## 3 Results and Discussion
Friction with the bench during the  
Figure 4: Experimental results of the DIC measurement of the non-deformed 3D geometry of the plate: rendered shape (the hollow region at the lower left edge is an actual pre-existing defect on the surface of the tested plate) (**a**) full-field depth map, (**b**) comparison of the z-coordinate contour plot (\(\Delta z=0.2\) mm) between the nominal geometry from CAD (**c**), and (**d**) the measured geometry. welding process resulted in some deterioration of the speckle pattern on the upper and lower horizontal edges of the plate (see Figure 4b). However, this did not affect the image correlation process and the entire surface of the plate was measured (within half the pixel subset size from the edge). Once assembled, the final part was returned to the University laboratories to acquire the two images of the front plate of the traction frame subassembly in the deformed configuration after welding (see Figure 3c,d), as well as to evaluate the corresponding displacement and strain maps. As the plate was moved and replaced between the two analyzed configurations, the two corresponding 3D point clouds were reconstructed in two different reference systems. As a first step, the gross rigid body motion (RBM) between the two reconstructed geometries was removed using the Iterative Closest Point algorithm (ICP) [42]. As a step used for further refinement, an optimization-based procedure aimed at minimizing the distance between the same set of 3D points belonging to the non-deformed and deformed reconstructed shapes was applied. This procedure certainly reduces the amount of RBM between the two geometries compared to the sole application of the ICP algorithm, but it still relies on the selection of the set of points used for alignment within the areas that are assumed to have suffered the least deformation. The strain maps can remove this ambiguity and assist in the selection of the 'non-deformed' reference data points, as they are not sensitive to RBM. The measured full-field displacement distribution over the plate surface is shown in Figure 6 (see reference system in Figure 4a). The maps show the expected folding of the side wings due to the welds #1 (Figure 5a). Large out-of-plane distortion also occurs along the 4 th weld path, with peaks at the intersections with the 5 th weld paths (compare Figure 6c with Figure 5c). Finally, the full-field Green-Lagrange strain maps were calculated after fitting the displacement distributions with NURBS according to the method described in detail in [43]. Strain maps show clear pattern symmetries and reveal the existence of equivalent peaks of von Mises strain between the bulges (compare Figure 7c with Figure 5b). It is worth noting that the deformation and strain maps have been obtained from a regular and dense distribution of data points which can eventually be interpolated and resampled to obtain values at any point of interest for the analysis (e.g., at the nodes of the corresponding FE model). Figure 5: Sequence of welding operations on the traction frame subassembly. (**a**) First weld bead (similarly on the opposite side). (**b**) Second and third weld beads (similarly on the opposite side). (**c**) Fourth and fifth weld beads. After the tests, to verify the resolution and accuracy of the measurement, three feeler gauges of 0.1 mm, 0.5 mm, and 1 mm thickness were attached to the plate with adhesive tape at their ends and provided with a speckle pattern (Figure 8a). Without changing the settings of the optical setup, the local topology of the region in Figure 8a was reconstructed using stereo-DIC. Figure 8b shows the results in the form of depth maps. The plot results are representative of the metrological performance of the DIC system and associated data processing routines used for the experiments reported in this paper. The variation in local geometry caused by the presence of the gauges was correctly retrieved, particularly for the 0.5 and 1 mm gauges.