## 4 Fatigue Analysis and Discussion
### LB-Pff 17-4 Ph  
The conventional 17-4 PH is a martensitic stainless steel. Due to the high cooling rates during SLM, which are much faster than the critical cooling rate specified in the CCT diagram for 17-4 PH stainless steels, similar proportions of \(\alpha^{\prime}\) and \(\gamma\) phases during martensitic transformation could form in LB-PfF 17-4 PH. Therefore, LB-PfF 17-4 PH samples might not be completely martensitic and contain retained austenite due to high solidification speeds during fabrication. The material chosen in this study has gone through the same heat treatment as its wrought counterpart, hoping to resume to the martensite phase as much as possible. The fatigue test data of H1025 heat-treated wrought 17-4 PH, CA-H1025 heat-treated LB-PBF 17-4 PH and the HIPed and CA-H1025 heat-treated LB-PBF 17-4 PH stainless steel \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & **Orientation** & **Treatment** & **Surface Condition** & \(\mathbf{R_{a}}\) (\(\mathbf{\mu}\mathbf{m}\)) \\ \hline Wrought 17-4 PH & - & H1025 & Machined & 0.010 \\ LB-PBF 17-4 PH & Horizontal & CA-H1025 * & As fabricated & 8.38 \\ LB-PfF 17-4 PH, & Horizontal & CA-H1025 & Mechined & 0.013 \\ LB-PfF 17-4 PH, & Horizontal & HIPed + & Machined & 0.011 \\  & & CA-H1025 & Machined & 0.010 \\ Wrought AA6061 & - & - & Machined & 0.010 \\ SLM AlSi10 Mg & Horizontal & Stress relieved & Polished & 1.5 \\ SLM AlSi10 Mg & Vertical & Stress relieved & Polished & 1.5 \\ Wrought Ti6 Al4V & - & - & Machined & 1 \\ DMLS Ti6 Al4V & Horizontal & HIPed & Polished & 10 \\ DMLS Ti6 Al4V & Horizontal & Stress relieved & As fabricated & 11–13 \\ \hline \hline \end{tabular}  
* CA-H1025 heat treatment condition is based on the ASTM A693 standard [10].  
\end{table} 
Table 1: Material conditions and surface roughness (data taken from [13; 14]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Material** & \(\mathbf{\
u}\) & **E (GPa)** & \(\mathbf{w_{s}}\) (\(\mathbf{j}\)/m\({}^{2}\))** & **b (\(\mathbf{10^{-10}}\) m)** \\ \hline Aluminum & 0.3 & 66.5 & 1.125 & 2.86 \\ Steel & 0.3 & 201 & 2.373 & 2.48 \\ Ti-6 Al-4V & 0.3 & 113 & 1.953 & 3.21 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material physical properties. specimens are shown in Tables 3-5, respectively. First, Equation (4) is used to analyze the fatigue data below the yield strength. Rearranging Equation (4), the fatigue strength for a given number of cycles can be expressed as:  
\[\sigma_{a}=\frac{1}{2}\sqrt{\frac{6\mu w_{s}R_{s}}{(1-\
u)bN_{c}}}+\frac{\sigma_ {0}}{M} \tag{5}\]  
where \(\sigma_{a}=\Delta\sigma/2\) is the stress amplitude. Equation (5) can be used to perform linear regression analysis of the experimental data below the yield strength (<1100 MPa), as shown in Figure 3. Especially, factors M and R\({}_{s}\) can be obtained from the intercept and slope of the regression line:  
\[slope=\frac{1}{2}\sqrt{\frac{6\mu w_{s}R_{s}}{(1-\
u)b}} \tag{6}\]  
\[intercept=\frac{\sigma_{0}}{M} \tag{7}\] \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 & 1.147 & 0.65 & 0.09 & 2132 & - \\ condition & 828 & 0.41 & - & 54,980 & 38,781 \\ Load-controlled & 828 & 0.41 & - & 62,330 & 38,781 \\ condition & 623 & 0.31 & - & 220,882 & 245,988 \\  & 623 & 0.31 & - & 377,820 & 245,988 \\  & 541 & 0.27 & - & 1,266,440 & 1,595,987 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Fatigue test results of CA-H1025 heat-treated AM 17-4 PH stainless steel with the machined surface under axial loading (test information and data taken from [13]).