3.2.1. Surface Residual Stresses and Cyclic Stability

For the unprocessed condition, it is highly necessary to know the residual stresses at the surface, since this is the location of the failure origin, and the condition within the failure initiation area is essential. The interaction between surface condition, residual stresses, and, furthermore, the microstructure as well as understanding the importance of their codependency is also reported in [67,68]. To ensure a proper assessment of the axial residual stresses at the surface, three measurements along the circumference in a distance of 120° are performed. The measurements are conducted before testing and clamping. For further analysis, the mean value is considered to serve as a base value with the scatter band representing a confidence level of 95%. The residual stress results are normalized to the UTS of the material and abbreviated as *σ*res,ax,surf. This allows for quantifying the intensity of residual stresses as a share of the ultimate tensile strength and enables a sophisticated valuation of the range in which the occurring stresses lie. All measured stresses are in the tensile region. The analysis reveals a significant decrease of residual stresses for both post treated conditions referring to the AB condition. It is found that HIPing reduces the axial residual stresses at the surface by 54.2% and solution annealing by 46.7%. Each specimen which reached the run-out criterion was measured again and showed no change. The outcome of the in situ residual stress measurements validate that testing at the fatigue limit (run-out load level) causes no notable changes of surface residual stresses. This case

is depicted by the two black lines in Figure 6. However, increasing the tensile load above the fatigue limit either leads to a relaxation of residual stresses or failure before measurable changes to the residual stress state; see red lines in Figure 6, occur. The findings therefore prove that residual stresses measured before testing are still present after testing at run-out level or remain even unchanged until failure. This enables to look at measured values before testing as permanent present mean stresses. All results are given in Table 3, whereby all stress values are normalized to the surface stress before testing but after the specimen is clamped.


**Table 3.** Axial surface residual stress measurement results.

**Figure 6.** Cyclic stability of residual stresses.

#### 3.2.2. In-Depth Residual Stress Distribution

To characterize the residual stress state directly at the crack initiation site for the machined specimens, it is necessary to electrolytically polish into the depth in which the failure responsible defects lie. The determination of the residual stresses at the crack origin is essential since they are substantially involved in failure initiation and crack growth; the present stress is denoted in the following as *σ*res,ax,surf for crack initiation at the surface and *σ*res,ax,bulk for failure from internal defects. To negate the effect of machining, an in-depth progression of residual stresses of the AB and HIP condition is performed. Based on the fracture surface analysis of the machined specimens, it is found that the average failure critical imperfection either lies at the surface or in a maximum depth of about 200 μm beneath the surface. Considering this, a conservative assumption is made to take the mean residual stress estimated within the aforementioned region for further analysis. The in-depth progression is shown in Figure 7, in which all stress values are normalized to the respective stress measured at the surface to highlight the distribution of residual stresses in depth. The greyed out area marks the machining allowance of 1 mm that is added to the building process. Beneath the unprocessed surface, a stress peak is observed for the HIP and AB conditions. Both show a similar progression with significantly increased axial tensile stresses in the area in which the critical imperfections lie, signalized by the red-shaded area. The results are summarized in Table 4.

**Figure 7.** Normalized in-depth axial residual stress progression of AB and HIP conditions.

**Table 4.** Axial in-depth residual stress measurement results.


Considering the comparably high residual stresses at the crack initiation spot as an existing mean stress, they change the present mean stress state and affect the crack initiation, propagation and consequently the fatigue strength in great measure [69,70].

#### *3.3. Surface Roughness Parameter Evaluation*

For the application of the notch effect concept by Peterson, mean values of all gathered data of St and *ρ* are taken into the calculation of Kt, since the most critical surface feature is a certain combination of notch depth and notch valley radius. Since the aim is to non-destructively determine the reduction in fatigue strength, the values for St and *ρ* are taken from the optical surface assessment and not from a subsequently performed fracture surface analysis. Empirical investigations show that the mean value of the maximum valley depth of all 12 segments describes the critical surface roughness properly. For a suitable assessment of the area-based roughness parameter St, comparison, and validation of the optical evaluation, the maximum surface deviation is also measured within the fractured surfaces. The non-destructive optical surface evaluation is in sound correlation with the mean values from measurements on fractured specimens. The average deviation of the two methods varies between 5.8% and 7.4%, which confirms the applicability of the used evaluation routine. The results for the surface roughness parameter St are normalized to the mean value evaluated by the fracture surface analysis and are summarized in Table 5. It is observed that both post treatments have a beneficial impact on the surface roughness; St is decreased by about 14%.

The specimens are printed in a vertical (axial) direction, which leads to a periodically repetitive formation of the surface shape in the building direction. This recurring surface texture for additively manufactured structures is also reported in [71]. Three-dimensional surface imaging allows the measurement of the recurring roughness valley radii (*ρ*) in the loading direction with only minor deviations; see Figure 8. The evaluation is based on line measurements at several selected specimens and different locations around each specimen. It is mentioned that the notch radii can not be measured

in the fractured surface since this would provide the notch radius within the wrong plane, namely perpendicular to the loading direction. The comparison of the investigated conditions reveals that the average roughness valley radius increases due to the post treatments, which mitigates the sharpness of the notch.

**Figure 8.** Surface notch valley radii measurement.

**Table 5.** Results of the surface roughness evaluation.

