*2.1. SEM Investigation*

To characterize the impact of the respective post treatment on the microstructure, backscatter-SEM images of microsections were taken with a Carl Zeiss EVO MA 15 microscope in accordance with [36]. Both post treatments were conducted above the solubility temperature of the investigated material [37–39]. It is mentioned that the solution temperature of the cast alloy is above 450 °C, and therefore a subsequent age hardening at low temperatures leaves the microstructural evolution unchanged [40].

## *2.2. High Cycle Fatigue Assessment*

For all test series, a modified staircase test method was utilized [41]. The high-cycle fatigue testing was carried out under a load stress ratio of R = −1 on an RUMUL Mikrotron resonant testing rig. The test frequency was in the region of 106 Hz. Specimens were gripped with collets at both ends. The test was aborted when total fracture occurred, or the run-out criterion of 1E7 load cycles was reached. In order to generate more data within the finite life region, conservatively not ruling out the possibility of pre-damaging at load levels below the fatigue limit, run-outs were reinserted [42]. In the following work, selected results referring to the AB and HIP conditions have been partially published within preliminary studies in [35]. All given stress values were normalized to the nominal ultimate tensile strength (UTS) of the base material without any post treatment, given by the powder manufacturer [33]. The fatigue strength at 1E7 load-cycles for a survival probability of 50% (*σ*f) was statistically determined by applying the arcsin√P-transformation, described in [43]. The assessment of the S/N-curve within the finite life region was done utilizing the ASTM E739 standard [44].

Mean stresses impact the fatigue strength whereby the endurance limit is decreased with growing mean stresses such as static loads along with cyclic loading [45]. The effect is usually depicted as fatigue strength amplitude plotted over mean stress. A large number of concepts have been developed in order to predict the fatigue strength for different mean stress states [46,47]. Two models, one according to Gerber [48] and another one developed by Dietman [49] were utilized within this work to consider a certain mean stress state caused by residual stresses and its impact on fatigue. Equations (1) and (2) serve as two models to correct the endured stress amplitude dependent on the present residual stress state. Both required the ultimate tensile strength *σuts* for the respective condition, which was provided by the specimen manufacturer. The parabolic Gerber concept as well as the empirical Dietmann equation showed high statistical correlation with experimental data, which is why those two models were applied. In the following, *σa*(−1) stands for the stress amplitude at a load stress ratio of R = −1, and *σ<sup>m</sup>* refers to the present mean stress. Considering this, the endurable stress amplitude *σa*, at a certain mean stress, can be estimated:

$$
\sigma\_d = \sigma\_{a(-1)} \left[ 1 - \left( \frac{\sigma\_m}{\sigma\_{\rm{uts}}} \right)^2 \right],
\tag{1}
$$

$$
\sigma\_a = \sigma\_{a(-1)} \sqrt{1 - \frac{\sigma\_m}{\sigma\_{uts}}}.\tag{2}
$$

#### *2.3. Residual Stress Measurement Methodology*

The holistic characterization of contributing factors to the fatigue strength causes the necessity to assess the residual stress state [31,32], especially in regard to the building process [50,51]. The analysis was performed with X-ray diffraction using an X-RAYBOT from MRX-RAYS, located in Brumath, France. A psi-mounting configuration with Cr-K*α* radiation was used along with a collimator size of 2 mm in diameter. The evaluation was based on the 2*<sup>θ</sup>* − *sin*2(*ψ*) method. The measurement setup was according to the ASTM E915-96 standard [52]. The exposure time was set to 30 s for each increment, opting for 25 *ψ*-increments, with a tilting angle of the X-ray tube from −40° to +40°. The measurement procedure corresponds to the ASTM E2860-12 standard [53]. The residual stress analysis is performed on all unprocessed specimens to avoid falsifying of the results due to influences of machining. Since the

fatigue strength at 1E7 load cycles is of interest, one should be aware of a possible depletion of residual stress under tensile loading. For this reason, the validation of the cyclic stability of residual stresses is necessary in order to ensure the usability of the measured stresses in following work. Therefore, in situ residual stress measurements were conducted while fatigue testing. For the assessment of the cyclic stability of the present residual stresses, the fatigue testing was stopped, residual stresses were measured, and, afterwards, the testing is continued. In order to avoid falsifying of the results, the specimen remains clamped in the testing rig.

#### *2.4. Surface Roughness Evaluation*

An engineering approach to characterize the reduction of the fatigue strength due to the surface roughness includes the maximum depth of roughness valleys as well as the roughness valley radius. Based on a concept of Peterson, the unprocessed surface, exhibiting micro notches due to the building process, was characterized. Considering the localized stress concentration of such features, the consequent reduction of fatigue properties can be described by the notch effect factor Kt; see Equation (3) [30]. This approximate solution for a shallow, assumed ideal elliptical notch, is only a function of the notch depth and radius of the curvature. Therefore, this concept incorporated the maximum surface deviation St and the notch root radius *ρ*. Based on recommendations by the author, the support effect was not taken into account and set to *n* = 1 due to a conservative approach; for this reason, Kt equals Kf. This concept finds application within this study to predict the reduced endurable stress amplitude of the unprocessed specimens, beginning with the fatigue strength of the machined ones, respectively, in mean (residual) stress free state:

$$K\_t = 1 + 2\sqrt{\frac{S\_t}{\rho}}.\tag{3}$$

Utilizing a light optical microscope and three-dimensional image processing, it was possible to determine the average maximum surface deviation (St) in a non-destructive way [54], shown in Figure 2. Since the specimen geometry is round and additionally possesses a curvature within the testing area, proper filtering of the captured surface topography is necessary. In a first step, the round specimen was partitioned into 12 sections that are individually captured and represent the entire surface. Exemplary, Figure 3a pictures the primary profile, respectively the geometrical structure of one surface segment, detected by the digital optical microscope. The thereby generated three-dimensional datasets were processed within a user-defined routine, as described in [55]. By means of a second order robust Gaussian regression filter, the roughness profile is calculated applying a cut-off wavelength *λ*<sup>c</sup> of 2.5 mm. The cut-off length was chosen as recommended by the authors in [55]. This results in the waviness profile as pictured in Figure 3b and the associated roughness profile, see Figure 3c, of the exemplified surface segment. The roughness profile now entirely reflects the surface topography as the waviness profile corresponds to the specimen geometry, respectively form. After areal roughness calculation, the evaluated area is separated into sub-areas, 1 × <sup>1</sup> mm<sup>2</sup> in size by means of the routine and plotted onto the measured surface image. An exemplary roughness map of the areal roughness parameter St is shown in Figure 2. Yellow areas mark high roughness values, and blue areas mark low ones. Due to that, not only can local areal roughness parameters be linked to surface topography properties, such as notch depth, but also information about the location of the structures are gained.

**Figure 2.** Exemplary surface roughness map.

**Figure 3.** Surface roughness evaluation process. (**a**) Primary surface profile. (**b**) Waviness surface profile. (**c**) Surface roughness profile.
