## 3 Results and Discussion  
Among the experimental combinations investigated in this research work (see Table 3), it is possible to highlight three main scenarios:  
1. laser treatments carried out at laser power lower than 150 W did not lead to significant changes in the substrates' morphology and any grain structure modification was observed;
2. the treatments at 150 and 200 W ensured the best performances. In fact, these process conditions led to a change in substrate properties without melting phenomena, especially with scan speed in the range 16 to 20 mm/s;
3. when increasing the laser power to 250 or 300 W, surface melting was observed regardless of the scanning speed. These results are in good agreement with the pertinent literature [40] and are supported by Figure 8, in which it can be observed that increasing the scan speed by values greater than 14 mm/s, increases the number of cycles until failure, which is almost double the number of cycles obtained with the untreated samples (U label). The improvement in the fatigue life can be attributed to the formation of a superficial annealed martensitic structure due to thermal phenomena induced by the laser treatment [15; 25]. In particular, the amount of thermal energy the steel can absorb during the laser treatment decreases, and the process reaches the condition in which it is possible to have the martensitic transition. The subsequent laser scan causes a further heat treatment which leads to a slight annealing of the steel, i.e., back tempering phenomenon [41; 42]. Figure 6: Random single-point crossover. Figure 7: Random single-point mutation. It is worth noting that, during the tests, the coordinate-measuring machine showed no appreciable deformations. In fact, the axial symmetry of the laser treatment helped to compensate for possible distortions. For sake of clarity, Figure 9 shows a cross section of the steel specimen treated at \(P\) = 200 W and \(S\)s = 20 mm/s. In particular, it can be seen that the martensitic structure, i.e., the light grey area, reaches a thickness of about 182 \(\upmu\)m. On the other hand, Table 4 reports the thickness of the martensitic structure, i.e., heat affected zone (HAZ), obtained for some of the investigated values of the scan speed. In particular, when increasing the scan speed the thickness of the martensitic structure increases, according to the fact that, for lower values of the scan speed, the interaction time is greater and the aforementioned back tempering phenomenon takes place. From this experimental campaign it is evident that, among the studied process parameter values, only some combinations allow the effective obtainment of the hardening of the samples (see Table 5). Therefore, only these values are used in the optimization process by means of genetic algorithm, as described in Section 2.1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Ss, mm/s** & **HAZ, \(\upmu\)m** \\ \hline
12 & 67 \\
16 & 127 \\
20 & 182 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Thickness of the martensitic structure (HAZ) for different values of scan speed. Figure 8: Number of cycles vs. scan speed for a laser power of 200 W. ‘U’ refers to the untreated samples. Figure 9: Optical micrography of a laser hardened cross-section: transition from the martensitic structure (light grey) to the ferrite and perlite structure (dark grey) for \(P\) = 200 W and \(S\)s = 20 mm/s. Among these optimal combinations, the best one is given by \(P\) = 150 W and \(Ss\) = 20 mm/s leading to an improvement in the fatigue life more than 4 times that of the untreated samples, i.e., 421,982 against 92,608 cycles until failure, as reported in Table 5.  
It is important to highlight here that the laser treatments were carried out in order to maintain a constant scan speed. To this end, the rotating speed of the sample was changed according to the varying section when moving from the largest section zone to the smallest one. Moreover, all the parameters were chosen to avoid, or at least limit, the overlapping phenomenon.