## 3 Results and Discussion
### Experimental Results
#### 3.2.2 Contour Method Results  
Figure 10 shows the contours of the cutting surface of the T-type rib after different processes. The maximum value is \(0.65\) mm for the quenched surface, which decreases to \(0.25\) mm and \(0.3\) mm for the cold pressing and artificial aging surfaces, respectively. The value of the contours reveals the value of the residual stress, indicating that the cold pressing and the artificial aging both play a significant role in the reduction of the residual stress.  
Based on the principle of the contour method described in Section 3, the longitudinal residual stress on the cutting surface can be obtained, as shown in Figure 11. It can be observed that there is a significant difference of the residual stress on the surface between the results using X-ray diffraction and the contour method. This can be explained as follows: the contour on the edges of the cutting surface is measured through the three-coordinate measuring machine. This may result in an inevitable error during the measurement of the contour on the edges of the surface due to the certain size of the head for the measuring machine. Therefore, significant errors of the residual stress on the surfaces of the T-type rib  
Figure 10: Contours of the cutting surface of the T-type rib after different processes: (**a**) quenching; (**b**) stepwise cold pressing; (**c**) artificial aging.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Process**} & \multicolumn{2}{c}{**Longitudinal Residual Stress**} & \multicolumn{2}{c}{**Transverse Residual Stress**} \\  & **Stiffened Surface** & **Smooth Surface** & **Stiffened Surface** & **Smooth Surface** \\ \hline Quenching & \(-195.5\pm 27.5\) & \(-203\pm 29.7\) & \(-200.3\pm 29.8\) & \(-202.5\pm 30.4\) \\ Quenching + cold pressing & \(-164.4\pm 40.8\) & \(-132.2\pm 26.7\) & \(-157.7\pm 39.8\) & \(-134.5\pm 32.7\) \\ Quenching + cold pressing + artificial aging & \(-100.5\pm 33.8\) & \(-107.4\pm 39.8\) & \(-95.3\pm 36.9\) & \(-114.3\pm 41.3\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Average surface residual stress after different processes.  
are generated. It can be seen from Figure 11 that the maximum tensile residual stress in the longitudinal direction at the stiffened area is 220 MPa in the quenched stage, which decreases to 128 MPa in the cold pressed stage and 110 MPa in the artificial aged stage. As a result, a stress reduction of 42% and 50% can be achieved by the cold pressing and artificial aging process, respectively. The stress reduction at the smooth area is more significant than that at the stiffened area. The maximum tensile residual stress decreases from 175 MPa in the quenched state to 80 MPa in the cold pressed stage and 70 MPa in the artificial aged stage. The stress reduction is 54% and 60% for the cold pressing and artificial aging, respectively.  
As discussed above, the contour methods bring large errors of the residual stress on the edges of the surface for the T-type rib. Therefore, residual stress on the surfaces through X-ray diffraction and the stress results on other regions of the T-type rib through the contour method are adopted to characterize the overall distribution of the residual stress. As shown in Figure 12, the FEM results in the quenching and cold pressing agree with the experiments, indicating the validity of the FEM models. It can be seen that most of the simulated residual stress is within the error bar of the experimental results. The error is defined in Equation (3). The maximum error is located at the bottom surface of the quenched sample as shown in Figure 12b. The maximum error is 9.5%, thus indicating that the FEM models can predict the residual stress distribution of the T-type rib.  
\[e=|\sigma_{\rm e}-\sigma_{\rm F}|/\sigma_{\rm e}\times 100\% \tag{3}\]  
where \(e\) is error, \(\sigma_{\rm e}\) and \(\sigma_{\rm F}\) are experimental values and simulated values of residual stress.