## 4 Fatigue Analysis and Discussion
### SLM AlSi10 Mg  
Aluminum alloys are also commonly used materials in AM. A recent review is provided by [PERSON] et al. (2018). Even though the number of Al alloys that are now processable by SLM with high fidelity is still limited, ongoing studies are expanding, aiming to widen the range. Most of the existing fatigue studies concentrate on SLM AlSi10 Mg with its conventional counterpart Al 6061 (14; 25; 26; 27; 28). The microstructure of SLM AlSi10 Mg typically consists of overlapping, segregated melt pools with distinct boundaries. The bulk material of SLM AlSi10 Mg contains voids, which grow in both horizontal and vertical directions, but are more numerous in the material grown in the vertical orientation (4; 14). In addition, voids are more prevalent in the surface layers (14; 27). In the present study, the fatigue behaviours of wrought Al 6061, SLM AlSi10 Mg in both horizontal and vertical orientations are analyzed using the modified TMW model, following the methods as described in the previous sections. The fatigue behaviours of SLM AlSi10 Mg are described using Equations (3) and (4) with \(R_{s}\) and M values obtained using the method of Equations (5) and (6) as given in Table 9. The calculated S-N curves are shown in Figure 6 in comparison with the experimental data. Interestingly, the horizontal AM microstructure factor (M = 1.7) is close to the other AM materials analyzed in this study. The vertical direction has a slightly higher microstructural factor (M = 2.08), but all within the range as caused by round ellipsoidal voids. The surface finish factor \(R_{s}\) of SLM AlSi10 Mg is 0.756 in both directions, as the polished surface roughness is quite low with \(R_{a}=1.5\) um. Fatigue crack nucleation in SLM AlSi10 Mg was found to originate from pores, either internal or at the surface (14). Once the surface finish factor is determined, the TMW model can be used to assess the fatigue endurance limit per coupon such that a statistical distribution may be obtained as follows. Figure 6: Fatigue behaviours of wrought and AM Ti6 Al4V. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Material** & **Orientation** & **Treatment** &
\begin{tabular}{c} **Surface** \\ **Condition** \\ \end{tabular} & \(R_{a}\) (μm) & \(R_{s}\) & M \\ \hline Wrought Al6061 & - & - & Machined & 1 & 1 & 1 \\ SLM AlSi10 Mg & Horizontal & - & Polished & 1.5 & 0.756 & 1.71 \\ SLM AlSi10 Mg & Vertical & - & Polished & 1.5 & 0.756 & 2.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Surface finish and microstructural factors for AlSi10 Mg (\(\sigma_{0}=125\) MPa). First, rearranging Equation (5), we have:  
\[\sigma^{\prime}{}_{0}=\frac{\sigma_{0}}{M}=\sigma_{a}-\frac{1}{2}\sqrt{\frac{6 \mu w_{s}R_{s}}{(1-\
u)bN_{c}}} \tag{8}\]  
Then, Equation (8) is used to evaluate the coupon level \(\sigma^{\prime}{}_{0}\) for every test, and the results are given in Table 10 for wrought Al 6061 and SLM AlSi10 Mg. This set of data can be turned into statistical distributions as shown in Figure 7, and the distribution functions and parameters are given in Table 11. The fatigue endurance limit of wrought Al 6061 can be represented by a log-normal distribution, but interestingly, that of the AM AlSi10 Mg materials appear to be a normal distribution. During the AM process, the material's microstructure is formed from powders under high energy input by a laser, which reasonably creates a new microstructure with a normal (symmetrical) distribution of properties. On the other hand, the wrought material has gone through complex thermomechanical processing, which may skew the property distribution. Other examples of the statistical distribution of properties can be found in metallic glasses [29; 30]. It is beyond the scope of the current study to completely characterize the statistical distribution of processing-microstructure-property relationships for AM materials, but it is certainly an interesting point of future study.