## 4 Fatigue Analysis and Discussion
### LB-Pff 17-4 Ph
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(\sigma_{a}\) (MPa) & \(\varepsilon_{a}\) (\%) & \(\Delta\varepsilon_{p}\)/2 &
\begin{tabular}{c} **2N\({}_{\text{f}}\)** \\ **(Reversals)** \\ \end{tabular} & **TMW (2N\({}_{\text{c}}\))** \\ \hline Strain-controlled & 1179 & 0.80 & 0.23 & 1218 & - \\ condition & 1021 & 0.49 & - & 7000 & 7265 \\ Load-controlled & 1020 & 0.49 & - & 10,930 & 7306 \\ condition & 771 & 0.37 & - & 102,672 & 77,815 \\  & 700 & 0.34 & - & 3,289,174 & 619,041 \\  & 560 & 0.27 & - & >5,000,000 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Fatigue test results of HIPed LB-PBF 17-4 PH stainless steel with the machined surface under axial loading (test information and data taken from [13]). The surface finish factor \(R_{s}\) and the microstructural factor \(M\) for these material conditions are summarized in Table 6.  
Above the yield strength, as seen from Table 3, plastic strain accumulates at nearly constant stress, causing the shortening of fatigue life. Therefore, the fatigue processes in this regime is LCF, and Equation (3) is used with \(R_{s}\) = 0.25. Note that the surface roughness effect for LCF is different from that for HCF. This is not totally unexpected as roughness may cause stress concentration under elastic loading, but it rather contributes directly to the formation of extrusions/intrusions during LCF when plasticity commences. The calculated fatigue lives are given in Tables 3-5 and the curves are shown in Figure 4 in comparison with the experimental data. It can be inferred from Table 6 results that the surface roughness in the range from 0.01 \(\upmu\)m to 9 \(\upmu\)m only causes about a factor of 3 variations in fatigue life. Normally, the surface finish factor \(R_{s}\) is less than 1; whereas surface enhancement treatment or residual stresses may cause it to be greater than 1, in the current context of the present model. It is noticed that in the case of CA-H1025-treated 17-4 PH with a machined surface, \(R_{s}\) = 1.5. It is uncertain whether this is due to a physical effect or simply an error in linear regression, as the data points are few. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Orientation** & **Treatment** &
\begin{tabular}{c} **Surface** \\ **Condition** \\ \end{tabular} & \(R_{s}\) **(\(\upmu\)m)** & \(R_{s}\) & **M** \\ \hline Wrought 17-4 PH & - & H1025 & Machined & 0.010 & 0.666 & 1 \\ LB-FBF 17-4 PH, & Horizontal & HIPed & Machined & 0.011 & 0.297 & 1.1 \\ LB-PBF 17-4 PH & Horizontal & CA-H1025 & As fabricated & 8.38 & 0.766 & 2.1 \\ LB-FBF 17-4 PH, & Horizontal & CA-H1025 & Machined & 0.013 & 1.523 & 1.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Surface finish and microstructural factors for 17-4 PH (\(\sigma_{0}\) = 729 MPa). Figure 3: Fatigue strength vs. inverse square root of cycle number. On the other hand, the AM microstructure, perhaps together with roughness too, has a significant effect, reducing the fatigue strength, i.e., the fatigue endurance limit, to the maximum by a factor of 2 for 17-4 PH steel. Generally, the microstructural factor M reflects the effect of inclusions, as described by the inclusion theory of [PERSON] [16]. [PERSON] and [PERSON] used [PERSON]'s formulation to calculate the stress concentration factors of oblate inclusions with various aspect ratios and found that the stress concentration factor of a spherical void is 2.5 [17]. [PERSON] also used [PERSON]'s theory to evaluate the effect of graphite inclusions (flake-like, vermicular or nodular) on the fatigue strength of cast irons [18]. As porosities in AM materials are elongated in the horizontal direction, as depicted in Figure 1, it should have a lesser stress concentration effect. The authors of the original experimental work examined the AM microstructure. They observed that the size of the pores in non-HIPed AM 17-4 PH was about 80 \(\upmu\)m, and it was reduced to less than 20 \(\upmu\)m after HIPing [13].