# Indentation Measurement in Thin Plates under Bending Using 3D Digital Image Correlation
## 3 Results and Discussion
The flexural stiffness and compliance of an edge-clamped plate is related with the cubic power of the thickness [43]. On the other hand, the superficial indentation stiffness and harness (i.e. at contact point) do not depend on the plate flexural thickness as it is an intrinsic material property. Then, when the plate thickness is increased, the bending effect is going lower due to the higher thickness, which follows a thickness to the third power function. Consequently, the local contact damage absorbs a higher amount of energy. As an example, for very high thicknesses, the bending energy tends to be zero (both plastic and elastic), whilst the energy at the contact point tends to be equal to the applied energy. As a result, the highest contact damage as indentation is found in thick plates, while the highest bending deflections are shown for the smallest thicknesses. According to these figures, when the thickness tends to zero, the contact-associated energy decreases quickly. Despite the high accuracy of the method, it could lead to insufficient exactitude in these cases, although further experimentation should be addressed. The proposed methodology could be used to characterize the contact behavior in dynamic events (e.g. impact) as high-speed cameras and DAQ are used, as well as indentation cycles experiments. Additionally, long-term effects (e.g. creep) could also be analysed at the different stages. It is specifically useful for thin or thick plates, when thicker geometry or raw material is not available, or the real application is based on thin plates. In these cases, bending effect cannot be neglected and the alternative methods find difficulties to analyze the contact and bending effect independently. Additionally, since the post-processing is able to evaluate the maximum indentation point and bending effect, the accuracy in the positioning is not affecting the final results. Alternative methods can be influenced by these factors. It could also be used for any material (such as metals or composites) and even for non-flat surfaces, specifically for high-stiffness materials. Further analyses could be performed in order to correlate this method with harness methods, to be highlighted as potential and alternative applications. The presented method does not require accurate measurement of the real length or diameter of the indentation, so surface roughness, quality or the operator skills are not affecting the measurement. As an  
Figure 13: Percentage of absorbed energy due to contact and bending as a function of the specimen thickness. example, when the values of permanent indentation after removing the load (for 4 mm, 5 mm and 6 mm) are used, the assessed Brinell Harness ranges between 32 HB and 33 HB are obtained. Although the real value has not been measured, the data from the manufacturer specify 35 HB, and then the mean error for thickness between 4 and 6 mm is lower than 8%. For 2 mm and 3 mm thick specimens, the error is higher and some conclusions are drawn. The variations can be associated to the high curvature of plate at the indentation point because of bending effect. In these cases, the material is reducing the indentation depth as the contact surface is higher. Then, it can be concluded that small ball diameters should be used as the specimen is thinner, in order to highlight the contact and attenuate the bending effects. The application of this methodology could be extended for using other indenters such as pyramidal or conical. Its application could be limited for very thin specimens of very hard materials even using small indenters and further experimentation is required.