively. For each displacement step of the cylinder (from 0 mm to 2 mm), indentation values were evaluated and the applied load was measured to obtain the experimental contact model. Figure 7 shows the experimental contact force for a 2 mm thick specimen. As it can be observed, the maximum indentation value was \(-\)0.111 mm, which corresponded to 731 N compression load. After this value was reached, an elastic recovery of the material was observed during the unloading path show in the graph. The measured permanent indentation was \(-\)0.059 mm. In the figure, it is observed a small scattering that could be associated with the material behavior during plasticity produced due to contact. Figure 6: Out-of-plane displacements at the region of analysis when a 2 mm thick specimen is analysed at different loads: (**a**) 0 mm and 0 N; (**b**) \(-\)0.05 mm and 320 N; (**c**) \(-\)0.096 mm and 611 N; (**d**) \(-\)0.111 mm and 731 N.  
The same procedure was followed to the rest of specimen thicknesses. Figure 8 shows the experimental contact force for 3 mm, 4 mm, 5 mm and 6 mm thick specimens. The indentations were \(-\)0.189 mm, \(-\)0.279 mm, \(-\)0.359 mm and \(-\)0.447 mm, which corresponded to a maximum compression load of 1758 N, 3745 N, 4791 N and 6274 N respectively. It is observed that, as the specimen stiffness (i.e., thickness) increases, more contact damage occurs. For 6 mm thick specimen, the highest contact damage is reached. The permanent indentation after the load was removed was \(-\)0.114 mm, \(-\)0.190 mm, \(-\)0.235 mm and \(-\)0.313 mm for the different specimen thicknesses of 3 mm, 4 mm, 5 mm and 6 mm, respectively. It is also noticed that the signal noise is being reduced as the thickness and load increases in both loading and unloading stages. To compare results for different specimen thicknesses, Figure 9a shows the normalized contact load as a function of the indentation/thickness ratio for different specimen thicknesses. It is observed an increase in the indentation/thickness ratio as the specimen  
Figure 8: Experimental contact force for: (**a**) 3 mm; (**b**) 4 mm; (**c**) 5 mm and (**d**) 6 mm thick specimens. Figure 7: Experimental contact force for a 2 mm thick specimen. thickness increases. An explanation for this effect is that the contact damage is more significant as the specimen stiffness increases. Although it is not presented in Figure 9, similar behavior was observed for 3 mm and 5 mm thicknesses. Thus, increasing the specimen thickness implies higher contact damage, showing indentations of 2% of the initial thickness in 3 mm thick specimens to 5% of the initial thickness in 6 mm thick specimens. Increasing the specimen thickness enhances the bending stiffness and the transferred ball pressure increases as the ball displacement is imposed. Nevertheless, the bending deformation is more relevant when the specimen thickness is smaller. Figure 9b shows the specimen maximum relative deflection experienced for different specimen thicknesses. As previously mentioned, the maximum specimen deflection was obtained as the out-of-plane displacement difference between the clamped edge and the position of minimum indentation, it represents the maximum bending deformation experienced by the specimen.