# Indentation Measurement in Thin Plates under Bending Using 3D Digital Image Correlation
## 2 Materials and Methods
### Experimental Validation of the Proposed Methodology  
Before performing the experimental analysis, a preliminary experiment was conducted to evaluate the measurement uncertainty of the proposed 3D-DIC setup. The test was carried out without specimen. Consequently, the movement of the hydraulic cylinder was entirely transferred to the loading frame. Then, only the motion as a rigid body was measured without any load application. The cylinder was moved up to 3 mm in six sequent  
Figure 4: Evaluation of the absorbed energy due to contact during an experiment. Figure 3: Flow chart illustrating the implemented experimental methodology to extract test results. displacement steps of 0.5 mm. Hence, the displacement data provided by the LVDT sensor in the hydraulic machine were compared with those measured by the 3D DIC system. Thus, the measurement uncertainty of the technique was evaluated. A statistical analysis was subsequently performed. The mean, \(\mu\), and variance, \(s^{2}\), of the measurement differences between 3D-DIC (values in the considered region of analysis) and the LVDT was calculated for each vertical displacement step according to the following expressions [42]. \[h_{i}=\frac{(3 DDIC-Cylinder)}{3 DDIC} \tag{3}\]  
\[\mu=\frac{1}{I-2}\sum_{i=1}^{I}h_{i} \tag{4}\]  
\[s^{2}=\frac{I}{I-2}\sum_{i=1}^{I}(h_{i}-\mu)^{2} \tag{5}\]  
where \(I\) is the number of experimental points evaluated and \(h_{i}\) is the relative error in the measurement. Values for the mean error, \(\mu\), and standard deviation of the error, \(s\), at each displacement step were evaluated. Table 2 shows the average mean and the standard deviation for the different displacements steps. In general terms, the experimental results from 3D-DIC matched with the LVDT measurements with a very low scatter. Statistical calculations such us the mean and the standard deviation clearly show the high level of concordance where values are lower than 0.20% and 0.15%, respectively. Moreover, the average mean for the different displacements step was lower than 2\(\cdot 10^{-3}\) mm and the average standard deviation lower than 1\(\cdot 10^{-3}\) mm. As a second part of the validation, two experiments were performed. Subsequently, the accuracy and repeatability of the setup were quantified using 2 mm thick specimens. A battery of 20 tests was performed to measure the indentation at different loading levels. Firstly, indentation measurements were performed 10 times using a dial indicator and also 10 times using 3D-DIC. During the experiments, the indenter was moved 2 mm down (once the indenter touched the specimen, as reference) in steps of 0.1 mm at 0.1 mm/s, as programmed in the hydraulic cylinder. Between steps, a dwell and a TTL pulse were set to trigger both cameras. Then, the load, the dial indicator measurement and both cameras' shots were logged at each step. As previously indicated, a 25 N preload was set for each test. The gauge head of the used dial indicator, which has an accuracy of 1\(\cdot 10^{-3}\) mm, was placed and vertically aligned with the center of the sphere, in the non-contact side of the specimen. Figure 5 shows the results obtained for four of these indentation experiments using the dial indicator and DIC technique simultaneously. Error bars show a deviation percentage of \(\pm 6\%\) respect to the average value. It can be observed that in all the cases, experimental results are within the error bars which indicate that repeatability of the results. During the unloading path, values were also inside of the 6%; however, more scatter in the results was found. Figure 5b shows the same test conditions as in Figure 5a, but in this case 3D-DIC was employed. Figure 5c overlays the results of both techniques. In all the cases, differences are smaller than 6%, using this value as a reference from the previously calculated dispersion bands of 3D-DIC. These differences in the indentation results could