## 4 Results and Discussions  
This study aims to develop a surrogate model or predictor that approximates the functional form of inter-ply shear stress on four parameters: relative fiber orientation angle of adjacent plies, forming temperature, pressure load, and ply pullout speed. The fidelity of the developed model was verified through different statistical techniques. The linear fit of predictor versus simulation, as well as residual versus predictor are shown in Figure 2a and Figure 2b, respectively. The closeness of the data points to the linear fit, in Figure 2a, shows that the model well predicts the functional dependency of inter-ply shear stress on the forming parameters. The horizontal line, in Figure 2b, shows the constancy of the average residual throughout the ranges of forming parameters. This in turn indicates that the accuracy of the developed model does not deteriorate over the ranges of forming parameters. Moreover, the random distribution (absence of pattern) of residual about the horizontal line shows that the surrogate model linearly fits the inter-ply shear stress. These statistical inferences indicate that the developed surrogate model is acceptable. Other statistical methods shown in Table 4 also re-affirm the developed model's fidelity. The adjusted R-squared percentage value assures that the inter-ply shear stress data obtained through computer simulation is strongly related to that of the data obtained using the constructed model. The NRMSE of 0.6% indicates that there is moderate residual variance. The 1.71% average deviation of the values obtained via the developed model from the values obtained through computer simulations also confirms that the developed model well captures the functional form of inter-ply shear stress. After the developed model was confirmed to be valid to predict the functional dependency of the inter-ply shear stress, the model was used to analyze individual and paired effects of the forming parameters. The effects of individual parameter on inter-ply shear stress are shown in Figure 3. In these plots, all but one parameter are kept constant, as shown in Table 5, and predictor response is plotted against the free variable. Referring to Figure 3a,b, the overall reduction in inter-ply shear stress is observed as the relative fiber orientation angle of adjacent plies or forming temperature increases. The increase in pressure load hinders inter-ply slippage and hence increases inter-ply shear stress (Figure 3c). As shown in Figure 3d, inter-ply shear stress increases with the increase in ply pullout speed up to, roughly, 0.8 mm/s and then reduces thereafter. The cause for the reduction of inter-ply shear stress could be an onset of ply slippage. \begin{table}
\begin{tabular}{c c} \hline \hline
**Validation Method** & **Value (\%)** \\ \hline R-squared & 98.99 \\ Adjusted R-squared & 97.58 \\ NRMSE & 0.6 \\ Standard deviation & 1.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Model validation. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Value (\%)** & **Unit** \\ \hline Relative fiber orientation angle & 45 & deg \\ Pressure load & 3.8 & MPa \\ Temperature & 389.6 & K \\ Ply pullout speed & 0.7 & mm/s \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Constant values of parameters. In Figure 4, surface plots of paired forming parameters versus inter-ply shear stress are shown. For each plot, two of the parameters were set to constant values, while the rest varied between their respective lower and upper bounds. In Figure 4a, the values of the relative fiber orientation angle of adjacent plies and the pressure load were kept constant (refer to Table 5), while the values of blank temperature and ply pullout speed were set to vary. The plot shows that inter-ply shear stress decreases due to an increase in temperature and moderately increases as ply pullout speed increases. This supports the fact that inter-ply slippage is low at low blank temperature and hence increases inter-ply shear stress.