# Indentation Measurement in Thin Plates under Bending Using 3D Digital Image Correlation
## 2 Materials and Methods  
The experimental stage was performed using specimens from commercial AL-1050 H-14 (see Table 1 for main properties from the manufacturer [34]) and cut by a waterjet technique from 2 m \(\times\) 1 m sheets with different thicknesses, namely 2 mm, 3 mm, 4 mm, 5 mm and 6 mm. In all cases, the adopted geometry was a square of 150 mm \(\times\) 150 mm.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**AL 1050-H-14** & **E (GPa)** & \(\
u\) & **Density (kg/m\({}^{3}\))** & **Yield Stress (MPa)** & **Hardness (HB)** \\ \hline  & 69 & 0.33 & 2700 & 105 & 35 \\ \hline \end{tabular}
\end{table}
Table 1: Aluminum 1050 H14 properties [34].  
Each specimen was clamped using a frame which covered the specimen 15 mm from each edge, leaving a free area of 120 mm \(\times\) 120 mm. To evaluate indentation when the monotonic load increased, 3D-DIC was adopted. For this purpose, the surface was treated by painting it first with white paint and subsequently black paint was sprayed to generate a speckle pattern over the surface. The presence of bending during experiments induced a break of the paint at the area where the indenter was contacting the specimen generating a lack of information. To overcome this problem, a wet white coating was applied instead.  
For 3D-DIC, two monochromatic CCD (Charge-Coupled Device) 5-megapixel cameras (brand Allied Vision Technologies, model Stingray F-504 B/C) were employed. Additionally, two 23 mm focal length lenses (brand Schneider) were employed. The cameras were synchronized and monitored from a laptop connected to a DAQ (Data Acquisition System) and a halogen light (brand Hedler, model DX15, 150W) to illuminate the specimen. The stereoscopic system was mounted on a tripod and subsequently calibrated. Finally, the displacements fields occurring at the specimen surface during loading and unloading stages were measured using the commercial software package VIC-3D, from Correlated Solutions Inc. [31; 35].  
To measure indentation during monotonic loading, 3D-DIC technique was adopted. Tests were conducted using a MTS 370.02 servohydraulic machine with a maximum load capacity of 25 kN, where grips were removed and replaced by a loading frame. The top part of the loading frame was clamped to the hydraulic cylinder, while the bottom part was attached to the machine body frame. Thus, the top part of the structure could move in a vertical direction through four guides to ensure a perpendicular application of the monotonic loading during experiments (Figure 1a). Each specimen was clamped using a frame which covered 15 mm of the specimen from each edge (the free area for analysis was a square of 120 mm side). Different specimen thicknesses were analyzed to evaluate the effect of bending during indentation.  
A \(\O20\) mm spherical indenter (steel ball bearing) was screwed using an adaptor to a load cell to acquire the load magnitude during experiments. During indentation experiments, the plate was loaded against the sphere. As recommended by [PERSON] [36], the plate was previously lubricated with industrial oil to consider an almost-frictionless contact. Even if the contact is not lubricated, the effect of friction could be neglected, especially  
Figure 1: (**a**) Schematic of the setup to perform the experiments; (**b**) laboratory-adopted setup for the proposed experimental methodology.  
for non-sharped indenters, where differences of 4% in loading curves were reported by [PERSON] et al. [37]. Figure 1b shows the setup of the experiment.