# A Numerical Investigation of Laser Beam Welding of Stainless Steel Sheets with a Gap
## 2 Simulation Model
### Model Calibration and Validation  
Before using the above-described model to simulate the process, some material properties, such as the complex refractive index and values for the surface energy of the material, need to be calibrated. Although some data on these properties are available in relevant literature, they are not material constants, but (at least) functions of alloy composition, impurities within the alloy, temperature and (in the case of the refractive index) laser wavelength. The dependency of surface tension on temperature is very sensitive to impurities in the form of surface-active elements, mainly oxygen and sulfur. Therefore, there are a lot of discrepancies in the available experimental measurements [26]. However, surface tension-related phenomena such as Marangoni currents are of great importance in weld pool dynamics [27], and therefore a fine-tuning of surface tension data against experimental results is necessary. In the case of the complex refractive index, this property and its temperature-dependence have a great influence on the laser-material interaction. Data are available for 304L stainless steel, e.g., in reference [28], but only one value is given for each melting and boiling temperature, respectively, with no information on temperature-dependency in between. Additionally, no information is provided as to which phases the values refer to, e.g., at the melting point, liquid or solid phase. As this property's influence on the process is high, validation is necessary. Apart from the aforementioned material properties, discretization schemes used by the solver and the amount interface compression within the volume-of-fluid method need to be appropriately chosen in order to obtain a good fit regarding the experimental data. For this purpose, longitudinal and cross-sections of 304L stainless steel sheets welded under the presence of a gap were used. The welding experiments EX1-EX4 within this study were conducted at the facilities of AIMEN. The experimental setup consisted of an ABB IRB6600 robot carrying an Optoskand LBW tool which can provide a minimum spot diameter of 100 \(\upmu\)m. The laser source was a Coherent fiber laser FL080 with a 100 \(\upmu\)m diameter fiber, a wavelength of 1070 nm and a beam parameter product of 3.5 mm \(\times\) mrad. No shielding gas was used. The experimental conditions are listed in Table 1.  
Figure 2: Refined computational grid during simulation S5 at time \(t=60\) ms. The model was calibrated to reproduce the results of EX1 (Table 1). Another experiment, EX2, was then used to validate the model, to ensure the prevention of overfitting to the calibration conditions. In EX2, the gap width, welding speed and laser power were different from those in EX1. To validate the values for the complex refractive index, the simulation should be able to reproduce the penetration depth measured from the experiments and general heat input estimated from the volume of material molten during the experiments. To calibrate values for the surface energy of the materials, the shape of the cross-sections gained from the experiments should be matched, especially at the weld bead top and at the interface, where capillary forces play an important role. As a starting point, values for the liquid phase from [PERSON] et al. [29] were taken and iteratively calibrated to fit the experimental data. The surface energy values for the solid phase were kept at a constant value, due to unavailability of concrete values for most metals. The final values for surface energy as a function of temperature and phase are plotted in Figure 3.  
Figures 4 and 5 show the comparison of experimental longitudinal and cross-sections of EX1 and EX2 and the corresponding simulations S1 and S2 (using the fully calibrated model), respectively. Both the penetration depth over most of the longitudinal section and the cross-sectional weld bead shape are in qualitative and reasonable quantitative agreement.