## 4 Results  
This HDM-DIC procedure was applied to different holes manufactured with an offset of a few millimetres with respect to the axis of the specimen, as shown in Figure 18a and motivated by Figure 15. In this analysis, the results of two tests at two different nominal depths of 1 mm and 0.5 mm are presented. The resulting hole diameters were 1.805 mm and 1.815 mm, respectively, and were obtained with the typical milling tools used for the HDM combined with the strain gases. The results obtained here can be directly compared to the stress distributions shown in Figure 15b at the corresponding initial depths, either 1 mm or 0.5 mm for the two cases. In principle, the stresses induced in the present specimen should not be defined as \"residual\", as the specimen is loaded remotely instead of actually carrying those stresses. More precisely, the initial depth could be affected by both residual stresses induced by the manufacturing operations and by the imposed bending stress. The possible residual stresses were not evaluated in this study; they were assumed to be relatively low with respect to the bending, as the spring back was almost imperceptible after manufacturing. Taking into account the shape of the IFs presented before, it is quite evident and obvious that the largest displacements are close to the hole rim and rapidly vanish. For this reason, not all of the observed points with displacements measured by the DIC should have the same significance when the stress inversion is performed; in particular, the points quite far from the hole should be excluded from the evaluation. In order to apply this, a simple approach could be to define an annular region of selection. However, according to the solution, the displacements could be high along some directions, while they could be rapidly falling along others. The strategy proposed here is an iterative procedure in which the remote points or those with little displacements are iteratively disregarded. Initially, all of the points are considered and a first solution is found. According to this first estimate of the stress distribution, the displacements are calculated at the DIC points themselves, then  
Figure 18: Measuring the hole diameter: (**a**) holes at the upper surface of the specimen, (**b**) observation of the thin movable frame, and (**c**) dial gage with a resolution of one hundredth of a millimetre. a selection criterion is implemented. A (dimensionless) accuracy factor \(f\) is initially found for each DIC point:  
\[U_{\text{N}}=\sqrt{U_{r,\text{N}}^{2}+U_{\theta,\text{N}}^{2}} \tag{10}\]  
\[f=\tfrac{1}{U_{\text{N}}}\sqrt{U_{r,\text{E}}U_{r,\text{N}}+U_{\theta,\text{E}} U_{\theta,\text{N}}}\]  
where \(U_{r,\text{N}},U_{\theta,\text{N}},U_{r,\text{E}},U_{\theta,\text{E}}\) are the radial and tangential displacement components, respectively obtained numerically (N), from the first solution, and the experimental ones (E). According to this, a first selection of the points was taken on the basis of this accuracy factor. An effective choice was \(0.667\leq f\leq 1.5\). This criterion was combined with the selection of those DIC points having \(U_{\text{N}}\geq 0.05\,U_{\text{N,max}}\), where \(U_{\text{N,max}}\) is the maximum displacement norm (numerically evaluated) of the whole observed field. The application of this criterion provides a deselection of both the outliers, which can have a significant weight (especially when the measured displacements are very different than expected), and of those points which are too far from the hole rim, thus showing small displacements. It is worth noting that the far points may have large weights, as the area of the peripheral region is significant with respect to the area close to the hole region. Moreover, some spurious effects (such as nearby constraints or lateral edges) can introduce inaccuracies between the measure and the model, even if at very small scale of the displacements, especially far from the hole.