# Indentation Measurement in Thin Plates under Bending Using 3D Digital Image Correlation
## 2 Materials and Methods
### Experimental Methodology  
During the experiments, the specimen loading and unloading stages were programmed and controlled using the registered displacement by the hydraulic cylinder. This issue was extremely important since the aluminum employed for experiments had an almost perfect elastic plastic behavior. Thus, when the material yielded, a force control was not possible since the results were inaccurate. The hydraulic machine was governing the adopted optical system to ensure that images were captured in a synchronized way. Thus, +5 V TTL pulse was generated to trigger the cameras. For each displacement step, the load, the cylinder displacement, and the time for each camera-acquired image were registered. As previously indicated, different specimen thicknesses were tested to evaluate bending during contact. The indentation was measured at the back of the contact surface of the plate, evaluating the thickness reduction of the plate, where the indenter is in contact with the specimen. Thus, the location with minimum out-of-plane displacement variation was identified for each image using a routine written in Matlab(r). The script takes the output data from VIC-3D (displacements in matrix structures) and a loop cycle links the minimum displacement with the corresponding load, as both systems were synchronized. The measured out-of-plane displacement values were referred to a reference image, corresponding to zero indentation to obtain the indentation value for each loading state. As illustrated in Figure 2, the location with minimum out-of-plane displacement provided the indentation value, \(\alpha\), for each displacement step, assuming that the indenter did not deform during the experiment. This assumption was realistic since the adopted aluminum material was very soft compared with the indenter material. In addition, the deformation due to membrane and transverse shear deformation was neglected, simplification considering that small displacements were induced to the plates [38]. Figure 2a shows that maximum out-of-plane displacement, \(d\), occurred at the edge of the plate or the clamped perimeter in this case. Therefore, the energy applied for bending deformation was obtained after evaluating the maximum deflection experienced by the plate during the experiment [39]. The maximum deflection was calculated as the displacement differences between the edge of the plate, \(d\), and the peak point where the indenter was contacting. During the test, the frame displacement was also measured using DIC. It was observed that there were some differences between the displacement provided by the hydraulic cylinder and the measured displacement at the loading frame. These differences were attributed to elastic energy absorption occurring at the loading frame during the test. Thus, the maximum bending displacement experienced by the plate is the difference between \(d\) and \(\alpha\). In Figure 2a, the area with the minimum out-of-plane displacement is highlighted. For a better understanding of the mechanical behavior of the plate at this area, a simple test was performed and illustrated in Figure 2b. It was obtained from an indented plate in which a section was made just in the profile in contact with the indenter. A profile projector using a 10X magnifier (brand Nikon, model V-20, Japan) was used to accurately measure the thickness. As is observed in Figure 2b, the plate experiences the greatest thickness reduction at the contact point with the bearing ball. On the back face of the plate, it was measured 0.19 mm out-of-plane displacement. Therefore, comparing the thickness measurement at this point (1.81 mm) shows the indentation value considering the assumption commented above. As a result of the test, a force versus the indentation plot was obtained. The analysis was performed for loading and unloading and indentations and deflection were inferred measuring at the edges of the specimen clamped to the load frame. Prior to start the tests, a preload of 25 N was applied to ensure a contact between the plate and the sphere.