# Weld Metal Microstructure Prediction in Laser Beam Welding of Austenitic Stainless Steel
## 3 Results
### Weld Zone Modelling  
Figure 3 shows the 3D modelling of the melt pool together with the comparison between the calculated FZ profile and the one detected experimentally in the cross-section plane. The calculated profile was obtained by projecting the maximum contour of the 3D model of the molten pool onto the yz plane (Figure 3a). In this way, the imprint of the maximum width of the FZ on the cross section of the joint was obtained. The fitting with the experimental profile was optimized by minimizing the sum of the squared distances along the y axis, between the experimental and the theoretically calculated profiles, at four different depths along the z axis, drawn by dashed lines in Figure 3b. The optimization was performed by the evolutionary solving tool implemented in Excel, obtaining the convergence to a stable solution that closely approximates the experimental profile. Both calculated and experimental profiles in Figure 3b include the grey rectangle, which indicates  
Figure 2: Properties of weld bead: (**a**) macrograph of the welded cross section (amplification power 1\(\times\)); (**b**) detail of the fused zone (FZ) (amplification power 200\(\times\)); (**c**) images elaborated for the determination of ferrite volume percentage. the area occupied by the four consumable inserts, demonstrating that thermal input is sufficient for their complete fusion together with a part of the base material. As a result of this procedure, the distribution parameters of the beam power (\(\gamma_{\rm{L}}\) = 0.81, \(\gamma_{\rm{P1}}\) = 0.10, \(\gamma_{\rm{P2}}\) = 0.09) and the absorption coefficient (\(\eta\) = 0.51) were obtained. In particular, the latter value is included within the range \(\eta\) = 0.50-0.80, which was defined on the basis of the minimum and maximum value available in the literature for laser beam welding of steels according to the \"keyhole mode\" [30; 31]. A further study quoted in the literature [32] presents a calculation model for the absorption coefficient that allows the estimation \(\eta\) = 0.55. However, the portion of energy that actually enters the keyhole is considered and that the wings of the incident radiation distribution are not so intense as to melt the material, in the case of steels [30] a further reduction in the laser beam power, around 6-10%, can be assumed, obtaining for \(\eta\) a range of values between 0.49 and 0.52. This observation further validates the fitting of the calculated profile to the experimental one. Once the model has been fitted, various simulations to evaluate the effects of the mobile heating source can be performed. In Figure 4a the isotherms in the plane xy at z = 5 mm are drawn for three significant temperatures: a 1400 \({}^{\circ}\)C solidus temperature, 500 \({}^{\circ}\)C lower limit and 850 \({}^{\circ}\)C upper limit of temperature for carbide precipitation. The temperature-time curves, obtained by means of x\(\rightarrow\)\(\xi\), transformation (8), are shown in Figure 4b at different distances y from the welding axis, starting from y = 1.37 mm, i.e., the FZ boundary. The rates of thermal variation in fixed points of the workpiece, which are the results of the derivation operations on the temperature-time curves, were calculated by Equation (9), and are shown in the Figure 5: it can be observed that within the FZ, at y = 0.2 mm, the cooling rate is very high, reaching a maximum value of 6\(\times\)10\({}^{4}\) K/s, while its value is reduced to 1\(\times\)10\({}^{3}\) K/s at the FZ boundary (y = 1.37 mm). The results of thermal rates calculation by Equation (9) are reported starting from y = 0.2 mm because, for lower values of y, that means greater proximity to the welding line, the Rosenthal-type equations lose reliability, being based on the incident point source hypothesis, that leads to infinite temperature at the sources (y = 0) [20].