## 4 Results
After the first selection of the points, the solution was calculated again and the selection was repeated. This new selection was performed starting back from all the initial points, as some points which were initially disregarded could turn out to be well correlated as the solution evolves. This iteration was repeated and the procedure was found to converge quickly to a stable selection of points in approximately 10 iterations. The results of the first hole (nominal depth 1 mm) are presented in Figure 19. The selection of the points at the end of the iterations is reported in Figure 19a, while the iterative solution is shown in Figure 19b; the same graph also presents the expected stresses for validation. The displacements at the end of the iteration procedure are shown in Figure 20, which presents both radial and tangential components, along with both the numerical and the experimental distributions, which are the variables involved in the evaluation of the accuracy factor in Equation (10). Figure 19: Residual stress determination for the hole with depth 1 mm: (**a**) selection of the points with accurate correlation and large displacement, (**b**) obtained stresses at the different iterations (lighter lines) and at convergence (solid lines), and validation with the expected stresses (dashed lines). The same analysis was repeated for the second hole with nominal depth 0.5 mm. In this situation, the solution was less stable in terms of component gradients because of the smaller depth. For this reason, the same procedure was equally repeated after imposing the condition of a uniform stress for each component along the entire depth of the solution. Recalling Figure 10, this was easily implemented by imposing the same levels of the superimposed triangular distributions; in other words, the same stress was shared by the two unitary distributions covering the entire depth, for each of the \(P,Q,T\) components, leading to just a single unknown for each of them. The obtained stress distribution and selection of the points are shown in Figure 21. In this situation, the procedure converged even faster (approximately 3 to 5 iterations were enough to find a stable result), and again the obtained stresses were found to be quite in agreement with the expected ones. The components of relieved displacements are shown in Figure 22. The pattern of the selected points changes slightly, and because of the smaller depth, the magnitude of the displacements is somewhat lower than the previous example. However, these displacements were still well detectable with the present settings by means of the DIC technique even for this shallower hole with 0.5 mm depth. Figure 20: Relieved displacement components for the hole with 1 mm depth: (**a**) radial experimental \(U_{r,\text{E}}\), (**b**) tangential experimental \(U_{\theta,\text{E}}\), (**c**) radial numerical \(U_{r,\text{N}}\), and (**d**) tangential numerical \(U_{\theta,\text{N}}\). The same approach could be proposed for the previous test with higher hole depth, as the slopes of the obtained stress distributions are not in perfect agreement with expectations. A similar stability and solution convergence rate was obtained for the 1 mm hole depth (not shown for brevity). However, the uniform stress combined with the proposed DIC point  
Figure 21: Residual stress determination for the hole with depth 0.5 mm: (**a**) selection of the points with accurate correlation and large displacement and (**b**) obtained stresses at the different iterations (lighter lines) and at convergence (solid lines), and validation with the expected stresses (dashed lines). Figure 18:0 Relieved displacement components for the hole with 0.5 mm depth: (**a**) radial experimental \(U_{\rho,\mathrm{E}}\), (**b**) tangential experimental \(U_{\theta,\mathrm{E}}\), (**c**) radial numerical \(U_{r,\mathrm{N}}\), and (**d**) tangential numerical \(U_{\theta,\mathrm{N}}\). selection procedure would be more interesting for shallow hole depths even lower than 0.5 mm.