## 2 Materials and Methods
### Methods
#### 2.3.2 Experiments  
The material and its size of the T-type rib were the same as that in the numerical models. Three comparative T-type ribs were comparatively studied: quenched, quenched and cold \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Temperature \(T\), \({}^{\circ}\)C** & **Thermal Conductivity** & **Elastic Modulus \(E\),** & & **Specific Heat Capacity** \\  & **\(\lambda\), W/m\({}^{\circ}\)C** & **MPa** & **Flow Stress \(\sigma\), MPa** & **c, J/kg\({}^{\circ}\)C** \\ \hline
20 & 114.8 & 71,000 & 455.9 & 835 \\
100 & 128.4 & 65,193 & 389.1 & 897 \\
150 & 135.7 & 60,594 & 346.6 & 916 \\
200 & 142.2 & 56,262 & 275.7 & 974 \\
300 & 152.7 & 37,980 & 47.1 & 1013 \\
400 & 160.8 & 31,200 & 35.5 & 1128 \\
500 & 166.7 & 25,000 & 16.3 & 1205 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of 7050 aluminum alloy. Figure 3: Schematic diagram of stepwise cold pressing process. pressed, as well as quenched, cold pressed followed by artificial aged. The variation of residual stress under different processes was analyzed. The quenching procedure was the same as that in the numerical models. Five passes of the cold pressing process were applied to component B and the reduction rate of each pass was 3%. The length of the upper mold was 120 mm, and the overlap length of the adjacent pass was 25 mm, as shown in Figure 3. The X-ray diffractometer (XRD, STRESSTECH OY, Jyvaskyla, Finland) was adopted to measure the surface residual stress of the T-type rib. Three paths on the smooth and the stiffened surfaces were selected, and the average value of the residual stress was calculated, as shown in Figure 2. The parameters for the X-ray diffraction are shown in Table 2.  
The contour method was adopted to obtain the distribution of the normal residual stress on the whole cross-section of the T-type rib. Figure 4 shows the principle of the contour method, which determined the residual stress via processes that consisted of cutting the component into two pieces and measuring the surface strain resulting from residual stress redistribution. Next, the measured data of the surface strain were used to calculate the residual stress through the finite element model. The initial normal residual stress on the surface perpendicular to the x axis was unknown and it could be calculated by Equation (1) based on Bueckner's superposition principle. Next, the component was cut into two pieces through the cross-section perpendicular to the x axis with a wire-cut electrical discharge machine. Deionized water cooling was applied to minimize the thermal effect on the stress. The contour of each cutting surface was measured with a three-coordinate measuring machine and the surface strain was calculated after averaging and smoothing of the two surface contours. The calculated surface strain was imported into the FEM and the external stress \(\sigma_{\mathrm{x}}\mathrm{{}^{C}}\) was applied to the cutting surface, which recovered the deformed surface after the cutting process into the surface in Figure 4a without cutting. The normal residual stress \(\sigma_{\mathrm{x}}\mathrm{{}^{B}}\) and shear stress in this cutting surface were almost zero as the residual elastic strain was released during the cutting process. Therefore, the initial unknown residual stress \(\sigma_{\mathrm{x}}\mathrm{{}^{A}}\) was equal to the applied external stress \(\sigma_{\mathrm{x}}\mathrm{{}^{C}}\), as shown in Equation (2). \[\sigma_{\mathrm{x}}\mathrm{{}^{A}}=\sigma_{\mathrm{x}}\mathrm{{}^{B}}+\sigma_ {\mathrm{x}}\mathrm{{}^{C}} \tag{1}\]  
\[\sigma_{\mathrm{x}}\mathrm{{}^{A}}\approx\sigma_{\mathrm{x}}\mathrm{{}^{C}} \tag{2}\]  
where \(\sigma_{\mathrm{x}}\mathrm{{}^{A}}\) is the unknown residual stress, \(\sigma_{\mathrm{x}}\mathrm{{}^{B}}\) is the residual stress after cutting and \(\sigma_{\mathrm{x}}\mathrm{{}^{C}}\) is the applied external stress that recovers the deformed surface after the cutting process into the surface without cutting.