*3.4. High Cycle Fatigue Testing*

The high-cycle fatigue test results for the HIP condition are displayed in Figure 9. The solid lines denote the machined surface condition, whereby black with square markings represents the AB condition and blue with triangle markers is used for the HIP condition. Solely, the comparison of both machined HIP to AB conditions is published within a previous study in [35]. The dashed lines stand for the unprocessed surface condition. The displayed SN-curves are evaluated at a survival probability of 50%. All results are summarized in Table 6. The finite life region is denoted as FLR, and the long life region is abbreviated as LLR. In order to obtain reasonable results and ensure testing within the linear-elastic region, the peak load level for testing is below the yield strength of the material.

Comparing the machined conditions, the HIP treatment leads to an increase in fatigue strength by 13.8% referring to the AB condition. A similar trend is observed for the unprocessed condition. The HIPed series exhibits a 25.3% higher fatigue strength than the AB series. For both post treatment conditions, the difference between machined and unprocessed surface condition is significant. The as-built surface decreases the fatigue strength for the HIP condition by 62.2% and by 65.6% for the AB condition. Hence, the assessment of the surface roughness is essential. Regarding the scattering between 10% and 90% survival probability, HIPing narrows the scatter band for each surface condition within the finite life region as well as in the long life region. It is observed that the HIP treatment also positively impacts the slope of the S/N-curves in terms of a less steep behaviour. Partially, these results are already published in [35].

**Figure 9.** S/N curves for the AB and HIP test series.

The following Figure 10 shows the fatigue test results for the solution annealed condition. As described before, black lines and markings refer to the AB condition. Analogous to Figure 9, the green solid line presents the results for the machined, and the green dashed line the results of the unprocessed condition. Green circular markings are used to flag the test data. Solution annealing reveals the same trend as observed for the HIP condition. The fatigue strength of the machined SA condition lies 5.9% above the fatigue strength of the machined AB. In regard to the unprocessed surface condition, solution annealing enhances the fatigue strength by 25.3%. One can observe that the unprocessed surface again has a major impact on the fatigue behaviour, as machining leads to an improvement of +146%. The scattering between 10% and 90% survival probability is again decreased for the machined condition. The slope in the finite life region is again found to be less steep than for the AB condition.

**Figure 10.** S/N curves for the AB and SA test series.


**Table 6.** High cycle fatigue test results.

#### *3.5. Fracture Surface Analysis*

In order to holistically characterize the fatigue behaviour of the investigated material, a fracture surface analysis is carried out for every tested specimen. It is found that there are different mechanisms that cause the failure.

#### 3.5.1. Failure from Intrinsic Imperfections

Investigating the fractured surfaces of the machined AB condition reveals that, in every case, surface-near pores are responsible for failure; see Figure 11a. The size and location of the imperfection are the determining criteria in terms of the fatigue strength [72–74]. For the machined HIP test series, the failure initiates from microstructural inhomogeneities. The debonding of Si-crystals is responsible for crack initiation, which is depicted in Figure 11b. This failure behaviour is already published within preliminary studies on this topic [35]. The post treatment of the SA condition is similar to the HIP treatment, which leads to a comparable microstructure. On the contrary, the fracture surface analysis displays a combined failure cause of microstructural inhomogeneities and porosity, as shown in Figure 11d. The occurring porosity may be attributed to the lack of isostatic pressure during the SA treatment. To be sure about the failure mechanism, an EDX-Analysis is performed on the fractured surface. In regard to Figure 11c, area 'a' shows a chemical composition of Al18.06Si65.41Mg16.53. Spots 'b' and 'c' consist of a great measure of Silicon, which leads to the interpretation of debonding Si-crystals, also found in [66]. In comparison, spot 'd', which lies beneath a delaminated Si-Slab, is found to be base material.

**Figure 11.** Fracture surface analysis of machined specimens. (**a**) Failure initiation spot of AB specimens. (**b**) Failure initiation spot of HIP specimens. (**c**) EDX analysis on the fractured surface of one HIPed specimen. (**d**) Failure initiation spot of SA specimens.

