## 3 Results and Discussion
### Effect of DB and Heat Treatment on Fatigue Behaviour of 304 Ss
The increased dislocation density due to DB was sufficient for strain ageing to occur during the subsequent heating at 350 \({}^{\circ}\)C for three hours, and the strain ageing led to surface layer strengthening. The movement of dislocations through the crystal was greatly hindered by the presence of small carbon atoms in the crystal flaws. Thus, the sliding resistance between the atoms increased significantly, which led to an increase in the yield strength. The hindered movement of the dislocations slowed down their clustering in a specific region along the grain boundaries. The clustering of dislocations in the boundary zone caused the formation of a focus (from which the fatigue micro-cracks originated) during cyclic fatigue. Therefore, the strain ageing increased the time it took to form a fatigue macro-crack (resulting from the coalescence of multiple micro-cracks), and, thus, increased the fatigue life. The presence of fine-grained tempered \(\alpha^{\prime}-\)martensite (also called \(\alpha^{\prime\prime}-\)martensite) with high dislocation density (see Figure 10(a.2)), as well as dispersed precipitates (see Figure 10(b.2)), led to an increase in the hardness and strength, which increased the fatigue strength. Another possible reason for the increased fatigue strength of as-received hot-rolled 304 SS was the dispersion of the carbides along the grain boundary, which increased the resistance to inter-crystalline deformation. However, this heat treatment after hardening single-pass DB did not significantly change the fatigue strength for either initial state of the material (Figure 17b). It is difficult to give a detailed explanation of this phenomenon because of the complexity and multifaceted nature of the ongoing processes. In summary, it can be concluded that the benefits (described above) of heating at 350 \({}^{\circ}\)C for three hours after hardening single-pass DB are balanced by the negative effect of residual stress relaxation and reverse transformation \(\alpha^{\prime}\rightarrow\gamma\). To isolate and evaluate the influence of initial heat treatment on the fatigue behaviour of 304 SS, two S-N curves of samples AR1 and HT7 (see Figure 16) were transformed into a double-logarithmic coordinate system (Figure 18) as tri-slope models using Basquin's equation [31]:  
\[\mathrm{S=CR^{b}} \tag{3}\]  
Figure 17: The effect of the annealing at 350 \({}^{\circ}\)C after DB on the fatigue behaviour: (**a**) smoothing DB and (**b**) hardening single-pass DB. where S is the stress amplitude used in each test and R is the number of repetitions of this stress required for rupture. It should be noted that the S-N diagram is only applicable for completely reversed stresses, i.e., the cycle asymmetry coefficient is equal to \(-1\). The approximating one-slope Basquin models are straight lines in the double-log coordinate system (the red dashed lines in Figure 18). The constants C and b are expressed in Equations (4) and (5):  
\[\mathrm{C=S_{u}} \tag{4}\]  
\[\mathrm{b=\frac{\log(S_{e}/S_{u})}{6}} \tag{5}\]  
where \(S_{u}\) is ultimate tensile strength and \(S_{e}\) is the fatigue limit. The numerical values of fatigue strength coefficient C and fatigue strength exponent b are calculated: (1) for the as-received state, \(\mathrm{C=734\ MPa}\) and \(\mathrm{b=-0.037}\); (2) for the initially heat-treated state, \(\mathrm{C=595\ MPa}\) and \(\mathrm{b=-0.052}\). The larger absolute value of the fatigue strength exponent for the HT7 specimens (\(|\mathrm{b}|=0.052\)) compared with the AR1 specimens (\(|\mathrm{b}|=0.037\)) shows that the initial heat treatment of 304 SS improved the crack growth resistance, but reduced the fatigue limit, i.e., reduced crack nucleation resistance [32]. Conversely, 304 SS in the as-received state had lower crack growth resistance, but its higher fatigue limit indicated higher crack nucleation resistance.