# Keyhole Formation by Laser Drilling in Laser Powder Bed Fusion of Ti6Al4V Biomedical Alloy: Mesoscopic Computational Fluid Dynamics Simulation versus Mathematical Modelling Using Empirical Validation

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## Abstract

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## 1. Introduction

## 2. Modelling

#### 2.1. Analytical Modelling

_{sp}(=k/ρ

_{sp}C

_{sp}) stands for the thermal diffusivity of the powder bed, $g\left(x,y,t\right)$ is the volumetric heat source, and ρ

_{sp}, C

_{sp}and ${k}_{sp}$ are the density, specific heat and thermal conductivity of the powder bed, respectively, that were calculated as:

_{p}is the average radius of spherical powder particle, and S is the surface area of the powder bed. The thermal distribution (${T}_{sp}(x,y)$) solution of Equation (1) is known in Ref. [36] and was modified by redefining the total sample absorption coefficient (${\alpha}_{sp}(z)$) based upon the surface absorption coefficient (r

_{sp}) and absorption coefficient voids (${\alpha}_{sp}$) [37]:

_{x}is the laser scanning speed, and R is the laser beam-powder bed distance, expressed as:

_{l}) is expressed as:

_{v}) and depth (d

_{v}), the incident laser beam will experience numerous reflections before coming out of the void. It, in return, increases the bulk laser absorption coefficient (${\alpha}_{sp}(z)$). In Equation (3), r

_{sp}is a dimensionless value; therefore, letting r

_{sp}equal to w

_{v}/d

_{v}gives:

#### 2.2. Numerical Modelling

_{b}denotes the laser beam spot radius, v denotes the scanning rate, and ${x}_{0}$ and ${y}_{0}$ represent the original position of the laser beam center [46]. The beam radius, ${R}_{b}$, is set as 27.5 m. However, evaporation is critical when considering the hot surface of the melt pool due to convection and radiation. As a consequence, the governing equation [46] may be represented primarily on the melt pool surface as:

## 3. Materials and Methods

## 4. Results and Discussions

## 5. Conclusions

- The temperature below the laser irradiation point rises rapidly in LPBF, whereas the powder layer around it remains at a localized temperature. Due to air between the powder particles and the relatively low particle–particle contact areas, laser transverse heat waves have a slower speed because of the high thermal resistance.
- Two types of laser keyholes can be generated during the LPBF process: shallow and deep keyholes. The mode type can be controlled and defined to an extent by the energy density. Increasing the energy density leads to an increase in the amount of energy delivered to a given region, and optical rays encounter numerous reflections due to voids available in the deposited powder layer. In return, this increases the laser beam absorption coefficient. As a result, the shallow keyhole converts into a deep keyhole.
- The deep keyhole usually generates numerous laser beam reflections and stream traces. A deep keyhole experiences a larger energy density compared with a shallow keyhole, pushing the material towards vaporization. The porosity usually occurs if the solid front hits quickly before they escape from the melt pool. Due to an elevated temperature distribution in the deep keyhole, the probability of pores forming is much higher than in a shallow keyhole, as the liquid material is close to the vaporization zone. However, both shallow and deep keyholes exhibited a clockwise direction.
- Due to the specific heat and fusion latent heat, the results demonstrated that, as the temperature increases, the material density decreases rapidly, elevating the fluid volume. This, in return, reduces the surface tension (ST), and is also known as Benard–Marangoni convection or thermocapillary convection. The ST difference largely determines the size of the melt pool. When a liquid’s ST difference widens, a significant pull arises from the high ST end toward the low ST end.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**(

