## 3 Results
### Vhcf Test Results  
Ultrasonic Vhcf tests were carried out at increasing levels of stress amplitude at the specimen center, \(s_{center}\), with the aim of collecting a large amount of failures in the Vhcf region (above \(10^{7}\) cycles). The first test was carried out at the \(s_{center}\) equal to 50 MPa, and then the applied stress amplitude was increased with steps of 5 MPa up to 85 MPa. In particular, two tests at stress levels of 55 MPa, 60 MPa, 70 MPa, 80 MPa, and 85 MPa and three tests at 75 MPa were carried out. A total of sixteen Vhcf tests were performed. Twelve specimens failed in the range \((9.82\,\times\,10^{5}\): \(8.94\,\times\,10^{8})\), whereas four runout specimens did not fail at \(10^{9}\) cycles.  
In the following analysis, the stress amplitude close to the defect location, referred to as the local stress amplitude \(s_{local}\), is considered in the following analysis, according to [20; 21; 27]. \(s_{local}\) was assessed through a finite element analysis (FEA) by considering the location of initial defects within the risk volume. The location of defects in the radial direction was measured through digital processing of the fracture surface images obtained with the optical microscope and the scanning electron microscope (SEM). The location of the defect along the longitudinal direction is measured by using a digital caliber with a nominal resolution of 0.01 mm.  
In Figure 3, the S-N plot of the experimental data is shown. In Figure 3a, \(s_{center}\), with respect to the number of cycles to failure, \(N_{f}\), is shown; in Figure 3b, \(s_{local}\), with respect to the number of cycles to failure, \(N_{f}\), is shown. Two markers are used to differentiate between the defects originating the fatigue failure (the defect was due to incomplete fusion and insufficient layer bonding, according to Section 3.3).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(\sigma_{u}\) [MPa] & \(\varepsilon_{f}\) [\%] & **Vickers Hardness [HV]** \\ \hline AlSi10 Mg vertical & 419 (\(\pm 8\)) & 4.1 (\(\pm 0.1\)) & 146 (\(\pm 4\)) \\ AlSi10 Mg [22] & 451 & 4.8 & 127 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Results of the tensile tests and of the Vickers hardness measurements.  
According to Figure 3, the difference between \(s_{local}\) and \(s_{center}\) is generally limited, but it is evident for two specimens that failed above \(10^{8}\) cycles. The maximum percent difference is about 10%, which confirms the well-known definition of risk volume (i.e., the volume of the material subjected to a stress amplitude larger than the 90% of the maximum applied stress [25]).  
According to Figure 3b, the experimental data exhibit a large scatter in terms of fatigue strength as well as of \(N_{f}\). When \(s_{local}=55\) MPa, a premature fatigue failure at \(N_{f}=~{}5.7~{}\times~{}10^{6}\)  and a runout coexist; at about \(10^{7}\) cycles, failures at \(s_{local}=55\) MPa and at \(s_{local}=85\) MPa occur. The reason for the large scatter found experimentally is investigated and discussed in Section 3. The explanations proposed are verified by comparing the defect size, type, and location found experimentally with those found in [22] by testing small hourglass machined specimens, even if obtained by slightly different process parameters.