*3.2. Dynamic Evaluation*

Let us calculate the steady temperature at the laser spot boundary for two laser modes and a laser power of 100 and 400 W. The experimental diameter of the laser spot will be approximately 100 μm (0.001 m) for the TEM00 mode and 300 μm (0.003 m) for the TEM01\* mode (Table 4) [57]. As can be seen, with an increase in the power of laser radiation to 400 W, due to excess heat, a multifaceted local overheating is predicted (the calculated temperature is 2.56 times higher than *T*max) at the boundary of the laser radiation of the Gaussian mode (as a result, active evaporation of metal from the processing zone). At the same time, when using the reverse Gaussian profile (donut), the temperature at the edge of the laser spot does not reach *T*min (less than 2.34 times), which means that there is no sufficient heat to initiate the CoCr alloy granule fusion. The powder consolidation temperature can be closer to the melting temperature. Implicit graphs of the function of temperature on the radius for a cobalt-chromium alloy (*λ* = 13 W/(m·K)) depending on the power of laser radiation are shown in Figure 7 (Equation (3)). It should be noted that Figure 7a is an implicit graph of the temperature (*T*max − *T*a) on the radius and laser power function for the material with the mentioned material thermal conductivity, where the solution area is marked red, since only values above zero can be taken into account for technological purposes, since other areas have no physical sense in the context of engineering.

**Table 4.** The steady temperature values at the laser spot boundary for two laser modes.

**Figure 7.** Implicit graphs of the function of temperature (*T*max − *T*a) on the radius depending on the power of laser radiation for *λ* = 13 W/(m·K): (**a**) 3D-plot; (**b**) *P* = 100 W; (**c**) *P* = 400 W.

Table 5 presents two evaluated groups of laser beam parameters based on the experimental data obtained by optical achievements of the laser beam profiles using an expander and profiler installed in the LPBF setup and optical evaluation of the obtained profiles [28]. Specific energy contribution (J/m2) was calculated by:

$$E = \frac{q\_0}{u\_s}.\tag{19}$$


**Table 5.** Parameters of laser powder bed fusion chosen for modeling.

Two numerical calculations for Gaussian (Equation (1)) and donut (Equation (4)) laser beam profiles are made for each group. Thermal diffusivity of CoCr alloy is presented in Table 6 [58,59]:

$$\alpha = \frac{\lambda}{\rho \cdot \mathbb{C}\_p},\tag{20}$$

where *ρ* is density, kg/m<sup>3</sup> and *C*p is specific heat capacity, J/(kg·K). The dependence of the Péclet number on the laser spot radius and scanning speed for a cobalt-chromium alloy is shown in Figure 8.

**Table 6.** Thermal diffusivity *α* of CoCr alloy.


**Figure 8.** The implicit graph of the Péclet number on the laser spot radius and scanning speed for a cobalt-chromium alloy (*α* = 5.2 × 10−<sup>6</sup> m2/s) (3D-plot).

Figure 9 shows the calculated temperature fields for two types of laser beam profiles: TEM00 and TEM01\* at laser powers of 100 and 400 W, correspondingly, when laser beam diameters are 0.109 and 0.310 mm, respectively. The difference from Figure 2 is that laser beam profiles are shown at the level of calculated steady temperatures (Table 4). Formation of the temperature plateau is explained by a small value of overheating sufficient for evaporation under the given conditions. In the case of mode TEM01\*, the characteristic temperature sink is still visible in the center. The energy losses for evaporation are listed in Table 7. The corresponding mass losses are proportional to the energy ones [43]. Comparison of values listed in Table 7 indicates that the change from mode TEM00 to mode TEM01\* decreases the evaporation loss for all four calculations made. Thus, the laser profile corresponding to mode TEM01\* seems to provide more efficient laser power density distribution (Figure 10).

**Figure 9.** Calculated temperature distributions (*T*max − *T*a) in CoCr alloy: (**a**) over the vertical plane of mirror symmetry *y* = 0 formed by the beam axis and the scanning line for *P* = 100 W, Pe = 0.71; (**b**) over the vertical plane of mirror symmetry *y* = 0 formed by the beam axis and the scanning line for *P* = 400 W, Pe = 2.86; (**c**) results of temperature fields modeling for *P* = 100 W, Pe = 0.71 (cross-section); (**d**) results of temperature field modeling for *P* = 400 W, Pe = 2.86 (cross-section).


**Table 7.** Calculated values of power loss for evaporation *Pv* for CoCr alloy for the laser beam profiles.

**Figure 10.** Calculated graphical presentation of power loss for evaporation *Pv*.
