## 1 Introduction
Generally, the surface condition of a component has a significant influence on the fatigue behavior as the surface represents the area being subjected to the highest stresses during cyclic loading. In addition to the load distribution, geometrically necessary notches as well as corrosion or wear often lead to crack initiation directly at the surface or within the near-surface area [40; 41]. Thus, the condition of the near-surface layer determines the properties, i.e., the surface integrity (SI), of a component under cyclic loading or tribological and corrosive stresses, amongst others. Mechanical surface treatment processes are well-known for establishing near-surface layers of a component that are characterized by high compressive residual stresses, increased hardness due to strain hardening and a smooth surface appearance, depending on the respective treatment process used [40; 42; 43; 44]. Furthermore, deformation-induced twinning or phase transformation, exemplarily shown in [39; 45; 46; 47], can be obtained as a result of high plastic deformation. In particular, residual stresses are of paramount importance for the service life of structural components. While compressive residual stresses increase the service life, tensile residual stresses, which are a direct result of many technological processes such as welding, have a detrimental effect as they promote crack initiation and accelerate crack growth [48; 49; 50; 51; 52]. Therefore, evaluation of residual stresses by experimental or theoretical analysis is mandatory for the assessment of components realized by different machining and manufacturing processes [53; 54]. Deep rolling and shot peening represent the most common mechanical surface treatment processes, however, a large variety of other techniques such as hammering, grinding, brushing, needle or water peening have been established [42]. Furthermore, several of these treatments can be conducted at differing temperatures, eventually promoting additional modifications of the near-surface layer. As a result of the pronounced work-hardening ability detailed above, HMnS are suitable candidate materials for mechanical surface treatment processes. However, only a few studies investigating the effect of mechanical surface treatments and, thus, the effect of residual stresses, hardness and roughness on the SI of HMnS TWIP and TRIP steels, can be found in the literature [47; 55; 56; 57]. In a previous study, the evolution of residual stresses, microstructure and cyclic performance of the X40 MnCrAl19-2 TWIP steel after deep rolling at RT, \(-196\) and \(200\)\({}^{\circ}\)C, was investigated by the authors' group [39]. Following deep rolling at RT and \(200\)\({}^{\circ}\)C, twinning in the near-surface area was detected to a similar extent, indicating that the increase in temperature and, thus, in the SFE was not high enough to suppress the TWIP-effect. In contrast, cryogenic deep rolling at \(-196\)\({}^{\circ}\)C led to a solid-solid phase transformation, promoting the formation of \(\varepsilon\)-martensite in the near-surface layer. The highest residual stresses with a maximum of \(-800\) MPa accompanied by high hardness values up to 475 HV0.1 were reported for the condition being deep rolled at 200 \({}^{\circ}\)C. Compared to the initial state, fatigue properties in the HCF regime were improved irrespective of the deep rolling temperature. However, the martensitic phase transformation induced by cryogenic deep rolling was shown to have a negative impact on the fatigue performance, at least at relatively high loading amplitudes. This was rationalized by an increased plastic deformation as well as microstructural notch effects in the two-phase region established in the near-surface area. In line with the similar microstructures, fatigue properties of the conditions deep rolled at RT and 200 \({}^{\circ}\)C revealed only minor differences. Still, data indicated a slightly improved performance at high stress amplitudes after deep rolling at elevated temperature.