*2.3. Typical Output from the Simulation Process*

As a result of the modeling process, involving the thermofluidic coupling and the phase and temperature dependency of the of the thermo-physical properties, the development of a consolidated ribbon is obtained. Figure 10 presents the consolidated ribbon obtained during the interaction time of the laser beam, *τ* (*τ = Ø/V*) for a process speed of 600 mm/min and a beam power of 1800 W with a beam diameter of 3 mm. The simulation during the interaction time allows for representing the effect of the full traversing of the laser beam for a given point and analyzing the characteristic dimensions of it, within manageable computation times. The model is also prepared to take into account the recoil pressure [24], although, provisionally it has not been considered for the proposed tests, given the relatively moderated heating conditions and the large amount of material involved.

**Figure 10.** Ribbon formed during the interaction time of the laser beam.

Figure 11 shows the way in which the results of the simulation are exploited, by comparing the height and width of the cross section predicted by the simulation with the experimental ones.

**Figure 11.** Theoretical (**left**) and experimental (**right**) cross sections.

The next section carries out some representative comparisons between theoretical and experimental results for some tests carried out with typical sets of process parameters.

#### **3. Results**

The main goal of the proposed model is the prediction of the shape and dimensions of the cross section of the consolidated material. The progress of the process, in terms of the advance in the direction in which the part is being grown, is determined by the final height of the cross section. In addition, the heat conduction conditions for the consolidation process of the successive layers depend on the geometry of the previously consolidated material, which configures the paths for the diffusion of the heat.

All the tests were made on a substrate layer of 1000 μm, with a gaussian laser beam with a diameter of 3 mm. The laser equipment was a fiber IPG laser with 6 kW of maximum output power releasing radiation with a wavelength of 900 nm.

Three different tests have been carried out. The corresponding conditions of power and scanning speed are shown in Table 2.


Figure 12 shows the cross section predicted by simulation (left) and the real result obtained in the experimental test number 1 (right). It can be seen that the theoretical calculation has been capable of predicting the height of the consolidated material, as well as the general shape of the area. In both the theoretical and the experimental cross section, the maximum height of the consolidated material, from the reference line of the substrate, lies around 1400 μm (note that the cross section displayed from the theoretical results starts at the level of the substrate, while in the experimental case the dilution under the substrate is shown). In the same way, the width of the cross section at the level of the line of the substrate is of about 2800 μm. The biggest discrepancies between the theoretical and the experimental cross sections appear at the sides of it, at the level of the substrate. It may be associated to dynamic viscosity attributed to the solid in the numerical simulation which predicts a slightly higher level of consistence for the consolidated material than in reality. No contrast of the amount of dilution of the consolidated material into the substrate is highlighted in the numerical simulation, which must be predicted by means of metallurgical consideration from the thermal cycle and will be considered in future developments of the model.

**Figure 12.** Theoretical (**left**) and experimental (**right**) cross sections corresponding to test 1. Note that in the case of the experimental one the dilution under the substrate is shown while the theoretical one represents exclusively the external part of the consolidated material, from the top of the substrate.

Figure 13 shows the theoretical (left) and experimental (right) cross sections corresponding to test 2.

**Figure 13.** Theoretical (**left**) and experimental (**right**) cross sections corresponding to test 2.

In Figure 13 it can be seen again, from the cross section of the experimental test, that the high thickness of the layer of metallic powder has given rise to a high dilution of the consolidated material into the substrate. Considering the dimensions of the external part of it, the simulation has been capable of predicting its maximum height and width.

Figure 14 represents the theoretical (left) and experimental (right) results for test 3. Once again, the general external dimensions predicted by the simulation match with an acceptable level of accuracy the dimensions of the experimental cross section. In this case, the use of the highest scanning speed has led to a shorter height of the consolidated material.

**Figure 14.** Theoretical (**left**) and experimental (**right**) cross sections corresponding to test 3.

#### **4. Discussion**

The use of temperature and phase-dependent thermo-physical properties has allowed an accurate prediction of the dimensions of the cross section. While the influence of the exclusively thermal properties, such as the thermal conductivity, cannot be directly analyzed; the proposed modelling for the surface tension and the dynamic viscosity is accurate enough to make the output of the simulation approach the experimental results.

From the experimental-theoretical comparison some ideas can be extracted. While the general dimensions of the cross sections can be satisfactorily predicted by the theoretical calculations in terms of height and width, the shape of it, at the level of the contact with the substrate is affected, in the theoretical calculations, by some effect of adhesion that makes the transition from the consolidated material to the substrate smoother than in the real case. It may be associated with the theoretical evolution of the dynamic viscosity which, when it is representing the behavior of the solid, tends to slightly overestimate the adhesion phenomena. Both, numerical calculations and experimental tests highlight the influence of the large thickness of the powder bed in the transformation experienced by the material, evolving from a flat layer of powder to a taller ribbon whose cross section has the shape of a drop. In other papers where a much shorter layer of thickness is considered, this evolution of the material during the drop formation is less evident. Reference [25] is capable of estimating the shape of the melt pool in the SLM process of nanocomposites just by means of thermal calculation. It is possible due to the subtle motion of the liquid metal derived from the small thickness of the powder bed. References [26–28] present different SLM process with applications in various fields. The powder bed is not lager than 50 μm in any of the cases. The comparison of the melt pool in the figures of that papers with Figures 12–14 of the present study highlights the influence of the thickness of the powder bed in the shape and size of the consolidated material, justifying the use of a thermo-fluidic approach.

