# A Numerical Investigation of Laser Beam Welding of Stainless Steel Sheets with a Gap
## 1 Introduction  
Keyhole laser beam welding (LBW) has gained importance in many industries--e.g., the automotive and aerospace industries--over the years. The advantages of LBW cover a high level of precision and speed, reduced distortion and a high potential for process automation [1]. It is difficult to experimentally investigate the many physical phenomena involved in laser beam welding, as post-experimental investigations do not provide sufficient information on process dynamics, and in-situ observations of the transient behavior, especially inside the keyhole, are not possible on all desired time and length scales. [PERSON] et al. [2] managed to directly observe the keyhole by employing a sandwich construction of stainless steel and a special type of glass, using a high-speed camera. However, such experiments require complex setups and do not allow for an investigation of real industrial specifications. Therefore, the development of models which are capable of accurately predicting the physical phenomena involved in LBW remains important and research is ongoing. Reliable models can then help gain understanding of the driving mechanisms behind the formation of defects such as lack of penetration, formation of humps, pores and end craters. Models of different levels of complexity have been introduced in the past. [PERSON] et al. [3] developed a model based on the level-set method for solving the multiphase flow problem, for which they employed some simplifications in the solution of the flow field. [PERSON] andChen [4] solved the Navier-Stokes equations for the fluid flow by assuming a fixed, cylindrical keyhole and a flat free surface of the liquid. [PERSON] et al. [5] developed a model for the calculation of the depth of a circular keyhole by exploiting characteristic time and length scales for laser beam welding processes. [PERSON] et al. [6] recently used a volume-of-fluid approach within OpenFOAM to investigate the effect of beam shaping on the melt pool behavior in conduction mode laser beam welding. While their implementation was similar, in the model presented in Section 2.1 a crucial component needed for keyhole laser welding was added by implementing an evaporation model. [PERSON] et al. [7] developed a model for keyhole laser beam welding based on a volume-of-fluid approach by implementing it in OpenFOAM and also taking into account evaporation phenomena. A novel addition to the state of the art is provided by the model in Section 2.1 through the further distinction between two or more gaseous phases, which is of paramount importance when trying to gain a deeper understanding into the process of pore formation as described in Section 4. Furthermore, commercial software is available for the simulation of laser beam welding, e.g., that by [PERSON] et al. [8] for the simulation of keyhole laser beam welding. This, however, comes with the inconvenience of proprietary source code and the inability to change or add models. Apart from models concerned with the fluid dynamical description of LBW, a topic of great interest and practical relevance is the thermo-mechanical modeling of the process to gain insight in the formation of stresses. This is mostly done by the means of finite element methods, as was done by [PERSON] et al. [9] and was more recently investigated by [PERSON] [10]. This topic is, however, not further discussed here, as the underlying method and approach are fundamentally different from what is presented here. Another issue of great practical importance in the field of LBW modeling is the prediction of the crystallographic microstructure of a weld bead, as its knowledge can help avoid problems such as solidification cracking. Such predictions have recently been made by [PERSON] and [PERSON] [11] using an analytical model. The linking of a mechanistic microstructural growth model to the simulation model presented here is currently being realized [12].