## 3.5.2. Failure from Surface Features

The main outcome of the fracture surface analysis for all test series and each specimen exhibiting an unprocessed surface is that the surface texture is in every case failure critical. The effect of the surface roughness dominates all other imperfections and microstructural features in terms of crack initiation and the consequential fatigue strength. This behaviour is also observed in [75]. Figure 12a,b highlight the failure origin from a roughness valley. The substantive effect of the surface roughness on the fatigue strength is well reported in [76–78]. The given examples are from the unprocessed AB series. No evidence of pores or microstructural inhomogeneities is found in the surrounding area for any test series. In conclusion, one can distinctively determine the surface condition as the crucial feature, which overshadows all other failure reasons and are therefore neglectable in the presence of an unprocessed surface.

**Figure 12.** Fracture surface analysis for one specimen of the unprocessed condition. (**a**) Fractured surface of unprocessed as-built specimen. (**b**) Failure responsible surface characteristic.

#### *3.6. Fatigue Assessment*

#### 3.6.1. Mean Stress Correction

Macroscopic residual stresses of the first order may be considered to overlay with load stresses and therefore act as mean stresses, encouraging a shift of the actual load stress ratio to an effective stress ratio Reff [79,80]. The intended testing is performed at a load stress ratio of R = −1, which means that the mean stress is zero. Taking the effective mean stress caused by load and residual stresses into account, the load stress R-ratio is shifted to an effective R-ratio, according to Equation (4):

$$R\_{eff} = \frac{\sigma\_{\text{min}} + \sigma\_{\text{res},ax}}{\sigma\_{\text{max}} + \sigma\_{\text{res},ax}}.\tag{4}$$

For the HIP condition, the present residual stresses lead to an effective stress ratio of Reff = −0.36 for the machined and to Reff = −0.38 for the unprocessed surface condition. The effective stress ratio for the AB machined condition calculates to Reff = 0.09 and even to Reff = 0.1 with an unprocessed surface. Hence, it is clearly shown that residual stresses alter the testing condition significantly. To independently assess the impact of the surface roughness, the stress amplitude is extrapolated to a ratio of R = −1. The aim is to eliminate all influencing factors but one, the surface roughness. This enables the independent quantification of it. This correction of the stress amplitude to a mean stress of zero accounts for the influence of residual stresses and simultaneously gives a conservative estimation of the endurable fatigue strength amplitude as if no residual stresses would be present. Figure 13 presents the mean stress corrected fatigue strength amplitude according to Gerber, which is denoted as *σ*f,M,cor,G in the following. The same procedure is applied for the correction according to Dietmann, denoted as *σ*f,M,cor,D, shown in Figure 14. The results are also summarized in Table 7. Comparing both concepts, the model according to Gerber is more conservative than the Dietmann one in regard to the experimental results *σ*f,exp. In conclusion, one can state that it is proven that the residual stress state contributes in great measure to the fatigue resistance; this effect can be observed by the increase of the endurable fatigue strength amplitude for the AB and HIP condition.

The difference in the residual stress free state between AB und HIP may be attributed to beneficial microstructural changes and the different failure initiation modes for the HIP condition, as previously presented and published within [35]. Both concepts lead to similar results, estimating a benefit due to HIPing of approximately +5.8% for the machined and 23.9% for the unprocessed condition, see Table 8.

**Figure 13.** Haigh diagram with residual stresses accounted for according to Gerber.

**Figure 14.** Haigh diagram with residual stresses accounted for according to Dietmann.

**Table 7.** Mean stress corrected fatigue strength values.


**Table 8.** Impact of the microstructure on the fatigue strength in residual stress free state.


3.6.2. Assessment of the Surface Roughness in Mean Stress Corrected State

The importance of the assessment of the surface roughness caused by the building process is obvious, since it is unequivocally found to be the fatigue strength determining factor. The fatigue test results as well as the fracture surface analysis emphasize the evaluation of the surface roughness and its influence. The results for the notch factor of all conditions are given in Tables 9 and 10, in which the estimated fatigue strength based on the analytical model is abbreviated as *σ*f,UP,mod, and the experimental results are denoted as *σ*f,UP,exp, respectively, for each unprocessed condition. As expected based on the roughness parameters, the notch effect is more pronounced for the AB condition than for the post treated conditions. Beginning with the corrected fatigue strength of the machined condition (*σ*f,M,cor) and dividing it by the notch factor (Kt), which acts as a reduction factor accounting for the surface roughness, estimates the fatigue strength of the unprocessed condition; see Equation (5):

$$
\sigma\_{f,IP,mod} = \frac{\sigma\_{f,M,cor}}{K\_t}.\tag{5}
$$

Eventually, the analytically estimated, mean stress corrected fatigue strength is compared to the experimentally determined fatigue strength, both in a residual stress freed state. The results of the analytical approach deviate in the range of +6.4% to +16.3% from the experimental results, which acknowledges the applied procedure to be deployable for the estimation of the reduction of fatigue properties due to the surface roughness starting from a machined surface condition in a residual

stress freed state utilizing mean stress corrected values according to Gerber, see Table 9 and Dietmann, summarized in Table 10.


