## 3 Results and Discussion  
The failure occurred for an unrepaired section, demonstrating that the repairing technique was able to carry a pressure value even higher than the undamaged part. This can be observed in Figure 8, in which the deformations obtained during the experimental test and from the FEM global model are compared. It is worth noticing that the repaired part presents a deformation much smaller than the undamaged part. Two pictures of the pipe after failure are shown in Figure 9. It can be noticed from Figure 9a that the failure occurred for an integer part of the pipe with a fracture direction perpendicular to the hoop stress, i.e., the maximum stress. This is rather typical for pipelines, pressure vessels as well as rotating components [42; 43; 46; 47]. Moreover, Figure 9b shows that the machined defect did not present any further damage after the test, thus highlighting again the load-carrying capacity of this composite-repairing technique. Figure 10 shows stress and plastic strains calculated numerically for the overall pipe (i.e., for the global FEM model). It is worth noting that the composite sleeve allowed to significantly reduce the deformation of the steel in the repaired section, i.e., a null plastic strain was calculated, in turn, corresponding to a behaviour of the material within the linear-elastic range. On the contrary, the integer parts present stresses having much higher values, corresponding to significant plastic deformations. This added structural loading capacity was allowed by the filler material that transferred the pressure from the steel to the outer composite layers. The distribution of results in the global FEM model was calculated in order to have a general understanding of the overall stress-strain distribution. More accurate results were calculated by means of the two sub-models shown in Figure 6, for which further geometric details and much finer meshes were adopted. Stresses and strains were extracted from the submodels' results along the two paths shown in Figure 11. Namely, Path1 (Figure 11a) included all the nodes for the inner surface along one-quarter of the repaired pipe section starting from the middle of the damage. Path2 (Figure 11b) was similar to Path1 but considered the inner surface of the composite sleeve. Finally, Path3 was simply defined along the radial direction (i.e., through-the-thickness) of an unrepaired part of SM2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Global model** & 11,568 quadratic hexahedral elements, type: C3D20 \\ \hline
**Submodel 1 (SM1)** & 23,934 quadratic tetrahedral elements type: C3D10M; 4480 quadratic hexahedral elements, type: C3D20. \\ \hline
**Submodel 2 (SM2)** & 10,800 quadratic hexahedral elements, type: C3D20. \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The number and type of elements used in each model. The variations of von Mises stresses along Paths1-2 are plotted against the related normalized distances in Figure 12. Radial displacement on the deformed shape of the steel part in the damaged section is shown in Figure 13. To better understand the related stress variations, some markers were added in Figure 12 corresponding to the positions shown in Figure 13. Vertical and horizontal axes in Figure 13 were selected as the starting and ending point of the normalized distance, respectively, whereas the latter increased in a clockwise direction. The size of the defect along the normalized distance was equal to 0.16 (Point 1 in Figures 12 and 13). Figure 8: Deformation of experimental and numerical pipes; units in m.  
Figure 9: Pipe after the burst test: (**a**) highlight of the fracture direction; (**b**) highlight of the defect after the test. Figure 11: Definition of the three paths along which results were extracted: (**a**) Path1 used for the steel in a repaired section; (**b**) Path2 used for the composite sleeve; (**c**) Path3 along the radial direction through the thickness of an unrepaired section of the pipe. Figure 12: Distributions of von Mises stresses along Path1 and Path2.