# A Numerical Investigation of Laser Beam Welding of Stainless Steel Sheets with a Gap
## 1 Introduction
An initial effort for developing a model capable of accurately simulating processes involved in laser-assisted manufacturing was made by [PERSON] et al. [13] and [PERSON] et al. [14] by developing a universal multi-physical laser-material processing model based on the open source C++ toolbox OpenFOAM [15], using the volume-of-fluid method for solving the multiphase flow field. The model has since then been substantially improved at the Institute of Production Engineering and Photonic Technologies at Vienna University of Technology. The solver includes the Navier-Stokes equations and continuity equation, coupled with appropriate models for laser beam propagation, laser-material interaction, phase change, keyhole vapor pressure, surface tension and many more physical phenomena necessary to adequately simulate such complex processes. It is capable of accurately predicting a broad range of laser-assisted processes, including LBW, laser cutting, laser ablation using ultra-short laser pulses and many additive manufacturing processes (laser powder bed fusion, laser cladding, etc.) due to the most recent integration of the Lagrangian library into the solver [16; 17]. In the automotive industry, welding of overlapping galvanized steel sheets is a common task, and thus much of the research on welding of sheets with the presence of a gap was done on this topic. As the boiling temperature of Zn lies well below the melting temperature of steel, the vaporization of Zn at the interface and its venting through the melt pool or keyhole can lead to the formation of various defects, including spatter, blowholes and lack of fusion. Several sophisticated techniques to overcome these problems have been suggested, e.g., cutting a slot along the to-be welded line, generating vent holes in the bottom sheet with a pulsed laser and producing humps on the interface surface. Additionally, many-pass strategies, and slow-speed welding, have been shown to mitigate the problem, but all of these techniques are irrelevant for the automotive industry because of increased processing time and complexity. By adding a suitable gap at the sheet interface, a stable process can be achieved, yielding high-quality weld seams [18; 19; 20]. On the flip side, the presence of a gap can cause different defects, including underfilling, porosity, \"false friends\" (misconnections without outside evidence), etc. These problems are inherent to gap welding and are independent from the previously described problem of Zn-evaporation and subsequent spatter formation. The reason for the occurrence of a gap in processes with stainless steel sheets that may not be galvanized is in part thermal deformation and the thereby introduced complexity of achieving perfect contact over the whole weld bead length by designing a reliable clamping system. These scenarios were the motivation behind the study presented here, and they study by [PERSON] et al. [21]. In the case of the CUSTODIAN project, the presence of a gap was not added deliberately, but was a consequence of the geometry of the parts to be welded (e.g., segments of exhaust pipes pressed together), where a zero gap is not reasonable without a massive increase in processing accuracy to reach such tight tolerances. To better understand and prevent the formation of such defects, the simulation model presented here is used to investigate keyhole laser beam welding of stainless steel sheets with a gap. Section 2.1 describes the simulation model used to perform the investigations presented here and points out further literature regarding the modeling approach. In Section 2.2, the calibration and validation of the model using results of laser beam welding experiments is presented and discussed. In Section 3, a methodology for process optimization through the use of the simulation model on a computationally inexpensive grid is presented.