## 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
#### 4.1.3 Analysis of Different Roughness Surface Deformation Effects  
In order to study the effect of surface roughness on the deformation of surface materials after shot peening, the surface displacements of five target materials with different surface roughness in the deformation zone after shot peening were simulated and analyzed. The stress and displacement of each node are extracted, and the selected nodes are on the surface of the target material in the stress distribution area under the direction marked in Figure 5. In the analysis process, the positive direction of displacement is consistent with the impact direction of pellets set in modeling, which is the positive direction of the \(Z\)-axis. The typical stress nephogram of the impact area on the material surface after shot peening is shown in Figure 6, and the range of residual stress is shown in Table 4. As can be seen, with the increase of surface roughness, the topography of the target material surface becomes more complex, and the range of residual stress distribution gradually decreases. The stress distribution nephogram slowly changes from a standard circle to an irregular shape. The stress value distribution gradually changes from \"first increases and then decreases\" into \"attenuation from the center of impact to all sides\". After the pellet impacts the smooth surface, the residual stress distribution is circular around the pit, generated by the impact. Due to the deformation and accumulation of materials on the target surface, the stress distribution first increases and then decreases \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Ra/\(\mu\)m**} & \multirow{2}{*}{**Range/mm**} & **Residual Stress in Central** & **Maximum Residual** & \multirow{2}{*}{**Edge Residual Stress/MPa**} \\  & & **Area/MPa** & **Stress/MPa** & \\ \hline
0 & 0.87 & 548.2 & 771.7 & 79.5 \\
10 & 0.99 & 269.9 & 771.5 & 80.4 \\
16 & 0.79 & 654.6 & 741.2 & 76.1 \\
24 & 0.75 & 864.8 & 864.8 & 85.6 \\
29 & 0.51 & 854.1 & 854.1 & 79.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Range of residual stress distribution. Figure 5: Sampling diagram of displacement analysis node. Figure 6: Deformation effect of different roughness target material surface. (**a**) Smooth Surface; (**b**) 10 \(\mu\)m; (**c**) 16 \(\mu\)m; (**d**) 24 \(\mu\)m; and (**e**) 29 \(\mu\)m.  
outward from the circle's center, the range of distribution is around 0.87 mm, and the residual stress rises from 548.2 MPa to 771.7 MPa and finally falls to 79.5 MPa. The stress generated by the impact distributed on the low surface roughness is 10 \(\upmu\)m and 16 \(\upmu\)m; the distribution trend of stress value and stress distribution shape is similar to that of a smooth surface, with a distribution range of 0.99 mm and 0.79 mm, respectively. The surface roughness is 10 \(\upmu\)m, and the residual stress rises from 269.9 MPa to 771.5 MPa and finally decreases to 80.4 MPa. The surface roughness is 16 \(\upmu\)m and rises from 654.6 MPa to 741.2 MPa and then decreases to 76.1 MPa. However, the pellets are affected by the surface target, resulting in stress concentration phenomena, as marked in Figure 6c. Due to its location at the edge of the pit, the target on the material's surface is subject to more significant stress and the accumulation of the combination of materials, resulting in stress concentration. When the roughness of the target is 24 \(\upmu\)m and 29 \(\upmu\)m, the surface residual stress distribution is greatly affected by the surface topography of the target, and the distribution range is relatively small, which the distribution range of 24 \(\upmu\)m and 29 \(\upmu\)m rough surface are 0.75 mm and 0.51 mm, respectively. The residual stresses both appear to have a decreasing trend, which decrease from 864.8 MPa and 854.1 MPa to 85.6 MPa and 79.4 MPa, respectively. There are two reasons for this phenomenon: the contact area between the target and projectile is relatively small; the angle between the target surface and the horizontal plane is large.