# Indentation Measurement in Thin Plates under Bending Using 3D Digital Image Correlation
## 2 Materials and Methods
### Experimental Methodology
Subsequently, when the test was started, a TTL pulse was automatically generated and sent to both cameras to acquire images from the 3D-DIC system. Figure 3 shows a flow chart summarizing the implemented experimental methodology. During step 1, the cylinder was moved with a displacement rate of 0.1 mm/s during both loading and unloading, controlled by the LVDT (Linear Variable Displacement Transducer). The maximum cylinder displacement was limited to 2 mm. During this displacement interval, images were captured. In step 2, images were post-processed to obtain the out-of-plane displacements field to infer the indentation and the deflection experienced by the specimen during each deformation step. Finally, during step 3, the load for every captured image was plotted (load from image) versus the measured displacements using 3D-DIC. The test was finished when the load cell reading was below 25 N, which meant that no contact existed between the sphere and the specimen. After the results were obtained, a post-processing analysis was conducted. For each test, it was plotted indentation results versus load, as Figure 4 shows as an example. For contact behavior, as it is shown in Figure 4, the area under the loading branch was the energy employed to indent the specimen, while the area under the unloading branch was the recovered elastic energy [39; 40]. The difference between both areas was the absorbed energy to produce local contact damage at the contact area [41]. In this case, it was plotted the maximum bending deflection vs. load. Again, part of the energy was stored during the loading and unloading paths. The stored energy (differences of areas between both paths) was the energy absorbed due to plastic deformation as a result of bending. Figure 2: (**a**) Schematic illustration showing the indentation measurement principle during a contact experiment which includes bending. (**b**) Real test illustrating the thickness reduction at the contact area and the indentation measurement. Therefore, for this case, the general energy balance is [39]:  
\[E_{T}=E_{c}+E_{b}+E_{sys} \tag{1}\]  
where the term \(E_{T}\) is the energy applied to the specimen, \(E_{c}\) is the involved energy due to contact, \(E_{b}\) is the involved energy due to bending and \(E_{sys}\) is the elastic energy absorbed by the loading frame during the test. Both energies terms \(E_{c}\) and \(E_{b}\), have an elastic component that is recovered during the unloading path, (\(E_{c}\)elastic and \(E_{b}\)elastic) and a plastic component that is absorbed by the specimen, which is responsible for the remaining permanent damage after the load is removed (\(E_{c}\)_plast_ and \(E_{b}\)_plast_). Thus, the energy balance is presented as:  
\[E_{T}=(E_{c,plest}+E_{c,elastic})+(E_{b,plast}+E_{b,elastic})+E_{sys} \tag{2}\]  
According to the experimental methodology previously proposed, it is possible to evaluate the energy transferred due to contact and bending for each loading state [39]. \(E_{sys}\) was evaluated by comparing the displacements of the machine actuator provided by the LVDT and those measured using DIC for the clamp frame holding the specimen.