# Metallurgical Aspects in the Welding of Clad Pipelines--A Global Outlook
## 3 Microstructure Evolution
### Solidification
#### 3.1.2 Numerical Simulation of Solidification Parameters  
In order to estimate solidification parameters by finite element analysis (ABAQUS 6.14 with DFLUX subroutine programmed in Fortran), combined double Goldak's ellipsoid and surface Gaussian heat source were used [38]. Different heat sources are needed to simulate the typical _finger_ penetration geometry of the GMAW welds, according to [PERSON] and [PERSON] [39], since there is an impingement of droplets from the electrode into the weld pool which transports the additional heat. A detailed modeling procedure and boundary conditions can be found in [40]. Applied thermophysical parameters for the materials are outlined in Table 2. The results of numerical simulation, achieved by a _trial-and-error_ method, are presented in Figure 6. The process parameters were set to 7 mm/s as the welding speed and 5.5 kW (220 A; 25 V) as the arc power. A good agreement with previous experimental results (for X70 carbon steel) welded under hyperbaric conditions of 10 bar [41] was found. Due to different spatial temperature gradients and complex weld pool physics, the cooling rate as well as solidification rate varies according to the specific location in the WM or the HAZ [43]. Therefore, in the same WM, different solidification modes are common, as illustrated in Figure 5. At the WM centerline, the temperature gradient is smaller and the solidification rate faster when compared to the area near the FL (fusion line or liquid/solid interface) for each selected material. The most widely used parameter to describe cooling in welding for carbon steel is the cooling time from 800 \({}^{\circ}\)C to 500 \({}^{\circ}\)C (denoted as \(\Delta t_{8/5}\)), since most phase transformations take place within this range [45]. However, for the crystal growth rate in WM for any kind of alloy, the cooling rate from the peak temperature to the solidus line is used. The finite element analysis (FEA) results at the centerline are compiled in Table 3. The centerline is illustrated in Figure 6. The solidification parameters are outlined in Table 4 for the liquid/solid interface located at 1/4 of the weld pool length at the solidification front, and in the case of the top plane, see Figure 7. For the mid-plane case, the angle of the \(G\) vector is more complex to find, since it is normal to the tangential plane for a curved solid/liquid interface. Moreover, this surface is constantly in motion because it follows the moving heat source. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Material** & **Density** & **Thermal Conductivity** & **Specific Heat** & **Solidus Point** & **Latent Heat of Fusion** \\
**(kg m\({}^{-3}\))** & **(W m\({}^{-1}\) °C\({}^{-1}\))** & **(J kg\({}^{-1}\) °C\({}^{-1}\))** & **(\({}^{\circ}\)C)** & **(J kg\({}^{-1}\) °C\({}^{-1}\))** \\ \hline Inconel 625/Al alloy 59 [42] & 8440 & 10 & 410 & 1290 & 227000 \\
316L SS [43] & 7200 & 19 & 712 & 1424 & 274000 \\ X65 carbon steel [44] & 7800 & 32 & 726 & 1494 & 277000 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Summary of thermophysical properties for Ni-based alloys and various steels. Figure 6: (**a**) Simulated weld of X65 carbon steel, and (**b**) fusion line geometries for different materials. [PERSON] et al. [37] established a solidification map of a Ni-based alloy (Inconel 690). For the top of the weld pool, the \(R\) and \(G\) values are similar to the estimated values for Inconel 625/Alloy 59 (Table 3; Table 4). Since fiber laser beam welding in the keyhole mode was applied, higher \(G\) values for the deeper part of the weld pool were obtained by [PERSON] et al. [46]. Along the weld centerline, the \(R\) parameter is very similar to the welding speed, meaning that the solidification angle (\(\alpha\)), used in Equation (6), is approximately equal to 0 (cos \(\alpha=1\)) at the centerline, and hence \(R\to v\). At the centerline, the X65 steel has a smaller \(G\) value due to higher heat conduction. For the same reason, the solidification rate for X65 is the highest for the materials studied here.