# Laser Operating Windows Prediction in Selective Laser-Melting Processing of Metallic Powders: Development and Validation of a Computational Fluid Dynamics-Based Model

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

^{®}Fluent, Release 17.1, developed by ANSYS, Inc. (Canonsburg, PA, USA). This choice offers the possibility of further model integrations with surface tension, pool convection and gas-cooling effects.

_{l}). The effect of adding this term is negligible for most metal alloys, being the mushy zone extension very small at such high cooling rates. Otherwise, the fluid-dynamics through the mushy zone could affect the thermal field when processing alloys have large solidification intervals.

_{v}assumes the following expression:

_{min}and f

_{max}the gas fraction respectively in the first and second path, the effective powder conductivity is calculated according to Equation (6):

_{1}and k

_{2}being the conductivities along each of the two paths. They are obtained by the inverse of the series of thermal resistances of metal and gas:

_{min}and f

_{max}values, consistent with the powder bed gas fraction. The resulting effective thermal conductivity is about 12%–14% of the metal conductivity, depending on the gas composition, imposing 0.4 as the gas fraction in the powder bed. This approach is designed to allow for future analysis of effects due to powder rarefactions or agglomerations, provided its specific calibration.

_{0}and h

_{0}. These two values have been used as calibration parameters for all the analyzed alloys. At the end of the calibration it was concluded that good fitting is achieved by setting:

- h
_{0}equal to the powder layer thickness plus 10 microns, which could be consistent with the high permeability of the powder bed to laser rays, due to its scarce compactness.

^{®}, Release 4.0, developed by Sente Software Ltd. (Surrey, UK).

## 3. Results

_{eff}) has been derived running the model several times varying k

_{eff}until fitting the track geometry measured for all available sets of parameters. Assuming for the correlation between k

_{eff}and the actual liquid metal conductivity (k

_{liq}) the form:

_{eff}evaluated for each alloy, the corresponding values of C

_{k}have been calculated and plotted against k

_{liq}in Figure 4. The fitting trendline, has the following expression:

#### 3.1. Comparison of Calculated and Measured Data of Track Geometry

_{0}). The resulting rising trends of both variables within the transition range, are quite close for the four alloys. The straight lines superimposed in Figure 6 are trendlines used for the extrapolation of the model fitting parameters. They are derived through the following relationships:

_{0}) at which the absorptivity reaches the maximum level. Figure 6 shows the range inside which this yield is met by all the analyzed alloys, denoted as range of deep keyhole start.

#### 3.2. Comparison of Calculated and Measured Data of Relative Density

_{eff}is assumed, to be distinguished from the nominal thickness: t

_{nom}. The relationship between: t

_{eff}and t

_{nom}is approximated by: t

_{eff}= t

_{nom}/f [35], being f the metal fraction of the powder, assumed to be equal to 0.6 in this work. Figure 8 shows the scheme adopted for deriving relative density from the track geometry.

- porosity for E < 50 J/mm
^{3}(porosity due to lack of fusion): calculated values are much lower than measured. Values of porosity as high as 65% are found in the reference source [30], which raise some doubt about the coherency of the measured sample. Therefore, no deep analysis about the reason of the discrepancy among calculated and measured data has been done, concerning the highest values, otherwise the information given by the measured porosity trend has been considered valid; - the calculated threshold of formation of porosity due to lack of fusion is calculated at 42 J/mm
^{3}against the experimentally observed at 50 J/mm^{3}; - the model cannot calculate porosity due to deep keyhole, but only the threshold which is found at E = 133 J/mm
^{3}. Experimental data show presence of 1% porosity at E = 87 J/mm^{3}and a net porosity increase above E = 100 J/mm^{3}. Thus, keyhole porosity could already form for a calculated value of α equal to about 0.85.

