# A Numerical Investigation of Laser Beam Welding of Stainless Steel Sheets with a Gap
## 4 Keyhole Dynamics and Pore Formation  
An interesting effect was observed in systematic simulations of various gap sizes. In the available experimental longitudinal sections of EX1 and EX2 and those of the corresponding simulations S1 and S2, there is no evidence of porosity; when increasing the gap width there is a small range of gap widths, depending on surface tension forces and exact welding geometries, at which the formation of pores can be observed, where the underlying process seems to be strongly linked to the penetration depth and the opening of the front keyhole wall towards the gap. When a pore is formed, the process leading to its formation is similar to the one described by [PERSON] et al. [33], where pore formation processes were experimentally observed by using a CO\({}_{2}\) laser and transparent materials (water and ice). In [33], two different types of gas bubbles appeared; those containing material vapor disappeared quickly, most likely due to full condensation of said vapor. Another type of long-lasting bubbles did not show signs of condensation. and it was therefore assumed that those were made up of ambient air. It was also observed that even during a stable process, a bubble could be formed due to a rapid change in absorption because of a change in keyhole geometry, followed by increased evaporation. When a thus formed bubble separates from the capillary, it becomes smaller and remains present to form a pore, with the size depending on the amount of ambient gas trapped inside. It was suggested in [33], that the ambient gas is sucked into the keyhole due to the low pressure at the lower end of the keyhole. More recently, [PERSON] et al. [34] analyzed the transition to keyhole welding in laser powder bed fusion of Ti-6 Al-4V by visualizing the process using high-speed x-ray imaging. During one experiment, pore formation in keyhole-mode welding was directly observed, with the underlying process being in agreement with both the findings of [33] and the simulation results presented here. As will be shown below, in welding with gaps, the presence of gaps can, for large gaps, lead to keyhole openings (e.g., shown in [13]), promoting the intake of ambient gas even further. Figure 11: Longitudinal and cross-sections of simulation S4-opt, where a secondary laser beam was added to the conditions of EX4 and iteratively optimized. All measurements in (mm). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Simulation** & **Width (mm)** & **Length (mm)** & **Power (W)** \\ \hline S2-opt & 1.3 & 1.5 & 950 \\ S3-opt & 2.2 & 1.3 & 1000 \\ S4-opt & 1.1 & 1.5 & 930 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimal secondary beam parameters. The parameters used for simulation S5, which are used for the discussion of pore formation below, are provided in Table 4. A series of longitudinal sections obtained with simulation S5 is provided, with the respective timestamps of the frames, in Figure 12.  
The process of pore formation in keyhole laser beam welding starts with a narrow and straight keyhole geometry (Figure 12a). Due to instabilities in the balance of capillary forces and recoil pressure from evaporated metal, caused by the rapidly changing geometry at the locations of inbound laser light, a bulge starts to form, extending into the liquid. As a consequence of fast evaporation and the resulting shear stresses at the liquid-vapor interface, upwards-traveling waves form within the melt. These waves, when their amplitudes reach sufficiently high peaks, can block some laser light from reaching the bottom of the keyhole, and thus condensation occurs in the deepest region of the keyhole, resulting in low pressure pulling in air from the gap between the plates (Figure 12b). Subsequent low-pressure areas form due to further condensation in the region of the lower plate, and thus more ambient gas is sucked in (Figure 12c). The remaining vapor in the cavity at the bottom of the keyhole in Figure 12c fully condensates.