*3.3. Density of Two Different Alloys*

The reliability of the proposed processing optimization approach was then studied for Fe [18] and AlSi10Mg [35] powders. The density predictions were made using the physical properties of Table 5 and the processing maps are plotted in Figure 7a,b. The experimentally measured density values were superposed, and the deviations between the model and the experiment corresponded to 0.8% for Fe and 0.7% for AlSi10Mg powders.

**Table 5.** Physical properties of Fe [3] and AlSi10Mg [20] powders used for melt pool modeling.


**Figure 7.** Processing maps for (**a**) Fe and (**b**) AlSi10Mg.

#### **4. Discussion and Application Example**

Notwithstanding that the simplified analytical model used in this study does not take into account the specificities of a given printing system in terms of heat exchange and powder spreading conditions, which both influence the density of the manufactured parts, it was demonstrated that such a model could provide useful information in terms of the energy density and the build rate values, which are potentially suitable for the printing of dense parts. However, to determine the exact set of processing parameters, such as the laser power, speed, hatching space, and layer thickness, an additional condition must be respected, and this condition corresponds to the ratio between the hatching space and the layer thickness, *h/t*.

To establish such a condition, the previously developed model was used to plot the density of IN625 components as a function of the *h/t* ratio for different layer thicknesses (Figure 8a). From this plot, it is clear that to maximize the material density, the selection of a hatching space must be related to the selection of a layer thickness (Figure 8b). For example, to guarantee the maximum material density ≥99.8%, with a layer thickness of *t* = 30 μm, the hatching space variations must be limited to the 50 to 80 μm range, while for a layer thickness of *t* = 90 μm, the hatching space variations must be limited to the 110 to 220 μm range.

These results are shown in Figure 8b to present the *h-t* area corresponding to the maximum density of IN625 parts. In the same figure, corresponding *h-t* areas are plotted for AlSi10Mg (Table 3) and Ti64 (Table 4) alloys, for comparison. Finally, once obtained, such plots provide guidance for the selection of the most appropriate hatching space/layer thickness combinations.

**Figure 8.** Hatching space/Layer thickness relations: (**a**) density as a function of the *h/t* ratio; (**b**) hatching space as a function of the layer thickness for maximum density ≥99.5% (IN625, AlSi10Mg and Ti64 powders for an EOS M280 LPBF system).

Note that even though this combined modeling-experiment approach was validated for only one specific LPBF system (EOS M 280), we hypothesize that it can be extended to any LPBF system, provided an adequate calibration experiment is carried out. To this end, after generating the first processing map assuming the physical properties of the material taken from the literature and a powder bed density of 60%, a series of calibration coupons must be printed. Once the density of the printed coupons is measured, the model must be adjusted to fit the experimentally obtained values, by modifying the coefficients of Equation 6. Finally, the relation between the hatching space and the layer thickness can be plotted for a maximum printed material density (see Figure 8b). Once all these conditions are met, the LPBF processing parameters (laser powder, scanning speed, hatching space and layer thickness) can be determined using the following protocol:


**Figure 9.** Steps needed for the printing parameters determination from a processing map: (**a**) selection of a layer thickness, (**b**) selection of an appropriate hatching space, and (**c**) determination of the corresponding laser power and scanning speed values.

As it is widely assumed that the smaller the layer thickness, the better the surface finish and part precision, but the lower the build rate, it is recommended to work with layer thicknesses of 30 or 40 μm when precision is required, and of 50 or 60 μm, when process productivity is more important.
