# Indentation Measurement in Thin Plates under Bending Using 3D Digital Image Correlation
###### Abstract
To illustrate the potential of the proposed methodology for the analysis of contact problems with the presence of bending deformation, a quasi-static contact experiment has been performed using a rigid bearing sphere on an aluminum plate to quantify the indentation occurring when increasing the contact load. The influence of bending in the contact law depends on the specimen thickness. To avoid some of the main difficulties reported by other authors to obtain accurate measurements, a full-field optical technique known as 3D-DIC (Three Dimensional Digital Image Correlation) has been used. Some authors, such as preliminary studies using DIC to analyze the contact phenomenon were reported for other applications [PERSON] et al. [20] and [PERSON] et al. [21] have performed preliminary studies using the DIC technique to analyze the contact phenomena for other applications. In a contact test using conventional techniques, the indenter usually hides the area of interest and it represents a limitation in the measuring process during the experiment, as it was reported by [PERSON] and [PERSON] [22] in the experiment designed. In the presented setup, the indenter was fixed while the specimen was rigidly clamped to a movable loading frame. Thus, cameras were placed to record the face of the specimen opposite to that where contact was taking take place. In this way, it was possible to quantify bending and indentation measurements during the loading and unloading path. With the proposed methodology, it is possible to quantify the portion of applied energy employed to generate contact damage and bending deformation. In addition, it is also possible to evaluate the portion of the elastically recovered energy for contact and bending deformation during the unloading. Therefore, the absorbed energy due to the permanent indentation and bending can be inferred. Another important aspect investigated has been the influence of the specimen stiffness. The proposed methodology has been validated using conventional indentation-measuring techniques reported in literature, highlighting the potential of the proposed approach for the analysis of contact problems and its extrapolation to dynamic events such as impact. The first attempt to develop a theory based on the quantification of indentation produced by two loaded bodies in contact was suggested by [PERSON] [1]. Hertz theory was developed to study a static loading event on isotropic linear elastic half-space. The particular case of a sphere and a planar surface gave the relation between indentation,defined as the relative displacement of the indenter and the bottom face of the specimen, and the contact load. It is well known that this theory considers elastic conditions on homogeneous isotropic materials without the presence of damage and deflection of the specimen. However, once the yield strength of the material is exceeded, permanent indentation is generated, even for low loads. Hence, literature shows that some efforts have been made in order to consider the effect of permanent deformation by contact during the loading and unloading in plates [23]. More complex theories using elastoplastic contact laws combining [PERSON] theory and the effect of plastic deformation produced by the contact load in composites materials are also available in the literature [24; 25]. In these theories, three phases are specified, elastic and elastoplastic during the loading and the unloading phases. In this case, the bending effect of the fully supported plate is not considered. However, not many experimental approaches for the determination of the contact law can be found in the literature. In addition, previous authors such as [PERSON] et al. [26] reported some difficulties in accurately measuring indentation. In some cases, bending was avoided even when it was known that it had a relevant influence in the contact law determination [27]. In addition, some investigators such as [PERSON] and [PERSON] [15] and [PERSON] et al.