**Table 9.** Assessment of the surface roughness on the fatigue strength after Gerber.

**Table 10.** Assessment of the surface roughness on the fatigue strength after Dietmann.


Both concepts present a minor non-conservative approach, but the scatter band (1:Ts) in the long life region of 1:57 for the UP-AB, and 1:43 for the UP-HIP condition, as given in Table 6, needs to be considered as well. Consequently, the estimated mean fatigue strength is well within the scattering of the experimental results.

The above presented concept is utilized to predict the fatigue strength of the SA condition. Both of the others, AB and HIP, reveal in machined and unprocessed conditions the same effective stress ratio due to residual stresses because only the residual stresses in unprocessed SA conditions are measured, assuming the same R-ratio in machined conditions. Applying this procedure, the fatigue strength of the machined SA condition can be properly predicted with both concepts, denoted as *σ*f,M,pred,G/D. The deviation from the experimental results is calculated to only +3.4%; see Table 11.


**Table 11.** Fatigue strength assessment of the SA condition.

#### **4. Discussion**

Based on the results presented in this paper, the fatigue strength of additively manufactured AlSi10Mg structures is altered by post treatments, the residual stress state and the surface condition. The fatigue strength is improved by HIPing and solution annealing, for a machined as well as a unprocessed surface, compared to the AB condition. This study also proves a beneficial effect of the investigated post treatments on the microstructure and consequently on fatigue.

The outcome of the investigations on the surface condition reveals that, by virtue of the roughness, fatigue properties are significantly reduced. Comparing the as-built surface to a machined surface, this work reveals that the unprocessed surface causes a significant reduction of fatigue properties of about −60%. The surface roughness analysis shows that the HIP as well as the SA treatment positively influences decisive surface related characteristics due to the heat input and the applied pressure during

the HIP process. The maximum roughness valley depth is decreased and furthermore the average roughness valley radius is mitigated compared to the AB condition. These beneficial changes to the surface topography contribute to an improved fatigue behaviour of +25.3% for both conditions compared to the AB condition.

This work leads to the conclusion that the residual stress state at the respective failure origin can be considered as a present mean stress, whereby a shift of the intended load stress ratio to an effective stress ratio occurs. Another finding of the conducted investigations is that, due to the heat influence of the post treatments, residual stresses are reduced by roughly 50%. An analysis of the in-depth progression reveals increased tensile residual stresses compared to the surface by a factor of almost three. By the means of the presented methodology, a prediction of the reduced fatigue strength of unprocessed specimen, in relation to the machined condition, is given. The developed model is shown to be well applicable to the investigated test series in a residual stress free state. Although the fatigue strength amplitude prediction is slightly non-conservative, the estimation is well within the scatter band of the the experimental results in the long life region.

**Author Contributions:** Conceptualization, W.S. and M.L.; methodology, W.S. and M.L.; validation, W.S. and M.L.; formal analysis, W.S.; investigation, W.S., S.P. and S.S.; resources, W.S.; data curation, W.S. and F.B.; writing—original draft preparation, W.S.; writing—review and editing, W.S. and M.L.; visualization, W.S.; supervision, M.L. and F.G.; project administration, M.L. and F.G.

**Funding:** This research received no external funding.

**Acknowledgments:** Special thanks are givento the Austrian Research Promotion Agency (FFG), who funded the research project by funds of the Federal Ministry for Transport, Innovation and Technology (bmvit) and the Federal Ministry for Digital and Economic Affairs (bmdw). Scientific support regarding the optical surface topography measurement and evaluation was provided in the course of the "Christian Doppler Laboratory for Manufacturing Process based Component Design".

**Conflicts of Interest:** The authors declare no conflict of interest.