**a**) Scanning electron microscopy images of Ti6Al4V powder particles and (

**b**) simulated powder bed using discrete element modelling.

**Figure 3.**Temperature field contour formation at various time intervals (

**a**) 0.695 ms, (

**b**) 0.795 ms, (

**c**) 0.995 ms and (

**d**) 1.3 ms.

**Figure 5.**Melt flow stream traces formation at various time intervals (

**a**) 0.695 ms, (

**b**) 0.795 ms, (

**c**) 0.995 ms and (

**d**) 1.3 ms.

**Figure 6.**Density evolution of the melt pool at various time intervals (

**a**) 0.695 ms, (

**b**) 0.795 ms, (

**c**) 0.995 ms and (

**d**) 1.3 ms.

**Figure 7.**Un-melted and melted regions at different time intervals (

**a**) 0.695 ms, (

**b**) 0.795 ms, (

**c**) 0.995 ms and (

**d**) 1.3 ms.

**Figure 8.**Transformation from shallow depth melt flow to deep keyhole formation when laser power increased from (

**a**) 170 W to (

**b**) 200 W.

**Figure 10.**A comparison between analytical and CFD simulation results for peak thermal distribution value in the deep keyhole formation.

**Figure 11.**A comparison among experiments [49], CFD and analytical simulations for deep keyhole top width and bottom width.

**Figure 12.**A comparison for thermal distribution among CFD simulation, literature result [58] and analytical computation for keyhole formation.

**Table 1.**The thermo-physical properties of Ti6Al4V [49].

Parameters | Values (Units) |
---|---|

Solidus temperature | 1878 (K) |

Liquidus temperature | 1928 (K) |

Boiling temperature | 3533 (K) |

Latent heat of fusion | 286 (kJ/Kg) |

Latent heat of evaporation | 9830 (kJ/Kg) |

Viscosity | 0.005 (Kg/ms |

Surface tension | 1.68 (N/m) |

Surface tension gradient | −0.00026 (N/mK) |

**Table 2.**Parameters for analytical and CFD simulations [50].

Parameter | Value | Parameter | Value |
---|---|---|---|

Substrate length × width × depth | 2500 µm × 200 µm × 400 µm | Average size of cell for CFD simulations | 3.3 µm |

Powder layer thickness | 70 µm | Ti6Al4V particle size distribution | D10 = 19 µm, D50 = 30 µm and D90 = 46 µm |

Laser power | 195 W | Laser beam entire absorption coefficient | 0.25 |

Laser scanning speed | 400 mm/s, 1000 mm/s | Number of cells generated for CFD simulation | 6,288,368 |

Effective laser beam radius where the heat flux is 1/e^{2} of its maximum value | 25 µm |

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**MDPI and ACS Style**

Ur Rehman, A.; Mahmood, M.A.; Pitir, F.; Salamci, M.U.; Popescu, A.C.; Mihailescu, I.N. Keyhole Formation by Laser Drilling in Laser Powder Bed Fusion of Ti6Al4V Biomedical Alloy: Mesoscopic Computational Fluid Dynamics Simulation versus Mathematical Modelling Using Empirical Validation. *Nanomaterials* **2021**, *11*, 3284.
https://doi.org/10.3390/nano11123284

**AMA Style**

Ur Rehman A, Mahmood MA, Pitir F, Salamci MU, Popescu AC, Mihailescu IN. Keyhole Formation by Laser Drilling in Laser Powder Bed Fusion of Ti6Al4V Biomedical Alloy: Mesoscopic Computational Fluid Dynamics Simulation versus Mathematical Modelling Using Empirical Validation. *Nanomaterials*. 2021; 11(12):3284.
https://doi.org/10.3390/nano11123284

**Chicago/Turabian Style**

Ur Rehman, Asif, Muhammad Arif Mahmood, Fatih Pitir, Metin Uymaz Salamci, Andrei C. Popescu, and Ion N. Mihailescu. 2021. "Keyhole Formation by Laser Drilling in Laser Powder Bed Fusion of Ti6Al4V Biomedical Alloy: Mesoscopic Computational Fluid Dynamics Simulation versus Mathematical Modelling Using Empirical Validation" *Nanomaterials* 11, no. 12: 3284.
https://doi.org/10.3390/nano11123284