## 4 Summary and Conclusions  
The present work represents a follow-up study to the results shown by [PERSON] et al. [39] and was conducted to investigate the consequences of deep rolling at elevated temperature on the near-surface and fatigue properties of the high-manganese TWIP steel X40 MnCrAl19-2. Analysis of the surface-treated area was conducted by X-ray diffraction and EBSD, as well as microhardness measurements and uniaxial tensile tests. Additionally, HCF properties studied by means of fully reversed tension-compression tests were critically discussed based on fracture surface appearance and analysis of residual stress stability. From the findings presented, the following conclusions can be drawn:  
* EBSD maps of the investigated condition reveal a highly deformed near-surface microstructure, indicating a high dislocation density. Despite the increase in the SFE due to the elevated temperature, deformation-induced twinning can still be seen as a result of the multiaxial stress state induced by deep rolling. * Deep rolling at 550 \({}^{\circ}\)C yields lower hardness and residual stress depth profiles when compared to RT deep rolled counterparts. Obviously, stress relaxation induced by recovery effects appears to outweigh the positive effects of warm deep rolling. * Despite the nominally lower residual stress values and hardness profiles, specimens deep rolled at elevated temperature are characterized by a noticeable increase in fatigue life due to a stabilized near-surface microstructure. Irrespective of the stress amplitude considered, fatigue properties were improved by a factor of two. As a result, deep rolling at elevated temperatures eventually paves the way for safe and reliable industrial applications of HMnS components being subjected to fatigue loading, such as whishbones in the automotive sector. * Fractography revealed crack initiation in the interior of the specimen for low- and medium-stress amplitudes, whereas at high-stress amplitudes, cracks were initiated at the direct vicinity of the surface. It is thought that the compressive residual stresses in the surface layer, shifting the location of crack initiation to the interior of the specimen, lose their effect at the increased stress amplitudes. * Residual stress profiles after half-life fatigue (NB/2) show superior stability after deep rolling at 550 \({}^{\circ}\)C compared to RT deep rolled specimens, rationalizing the results obtained based on fatigue and fractography investigations. The superior residual stress stability can be attributed to dynamic strain aging effects. * Future work should focus on in-depth evaluation of the plastic strain amplitude of the conditions deep rolled at different temperatures in order to further analyze the different elementary effects being active. Additionally, the stability of residual stresses under thermal load should be part of future investigations. Conceptualization, T.W. ; Methodology, T.W. ; Investigation, T.W., M.K. and T.O. ; Visualization, T.W. ; Writing--Original Draft Preparation, T.W. and M.K. ; Writing--Review and Editing, T.W., M.K., T.O. and T.N. ; Supervision, T.N. ; Project Administration, T.N. ; Funding Acquisition, T.W. and T.N. All authors have read and agreed to the published version of the manuscript. The present study was funded by \"Deutsche Forschungsgemeinschaft\" (DFG) (German Research Foundation), Grant No. 406320672, within the research project \"Mechanische Oberflachenbehandlung von hochmananhaltigen TWIP/TRIP Stahlen--Mikrostrukturelle Stabiliitat und mechanische Eigenschaften\". The data presented in this study are available upon request from the corresponding author. **Acknowledgments:** The authors would like to thank [PERSON] and [PERSON] for technical support regarding the maintenance and operation of the laboratory equipment. The assistance of [PERSON] is greatly appreciated. The authors acknowledge thyssenkrupp Hohenlimburg GmbH (Hagen, Germany) for providing the material. **Conflicts of Interest:** The authors declare no conflict of interest.