## 4 Simulation Analysis of Roughness on Shot Peening Residual Stress and Surface Deformation
### Effect Analysis of Roughness on Residual Stress and Deformation of Shot Peening
#### 4.1.2 Discussion of Relation between Surface Roughness and Maximum Surface Residual Stress  
The reason for the phenomenon may be that during the shot peening process, the kinetic energy of the pellet decreases rapidly with the increase of impact indentation depth. When the kinetic energy decreases to zero, the rebound effect of plastic and elastic deformation on the target material surface pushes the pellet apart. During the impact process on the smooth surface, the depth of impact and pit size gradually increases. Moreover, the contact area of the pellet and target surface increase with the deformation degree of the target material, which reduces the stress effect caused by the impact of the pellet on the surface of the target material. This reason, reflected in Figure 4, is that the average maximum residual stress caused on low rough surfaces such as 0 and 10 \(\upmu\)m surfaces is relatively small. Meanwhile, the generated surface with a roughness of 10 \(\upmu\)m is relatively smooth; there are no noticeable surface features such as bumps and pits. Therefore, the maximum residual stress caused by impact on those surfaces increased relatively small than that on a smooth surface, only increasing by 1.51%.  
Surface waviness increases with the increase of surface roughness, and more apparent peaks and pits form on the surface. The actual contact area in the shot peening process converts a smooth surface to a small plane or curved surface. During the pellet impact on the surface with the same kinetic energy, the contact area of the surface and pellet reduces, and the topography limits the deformation of the target surface. The two reasons lead to the contact area on a rough surface being smaller than the contact area on a smooth surface with the depth increase of the impact and the stress effect increase caused by the pellet impact.  
Therefore, the maximum residual stress on the rough surface caused by the pellet impact is relatively high. The maximum residual stress increases with the increase of target material surface roughness. Therefore, in Figure 4, the average maximum residual stress generated by the surface with a pellet impact roughness of 16 and 24 \(\upmu\)m is, respectively, 16.5% and 18.4% higher than that of the surface with impact roughness of the smooth surface. The maximum residual stress of the 29 \(\upmu\)m surface is 13.7% higher than that of the smooth surface.  
It also can be seen that in Figure 4, the average maximum residual stress on the roughness of 29 \(\upmu\)m is slightly smaller than that of the roughness of 24 \(\upmu\)m. The main cause of the trend of average maximum residual stress first increases and then decreases. With the increase of surface roughness, the surface topography becomes more complex, and the stress effect caused by pellet impact would be increased, so the average maximum average residual stress on the workpiece surface after the impact has a trend of increasing. When the surface roughness is larger than 24 \(\upmu\)m, the surface topography becomes over complex, which could limit the deformation of impact; the stress caused by impact could easily be released, so the trend of average maximum residual stress decreases. The average maximum residual stress first increases and then decreases.  
It also should notice that under the condition of current simulation model settings, when the surface roughness of the simulation model is Ra 24 \(\upmu\)m, after the pellet impacts on different positions, the average maximum residual stress could be obtained. This phenomenon could assume that, under the condition of the built model, the surface roughness of Ra 24 \(\upmu\)m is the best initial surface roughness.