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Nomenclature

C_{k} | multiplying factor |

D | distribution factor |

f | metal fraction in the powder bed |

f_{l} | metal liquid fraction in the mushy zone |

g_{i} | gravity acceleration components (m s^{−2}) |

h | height of the cylinder of laser heat application |

ha | hatch spacing (mm) |

H | enthalpy (J kg^{−1}) |

k_{eff} | effective thermal conductivity (W m^{−1} K^{−1}) |

k_{liq} | thermal conductivity of the liquid metal (W m^{−1} K^{−1}) |

K | mushy zone permeability (m^{2}) |

p | pressure (Pa) |

P | laser power (W) |

PDAS | primary dendrite arm spacing (m) |

r_{l} | laser beam radius |

S_{v} | volumetric heat source (J m^{3}) |

t | time (s) |

t_{eff} | printing regime bed powder thickness (μm) |

t_{nom} | nominal powder bed thickness (μm) |

T_{liq} | liquidus temperature (K) |

T_{sol} | solidus temperature (K) |

u_{i}, u_{j} | velocity components (m s^{−1}) |

v | scanning speed (m s^{−1}) |

x, y | coordinates in a frame relative to the laser beam (m) |

x_{i}, x_{j} | coordinates (m) |

α | laser absorptivity |

β | fraction of the track surface contacting powder |

η | laser efficiency |

μ | viscosity (Pa s) |

ρ | metal density (kg m^{−3}) |

ρ_{p} | part density (kg m^{−3}) |

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**Figure 1.**Scheme showing the ideal cylindrical volume inside which the laser energy source is applied, moving with the laser beam at velocity v.

**Figure 2.**Scheme showing the bead surface in contact with the powder layer and its subdivision into regions contacting powder–gas mixture zones having different density.

**Figure 3.**Thermal field and detail of fluid-dynamics around the melt pool, on the longitudinal symmetry plane (case of pure copper printed at 800 W and 1000 mm/s).

**Figure 6.**Values of absorptivity α and depth of energy deposition h vs the difference of specific energy and yield value of specific energy between conduction and evaporation. All adjusted values for the alloys: Ti6Al4V, Inconel 625, Al7050 and 316L are included in the diagram.

**Figure 7.**Comparison of measured [21] and calculated values of total absorptivity of alloy 316L.

**Table 1.**Thermo-physical properties used in the model for the five commercial alloys used for the calibration. Experimental data have been found in the references shown in the table.

Property | Ti6Al4V | INC625 | Al7050 | 316L | Cu(99,9%) |
---|---|---|---|---|---|

Density (kg/m^{3}) | 4000 | 8440 | 2810 | 7890 | 8960 |

Liquidus Temperature: T_{liq} (K) | 1986 | 1607 | 906 | 1710 | 1356 |

Solidus Temperature: T_{sol} (K) | 1970 | 1513 | 787 | 1608 | 1356 |

Specific Heat (J/(kgK)) | |||||

T_{amb} | 550 | 440 | 860 | 450 | 481 |

T_{sol} | 830 | 650 | 1050 | 750 | 481 |

T_{liq} | 980 | 670 | 1120 | 770 | 531 |

Thermal Conductivity (W/(mK)) | |||||

T_{amb} | 5 | 11 | 117 | 16 | 397 |

T_{sol} | 32 | 30 | 156 | 33 | 317 |

T_{liq} | 32 | 30 | 87 | 30 | 157 |

Latent Heat of Fusion (J/m^{3})·10^{9} | 1.4 | 1.99 | 1.05 | 1.37 | 2.07 |

Boiling Temperature (K) | 3600 | 3000 | 2800 | 3100 | 2840 |

Reflectivity at 1.06 μm (T≈900K) | 0.52 | 0.71 | 0.65 | 0.63 | 0.84 |

Reference | [30] | [15] | [29] | [24] | [31] |

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**MDPI and ACS Style**

Ridolfi, M.R.; Folgarait, P.; Di Schino, A.
Laser Operating Windows Prediction in Selective Laser-Melting Processing of Metallic Powders: Development and Validation of a Computational Fluid Dynamics-Based Model. *Materials* **2020**, *13*, 1424.
https://doi.org/10.3390/ma13061424

**AMA Style**

Ridolfi MR, Folgarait P, Di Schino A.
Laser Operating Windows Prediction in Selective Laser-Melting Processing of Metallic Powders: Development and Validation of a Computational Fluid Dynamics-Based Model. *Materials*. 2020; 13(6):1424.
https://doi.org/10.3390/ma13061424

**Chicago/Turabian Style**

Ridolfi, Maria Rita, Paolo Folgarait, and Andrea Di Schino.
2020. "Laser Operating Windows Prediction in Selective Laser-Melting Processing of Metallic Powders: Development and Validation of a Computational Fluid Dynamics-Based Model" *Materials* 13, no. 6: 1424.
https://doi.org/10.3390/ma13061424