## 3 Results and Discussion
### Material Behavior under Quasistatic and Cyclic Loads  
In order to determine the influence of deep rolling temperatures on the macroscopic material behavior, both tensile and HCF tests have been conducted and will be discussed hereafter based on a direct comparison to findings of [PERSON] et al. [39] (acting as a benchmark). As depicted in Figure 4 and discussed in [39], both YS and UTS are increased compared to the initial state after deep rolling, irrespective of the process temperature. Here, especially the higher YS is to be considered for the application of high-manganese steels [23]. Comparing the deep rolled conditions with each other, temperature does not seem to have a pronounced effect on the monotonic stress-strain response as the curves of dr_855_550 \({}^{\circ}\)C and dr_855_RT only deviate marginally, revealing only slight differences in YS and UTS. In [39], it was shown that deep rolling at 200 \({}^{\circ}\)C resulted in an increased YS as compared to the RT deep rolled counterparts. In line with data from hardness measurements shown in Figure 2, a slightly lower YS can be seen for dr_855_550 \({}^{\circ}\)C, once again indicating the turnaround point with respect to the elevated process temperatures, as discussed above. Additionally, a decrease in ductility compared to the RT deep rolled specimen can be seen for dr_855_550 \({}^{\circ}\)C, following the same trend already seen after deep rolling at 200 \({}^{\circ}\)C [39]. During fatigue testing, all deep rolled specimens are characterized by an improved fatigue life in direct comparison to the initial state recompiled from [39], as can be derived from the S-N curves with corresponding trendlines depicted in Figure 5. This observation can be credited to increased YS as well as the compressive residual stresses impeding crack initiation. At lower stress amplitudes, the effect of the strengthened surface layer diminishes consistently. The overall improvement in specimen lifetime is in line with data available in literature for surface-treated austenitic steels and other alloys [65; 66; 67]. Notably, the specimens processed at elevated temperatures of 550 \({}^{\circ}\)C show a significant increase in fatigue life in comparison to their RT deep rolled counterparts. From the trendlines plotted for dr_855_550 \({}^{\circ}\)C and dr_855_RT respectively, being characterized by almost identical slopes, enhancements in fatigue life after deep rolling at an elevated temperature of 550 \({}^{\circ}\)C seem to be persistent for all stress amplitudes considered. The results presented by [PERSON] et al. [39] revealed that, despite highest compressive residual stresses and depth effect as well as increased YS, UTS and near-surface hardness, increased temperatures of 200 \({}^{\circ}\)C during deep rolling only resulted in slightly improved fatigue performances at high stress amplitudes, whereas at lower stress amplitudes, no differences could be identified compared to the RT deep rolled counterparts. In contrast, a further increase of the deep rolling temperature to 550 \({}^{\circ}\)C benefits fatigue in the HCF regime by a constant factor of about 2, as evidenced by the results presented in Figure 5. With the above discussions in mind, this behavior can neither be attributed to higher static strength nor increased residual stresses or surface hardness. In order to rationalize these (at first glance contradicting) results, both fracture surface analysis and residual stress stability tests have been conducted and are discussed in the following. Figure 6 shows representative post-fatigue fracture surfaces of selected specimens for the dr_855_550 \({}^{\circ}\)C condition. Generally, well-known features of a fatigue tested specimen, i.e., areas of crack initiation (marked by the white arrows in the overview images) and propagation as well as a final overload fracture region, can be derived from the micrographs irrespective of the stress level considered.