## 3 Results and Discussion
Figure 10: Von Mises stress [Pa] and plastic strain distributions in the FEM global model. Considering the results of Figures 12 and 13, the maximum value of von Mises stresses occurred between the range 0 (T direction) to 0.16 (Point 1), thus along the damaged area. Such a result is consistent with the fact that a reduced thickness induces a steep increment of stresses. At Point 1, further stress concentrations were expected due to the sharp changes in the thickness of the pipe, whereas between Points 1 and 2, the increment of the pipe wall resulted in a considerable reduction of stresses. According to these explanations, also the radial displacements presented a similar trend (Figure 13), and the highest displacement was observed between Points 1 and 2. Even though the lowest thickness was in the damaged area, the presence of the filler material allowed to transfer pressure stresses from the thin layer of steel to the outer sleeve, in turn resulting in high but not excessive magnitudes for displacement and stresses. As a matter of fact, maximum displacement occurred just outside the damaged part between Points 1 and 2. Further, stress and displacement variations between Points 2 to 4 can be explained by looking at the plastic hinge generated between positions 3 and 4, see also Figure 14. Such plastic hinge occurred in the position where the minimum displacement was calculated. This represents also the reason why the increase in stress in the composite layers in this geometric position was observed (Figure 12). After Point 4, the plastic zone vanished and small changes in stress and displacements were noticed, with the stress distribution becoming uniform moving away from the damaged area. The trend of von Mises stresses for Path2 were similar to those for Path1. Considering that the radius and thickness of the composite layers were larger than those of the pipe, the magnitude of stresses were slightly lower but presented a comparable behaviour. Further contour plots of von Mises stresses and plastic strains for SM1 are reported in Figure 12.0 It can be observed that the maximum values of stress and plastic strains were reduced if compared to the global model ones. This is due to the addition of the fillet radii to the defect that was not explicitly modelled for the global model. In addition, an appropriate density of elements in this zone was also considered for the SMs, thus improving the accuracy of the analyses. Considering SM1, the von Mises stress distribution through the thickness (Path3) was also extracted, see Figure 12.1 The maximum von Mises stress values measured along the paths in the repaired section, in the composite layer, and for an undamaged section were 506.5, 390, and 554.5 MPa respectively. For the undamaged section (SM1), the maximum stress value was measured as 9% higher than the maximum value for the repaired part (SM1), thus demonstrating that the repairing technique was able to increase the maximum loading capacity of the repaired structure. Figure 12.2 Radial displacement [m] on the deformed shape (magnification 5\(\times\)) of the pipe section in the damaged part; highlights of the geometric Points considered in Figure 12.3  
Figure 12.4 Distribution of von Misses stress in the radial direction along the thickness in the SM1. Figure 12.5 Plastic strain distribution through the mid-side section of SM1. Figure 12.6 (**a,b**) Von Mises stress [Pa] and equivalent plastic strain distributions for SM1; red circles in (**b**) to highlight the stress concentration positions. Additionally, if looking at the overall maximum stress values (Figures 15a and 16), the highest stresses in the damaged part and in the healthy part are nearly 3% different from each other. This clearly indicates that repairing has almost eliminated both the noteworthy thickness reduction of 80% and the related stress concentration in the pipe body.