## 4 Application
### Dilution and Yield Strength of Stainless Steel-Based Weld Metal in 3.5-9% Ni Steels  
For a specific combination of welding consumables and base metals, the degree of chemical heterogeneity within the weld is influenced by the dilution, which significantly affects the metallurgical microstructure and mechanical properties of steel welds [50, 51, 52, 53, 54]. Considering the chemical composition of the final weld metal resulting from the amalgamation of the base metal and welding consumable, the dilution rate can be expressed by the following equation [28, 55]:  
\[D\left(\%\right)=\frac{C_{w}-C_{wc}}{C_{b}-C_{wc}}\times 100 \tag{2}\]  
where \(D\) represents the dilution rate; and \(C_{w}\), \(C_{wc}\), and \(C_{b}\) denote the elemental compositions of the weld metal, welding consumables, and base metal, respectively. The ANN-based yield strength prediction model of the weld metal developed in this study can predict the variation in the yield strength of the weld metal, considering dilution when welding 3.5-9% Ni steel, primarily used for low-temperature environments [56, 57, 58, 59, 60], using stainless steel-based welding consumables. To predict the change in the yield strength, four types of base materials (3.5% Ni, 5% Ni, 9% Ni steel, and high-Mn steel) and one fully austenitic stainless steel-based welding consumable were employed, as outlined in Table 5. High-Mn steel was included for comparison with the predicted results for 3.5-9% Ni steel. Figure 9: R\({}^{2}\) values of deep-learning models with five nodes in hidden layers. The predicted yield strength with respect to the change in chemical composition owing to dilution is shown in Figure 10. Considering that dilution varies depending on the welding position, current, speed, and heat input, the heat input per unit length was fixed at 10 kJ/cm. As shown in Figure 10, a similar trend was observed for the 3.5%, 5%, and 9% Ni steels, where the predicted yield strength decreased as the dilution increased. However, the opposite trend was noted for high-Mn steel, where the predicted yield strength increased as the dilution increased. The main reason for these results is that, in the case of 3.5-9% Ni steel, the C, Cr, and Mo contents in the fully austenitic welding consumable are relatively high compared to the base metals used in this study. Conversely, in the case of high-Mn steel, the primary reason is that the C and Cu contents of the base metal are higher than those of the filler consumables. Based on the minimum yield strength requirement of 9% Ni steel, 400 MPa [19], the predicted yield strengths are summarized in Table 6 to analyze the limiting dilution at a fixed heat input of 10 kJ/cm for 9% Ni steel, 3.5% Ni, and 5% Ni. According to Table 6, the predicted yield strength was not expected to satisfy 400 MPa for 3.5% Ni steel in the 45-50% dilution range and 5% Ni steel and 9% Ni steel in the 40-45% dilution range. Figure 10: Predicted yield strength according to dilution and chemical composition changes by base metals. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & **C** & **Si** & **Mn** & **P** & **S** & **Ni** & **Cr** & **Mo** & **Cu** \\ \hline Base metal—3.5\% Ni steel & 0.097 & 0.287 & 0.635 & 0.005 & 0.0007 & 3.49 & 0.03 & 0.06 & 0.03 \\ \hline Base metal—5\% Ni steel & 0.05 & 0.2 & 0.74 & 0.001 & 0.0005 & 5.08 & 0.02 & 0.04 & 0.02 \\ \hline Base metal—9\% Ni steel & 0.054 & 0.235 & 0.537 & 0.003 & 0.0008 & 9.24 & 0.01 & 0.05 & 0.01 \\ \hline Base metal—high-Mn steel & 0.42 & 0.27 & 23.84 & 0.014 & 0.002 & 0.027 & 3.16 & 0.01 & 0.43 \\ \hline Welding consumable—fully austenitic & 0.19 & 0.3 & 1.05 & 0.011 & 0.004 & 18.04 & 16.86 & 3.33 & 0 \\ \hline \end{tabular}
\end{table} 
Table 5: Chemical composition of base metals and welding consumables (wt%).