## 3 Results and Discussion  
### Near-Surface Properties  
Microstructural analysis of the near-surface layer after deep rolling at an elevated temperature of 550 \({}^{\circ}\)C was carried out by EBSD. Figure 1 shows a representative EBSD inverse pole figure (IPF) map with superimposed image quality (IQ). Similar to the initial state and the dr_855_RT condition shown in [39], the overall microstructure shows no preferred orientation. Furthermore, grains are pervaded with sub-grain structures. In line with the conditions detailed above, grain refinement, being numerously reported for mechanical surface treatments such as deep rolling [42], becomes obvious in the near-surface layer. Despite the increased deep rolling temperature of 550 \({}^{\circ}\)C and a corresponding increase in the SFE, mechanical twins can be still seen in some grains of the dr_855_550 \({}^{\circ}\)C condition, i.e., in an area of about 50 \(\upmu\)m below the surface. Although these twins are present to a lesser extent compared to the dr_855_RT condition, it can be deduced that an increase of the deep rolling temperature to 550 \({}^{\circ}\)C is still not sufficient to fully suppress the TWIP effect here. In contrast to the results of [PERSON] et al. [38], revealing no deformation twinning after uniaxial tensile testing at a deformation temperature of 400 \({}^{\circ}\)C, this observation clearly demonstrates that the multiaxial stress state induced by deep rolling is still able to activate the TWIP effect despite the even higher process temperature of 550 \({}^{\circ}\)C. Nevertheless, besides the low extent of deformation-induced twinning, the austenite grains seem to be mainly deformed by dislocation slip. This can be deduced from the high amount of EBSD zero solutions displayed in black in the direct vicinity of the surface, clearly indicating high dislocation densities in a region about 15-20 \(\upmu\)m below the surface. In line with the literature detailed before, deep rolling at 550 \({}^{\circ}\)C leads to increased surface layer hardness when compared to the initial state (recompiled from [39]). This is demonstrated by the hardness distribution in the near-surface area, as shown in Figure 2. A peak hardness value of approximately 425 HV0.2 has been measured at a distance of 0.08 mm to the surface for the dr_855_550 \({}^{\circ}\)C condition, which is lower than the corresponding peak hardness of the dr_855_RT specimen examined in the prior work by [PERSON] et al. [39]. This trend continues until both graphs intersect at a depth of 0.45 mm. Afterwards, dr_855N_550 \({}^{\circ}\)C shows higher values in all cases. The different work-hardening effects after deep rolling at RT and 550 \({}^{\circ}\)C are further illustrated by the integral width distributions depicted in Figure 3c,d, where the dr_855N_550 \({}^{\circ}\)C condition is generally characterized by lower values than dr_855N_RT in both longitudinal and circumferential directions. These observations can be attributed to stress relaxation induced by recovery effects at the given temperature. Such effects are able to soften the material, as numerously  
Figure 1: IPF map with superimposed IQ depicting the near-surface microstructure following deep rolling at 550 \({}^{\circ}\)C using a deep rolling force of 855 N. Color coding with respect to loading direction is in accordance with the standard triangle shown on the right. shown in the literature [58; 59; 60; 61; 62]. Here, recovery effects mainly set in in the severely deformed near-surface area of the specimen, leading to a reduction in the hardness values. At larger distances from the surface, the positive effects of the warm deep rolling, i.e., a more pronounced work-hardening accompanied by an increase in hardness, appear to overcome the effects related to the recovery processes, eventually explaining the intersection point of the dr_855_550 \({}^{\circ}\)C and dr_855_RT conditions displayed in Figure 2. As [PERSON] et al.