## 4 Results
### Effect of Deep Rolling Offset  
Figure 16a presents the analysis of the effect of deep rolling offset on the material's deformation, with a deep rolling offset of 0.1 mm from the experimental setup. The figure on the top shows a color-coded deformation map, while the graph on the bottom illustrates the total deformation variation over time. The deep rolling offset is the lateral shift of the tool relative to its previous pass, and this factor is critical in ensuring uniform stress distribution and deformation across the material surface. The color-coded map represents the total deformation experienced by the material during the deep rolling process, expressed in millimeters. The deformation values range from 0 mm to 2.744 mm, with colors indicating different levels of deformation. The red and orange areas under the rolling tool show the regions of maximum deformation, reaching up to 2.744 mm. These areas experience the greatest displacement as the tool presses into the material, which is consistent with the 0.1 mm offset applied in the experiment. This high deformation is expected as the tool repeatedly rolls over closely spaced regions of the material, inducing compressive residual stress and plastic deformation. The yellow and green regions represent areas with less deformation, ranging from 1 mm to 1.6 mm. These regions are further away from the point of contact and thus experience lower levels of displacement. The deformation gradually decreases as the distance from the tool increases, indicating that the deep rolling process primarily affects the surface directly under and near the tool. The deformation is highly localized under the tool, reflecting the concentrated nature of the deep rolling process. The small offset of 0.1 mm ensures that the tool covers almost the entire surface with minimal gaps, leading to uniform deformation. However, some areas experience slightly lower deformation due to the tool's offset not fully overlapping with the previous pass. The graph on the bottom shows the total deformation variation over time, measured in seconds, with deformation values on the Y-axis in mm. The horizontal axis represents time, ranging from 0 to \(7\times 10^{-3}\) s. This period corresponds to the duration of the deep rolling process as the tool moves across the surface. The vertical axis shows the deformation in millimeters, with the colored lines representing the deformation at specific points on the material surface. The green and blue lines show periodic peaks, corresponding to moments of maximum deformation as the tool moves over specific points on the surface. The peaks reach up to 2.744 mm, indicating that the material experiences significant displacement during each pass of the tool. The valleys reflect moments when the tool moves to a different point or reduces pressure, causing lower deformation. Despite some fluctuations, the deformation peaks remain relatively stable, reflecting the consistent 0.1 mm offset applied throughout the process. This consistency ensures that the tool applies pressure evenly across the material, leading to uniform deformation and stress distribution. The deep rolling offset plays a crucial role in determining the uniformity of deformation and residual stress distribution across the material. The 0.1 mm offset ensures that the rolling tool passes very close to its previous path, covering almost the entire surface without leaving significant gaps. This small offset helps achieve uniform deformation across the material, as shown by the consistent deformation peaks in the graph and the widespread red and orange zones in the deformation map. The high deformation observed under the tool translates into the formation of compressive residual stresses. These stresses improve the material's fatigue resistance by preventing crack initiation and propagation. The uniform deformation induced by the small offset ensures that compressive stresses are evenly distributed, reducing the likelihood of stress concentrations that could lead to material failure.