## 3 Results and Discussion  
This section shows the steps performed during the processing, through software, of the thermal data on the specimen surface, to obtain the stabilization temperature and the fatigue limit. A Matlab script was implemented to open and process the.asc files, exported from the Altair thermal camera acquisition software. This file has a data structure similar to a three-dimensional matrix, in which the third dimension is represented by the acquired frames, or in other words by time. Each plane of the matrix represents, however, the thermal image where the rows and columns identify the coordinates of each point of the specimen in a specific frame, to which the corresponding temperature value is associated. The frames acquired for each step are 500 (i.e., 5000 load cycles) while the thermal image returned by the thermal imaging camera has a resolution of 360 \(\times\) 256. This implies that the 3D matrix is of the type [360 \(\times\) 256 \(\times\) 500]. Therefore, the script allows determining the average temperature increase (i.e., averaged over the pixels) of an area of interest, normalized concerning the value of the initial instant, as the frames vary. The trend is reported in a \(\Delta\)T-N graph, where N is the number of cycles, obtained by multiplying the number of frames by a factor of 10 (being 10 Hz the load frequency), as a result of the previous settings on the thermal camera. At this point, the script proceeds with the calculation of the limit temperature, always as \(\Delta\)T, through a non-linear least-squares fitting. At the same time, the data are exported to the Mathematica environment, to perform a more specific analysis where necessary. In this case, the optimization allows normalizing the residues in order not to incur in estimation errors due to the shift or drift of the trend. This processing is repeated for all specimen geometries, both taking into consideration the hot and cold areas. Figures 6 and 7 show an example of what has been achieved for AA03 specimen for hot and cold zones considering only the higher load steps. A brief discussion is required to justify the statistical treatment carried out by data processing. At lower loads, in fact, thermal data are characterized by a higher scatter, especially in the cold zone (Figure 7). The problem is represented by the fact that at lower loads \(\Delta\)T falls in the thermocamera resolution range. At higher loads, that are the most significant, the scatter vanishes. Since the physical phenomenon that originated the temperature change is the same, the exponential law, which is typical of the thermal phenomena, is correctly assumed for the thermal behaviour at higher loads. In these cases, experimental data justifies this assumption. For lower loads, where experimental data would not allow assuming an exponential law effectively, it is reasonable to infer that the same law governs the physical phenomenon, justifying the adopted procedure. Once the limit temperature values have been obtained, a further script is used, which allows diagramming these values with the corresponding stress levels. Subsequently, the asymptotes are traced, as described in the procedure [1], and the fatigue limits are identified. In Figure 8, the result of this operation is shown for specimens AA03 as an example. The stress values have been obtained considering the net section in the hot area and the gross section in the cold area. Moreover, the steps considered for the hot and cold zones are not the same since in the gross section, the damage occurs at higher loads. Figure 6: Identification of the limit temperature by least-squares interpolation at different load steps (specimen AA03 hot zone). Figure 7: Identification of the limit temperature by least-squares interpolation at different load steps (specimen AA03 cold zone). Table 3 reports the resulting fatigue limits for notched and smooth specimens, i.e., for hot and cold areas, respectively.