From a strictly experimental point of view, the use of a high thickness powder layer is associated to a high degree of dilution of the consolidated material into the substrate. It can be related with the greater amount of material which is melted because of the large thickness of the layer and the size and big power of the laser beam. The inclusion of metallurgical considerations in new versions of the model will focus on calculating the magnitude of the dilution. The aggressiveness of the process parameters used in the present study in comparison with studies with a shorter powder layer can be checked considering the process parameters in the tests of references [29,30].

The relation of the process parameters from the experimental tests with the dimensions of the melt pool, as a function of the thermo-fluidic properties of the material, provides a deep understanding of the physics involved in the consolidation process. In test 1, despite having a relatively low value of laser power, 1000 W, the large interaction time associated to the relatively low process speed, 400 mm/min, has permitted an efficient absorption of the energy to be achieved. In Section 2.1.1 the high efficiency of the powder to absorb radiation was shown. Additionally, in Section 2.2, the poor thermal conductivity of the powder was indicated; it favors the concentration of the heat around the laser-powder interaction area. The combination of a large interaction time with an efficient absorption and concentration of the laser power has led to a melt pool of relatively large dimensions. The hypothesis of considering the powder around the melt pool as a fluid with very low friction (very low dynamic viscosity), can be accepted from the result of this test: the spherical shape of the cross section indicates that the melt pool has not found appreciable resistance to move under the effect of surface tension. No signs of porous in the cross section, which suggests that the density of the material has evolved from the value corresponding to the powder to the value of the solid during the consolidation process.

Test 2 presents a more aggressive combination of process parameters than test 1. The higher level of power, 2000 W, has allowed a larger amount of energy to traverse the powder to the substrate, which, in combination with an intermediate level of process speed, 600 mm/min, has favored a deeper penetration of the melt pool into the substrate. Once again, the low friction of the powder around the melt pool has allowed the external part of it acquire spherical shape. The high degree of symmetry of this contour reinforces the idea of the very limited restriction of the powder to the movement of the melt pool, as considered in the thermo-fluidic coupled model.

In the case of test 3, the use of the most aggressive combination of process parameters highlights the importance of the dynamic effects during the consolidation phenomenon. Despite having the largest level of power, 3000 W, the shorter interaction time has limited both the process of drop formation and the penetration of the melt pool into the substrate. The shape of the external part of the melt pool presents a profile which is not as close to a sphere as the profile of the previous tests: the limited interaction time has led to the cooling of the material before it has been capable of finishing its evolution to a spherical profile. In addition, the heating and cooling processes, happening more quickly than in the previous tests, limits the time of the molecules of the material to move from their equilibrium positions, restricting any diffusion process which might occur as a consequence of the thermal cycle.

The numerical aspects of the theoretical model have allowed the convergence of the calculations to be achieved. The mesh deformed under the effect of the loads affecting the fluid, and automatically re-meshed when the distortion of the elements reached the user-defined maximum permitted value.

#### **5. Conclusions**

The thermo-fluidic coupling has been revealed as a valid tool to evaluate the behavior of the material in its evolution from powder to liquid and from liquid to solid. The dimensions of the cross section predicted by the simulations matched the experimental results with an acceptable level of accuracy. It reinforces the idea of phase and temperature-dependent thermo-physical properties to understand the behavior of the material during the different stages that it experiences in the Selective Laser Melting Process.

The use of the finite element method in combination with advanced numerical tools has allowed realistic domains with large dimensions to be used, thus favoring, in this way, the study or real processes at an industrial scale, surpassing the capabilities of conventional models with domains at the microscale level.

The governability of the process with a large thickness powder bed has been revealed to be possible, since the simulations have been capable of estimating the dimensions of the cross section resulting from a particular combination of process parameters. Specific consideration about the amount of dilution associated with large powder beds are necessary. Future works dealing with metallurgical aspects of the process will be carried out.

**Author Contributions:** F.C.: He was the main developer of the thermo-fluidic model and postulated the temperature and phase dependency of the thermo-fluidic properties. He also adjusted the use of the advanced numerical tools such as the Arbitrary Lagrangean-Eulerian Method and the Automatic Re-meshing. Á.G.-B.: He assisted in the development of the model in all the different stages of the process. M.G.: He contributed with the firsts version of developments of the model and provided fundamental assistance during all the stages. D.A.M.: He contributed with the firsts version of developments of the model and provided fundamental assistance during

all the stages. J.L.O.: He participated and led in all the stages in the development of the present work. He provided fundamental knowledge for the theoretical model as well as for the interpretation of the experimental results.

**Funding:** This research was funded by the spanish Centre for the Development of Industrial Technology (CDTI) in the frame of the CIEN-FRACTAL project with grant number MQM-2010290.

**Acknowledgments:** The Authors wish to acknowledge the assistance of Piera Alvarez and María Ángeles Montealegre from Ikergune A.I.E. (Etxe-Tar group) who helped during the preparation and analysis of the experimental tests.

**Conflicts of Interest:** The authors declare no conflict of interest.
