# Metallurgical Aspects in the Welding of Clad Pipelines--A Global Outlook
## 3 Microstructure Evolution
### Solidification
#### 3.1.1 Fundamentals of Solidification Theory
The solidification pattern follows Equation (3), where primary dendrites of \(\gamma\) solidify first with a final microstructure of \(\gamma\) with NbC and Laves phases precipitated in the interdendritic regions. \[L\to L+\gamma\to L+\gamma+NbC\to L+\gamma+NbC+\text{Laves}\rightarrow\gamma+ \text{NbC}+\text{Laves} \tag{3}\]  
Niobium-free alloys, such as Alloy 59, solidify by a simple \(L\rightarrow\gamma\) transformation without any eutectic-like reaction and exhibit a relatively narrow solidification temperature range. Solidification cracking is therefore not expected. When compared with carbon and low-alloy steels, Ni-based alloys have a high temperature gradient (in WM) due to lower thermal conductivity, which is related to the high alloying level. Therefore, a planar solidification front may not be stable, and the primary solidification mode is cellular-dendritic, as shown in Figure 5. Here, only the grains with a crystallographic preferential growth orientation (along the (100) direction, Miller index, for metals having a cubic crystal lattice structure [34]) relationship aligned with the heat flow direction will continue to grow. When the preferential growth direction of the solid starts to deviate significantly from the heat flow direction, the growth stops, and new grains nucleate successively with the preferential growth direction nearly along the heat flow direction. The criterion for constitutional supercooling for plane front instability can be mathematically estimated [35] as follows:  
The plane front will be stable when:  
\[\text{FA (ferritic-austenitic) mode: $L$ \to L+\delta\to L+\delta+\gamma\rightarrow\delta+\gamma \rightarrow\gamma$}\qquad\text{for $1.5<\text{Cr}_{\text{eq}}$/Ni${}_{\text{eq}}$ $<$ 2.0}\]0 (4a) Planar instability will occur when: \[\text{FA (ferritic-austenitic) mode: $L$ \to L+\delta\to L+\delta+\gamma\rightarrow\delta+\gamma \rightarrow\gamma$}\qquad\text{for $1.5<\text{Cr}_{\text{eq}}$/Ni${}_{\text{eq}}$ $<$ 2.0}\]1  
Here, \(G\) is the temperature gradient (\({}^{\circ}\)C/m) in the liquid, \(R\) denotes the solidification front (or crystal) growth rate (\(\upmu\)m/s), \(\Delta T_{0}\) is the equilibrium solidification temperature range (at composition \(C_{0}\)), and \(D_{L}\) represents the solute diffusion coefficient (m\({}^{2}\)/s) in liquid. The frequently used \(G\)/\(R\) ratio is a solidification morphology parameter. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Alloy** & **Ni** & **Cr** & **Mo** & **Fe** & **Nb** & **Co** & **Mn** & **Ti** & **Si** & **C** \\ \hline Alloy 59 & 59.0 & 22.0–24.0 & 15.0–16.0 & \(\leq\)1.5 & - & \(\leq\)0.3 & \(\leq\)0.5 & - & \(\leq\)0.1 & \(\leq\)0.01 \\ \hline Inconel 625 & 58.0 & 20.0–23.0 & 8.0–10.0 & 5.0 & 3.15–4.15 & 1.0 & \(\leq\)0.5 & 0.4 & 0.5 & 0.1 \\ \hline X65 & 0.5 & 0.02 & - & 98.5 & 0.05 & - & \(\leq\)1.4 & 0.04 & 0.25 & 0.07 \\ \hline
316L & 10.0–14.0 & 16.0–18.0 & 3.0 & 63.0–64.0 & - & - & \(\leq\)1.3 & - & 0.75 & \(\leq\)0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of nominal chemical composition (wt %) of different materials. In the diagram shown in Figure 5, the range of solidification modes are assumed. Carbon steel (e.g., X65) has planar solidification in a wide range of temperature gradients due to low alloy content. The product \(GR\) is related to the cooling rate \(\varepsilon\) (\({}^{\circ}\)C/s) as follows [36]:  
\[\varepsilon=GR \tag{5}\]  
This means that the dendrite spacing increases with increasing cooling time, i.e., with increasing heat input in welding. The solidification rate parameter (\(R\)) can be estimated empirically based on the angle (\(\alpha\)) between the welding direction and solidification growth direction, or molten surface normal, as shown in Figure 5. The solidification rate (2D, the top surface) is calculated by the following equation:  
\[R=v\cos\alpha \tag{6}\]  
where \(v\) is welding speed.