# Multi-Physics Modeling of Melting-Solidification Characteristics in Laser Powder Bed Fusion Process of 316L Stainless Steel

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## Abstract

**:**

## 1. Introduction

## 2. Computational Models

- The fluid in the molten pool is assumed to be Newtonian and laminar flow;
- The mushy zone is assumed to be isotropic during the solid–liquid phase change process;
- The distribution of powder particles is assumed to be fixed in space;
- The effect of the surrounding argon’s flow on the molten pool is neglected;
- The influence of ambient gas on laser energy absorption is neglected.

#### 2.1. Governing Equations

_{s}is the local solid fraction in the computational domain; C is a constant that depends on the mushy zone microstructure; B is a small constant that is used to avoid D being infinity when Fs = 1.

#### 2.2. Initial and Boundary Conditions

_{0}is the ambient temperature; n is the vector along the normal direction of the top surface of the powder bed; q(x, y, z, t) represents the laser energy distribution; ε

_{r}is the surface radiation coefficient; σ

_{s}is the Stefan–Boltzmann constant (5.67 × 10

^{−8}W/(m

^{2}·K

^{4})); h

_{c}is the natural convection heat transfer coefficient; q

_{ev}is the heat taken away as the molten pool evaporation.

_{0}is the laser beam intensity at r = 0. Thus, q

_{0}can be written as:

_{0}is atmospheric pressure; ΔH* is the effective evaporation enthalpy; M is the molar mass; T

_{v}is the evaporation temperature.

_{e}is the latent heat of evaporation; T

_{v}is the evaporation temperature; P

_{0}is the atmospheric pressure.

_{1}and R

_{2}are the principal radii of molten pool surface curvature. The temperature-dependent surface tension coefficient can be described as $\sigma ={\sigma}_{0}-\partial \sigma /\partial T\left(T-{T}_{ref}\right)$.

#### 2.3. Simulation Cases and Computation

Material Property | Value |
---|---|

Surface tension coefficient | 1.76 N/m [37] |

Change rate of surface tension | −4.002 × 10^{−4} N/m/K [37] |

Density | see Figure 2a |

Thermal conductivity | see Figure 2b |

Specific heat capacity | see Figure 2c |

Solidus temperature | 1658 K [38] |

Liquidus temperature | 1723 K [38] |

Evaporation temperature | 3086 K [38] |

Latent heat of fusion | 2.8 × 10^{5} J/kg [10] |

Latent heat of evaporation | 7.45 × 10^{6} J/kg [38] |

Molar mass | 5.58 × 10^{−2} kg/mol [38] |

Dynamic viscosity | 5.6 × 10^{−3} Pa·s [39] |

Surface radiation coefficient | 0.4 [39] |

Absorption coefficient | 0.55 (solid), 0.3 (liquid) [10] |

## 3. Results and Discussion

#### 3.1. Molten Pool Morphology Analysis

#### 3.2. Temperature Distribution Analysis

#### 3.3. Keyhole Depth Analysis

#### 3.4. Hatch Space Analysis

#### 3.5. Analysis of Powder Bed Distribution Effects

## 4. Conclusions

- The convection flow in the molten pool can effectively widen the molten pool width and promote strong bonding between adjacent scan tracks. Therefore, the hatch space can be enlarged by increasing the laser power or decreasing the scanning speed to enhance the convection flow behavior.
- When the LED decreases to 240 J/m, the keyhole depth becomes too small to fuse the previously processed layer with the currently processed one, potentially leading to degradation in part densification. To ensure better densification of the final parts, it is suggested that the LED be set to over 400 J/m when the layer thickness is 45 μm.
- The keyhole depth can be enlarged more effectively by further increasing the energy input after the keyhole is formed, such as by increasing the laser power or decreasing the scanning speed.
- If the hatch space is too large or the powder bed is sparsely distributed, internal void defects may form, significantly affecting workpiece quality. To prevent these defects, it is suggested that the hatch space be narrower than the single-track width.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic diagram of the LPBF process. The gray represents the unprocessed steel; the blue represents the molten pool; and the baby blue represents the molten pool after solidification.

**Figure 3.**Flow behavior in the molten pool with different cross sections (laser power = 120 W, scanning speed = 0.2 m/s). The black arrows show the fluid flow; the arrow length shows the velocity magnitude; and the color scale shows the temperature field in Kelvin.

**Figure 13.**Cross section of molten pool after solidification under different hatch space: (

**a**) single-track scanning; (

**b**) hatch space = 0.14 mm; (

**c**) hatch space = 0.12 mm.

**Figure 14.**The effects of the powder bed distribution: (

**a**) sparse region at the boundary of scan track; (

**b**) defect region caused by the sparse region in (

**a**); (

**c**) sparse region at the center of the scan track; (

**d**) defect region caused by the sparse region in (

**c**); (

**e**) normal morphology of the scan track after increasing the laser power.

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**MDPI and ACS Style**

Shan, X.; Pan, Z.; Gao, M.; Han, L.; Choi, J.-P.; Zhang, H.
Multi-Physics Modeling of Melting-Solidification Characteristics in Laser Powder Bed Fusion Process of 316L Stainless Steel. *Materials* **2024**, *17*, 946.
https://doi.org/10.3390/ma17040946

**AMA Style**

Shan X, Pan Z, Gao M, Han L, Choi J-P, Zhang H.
Multi-Physics Modeling of Melting-Solidification Characteristics in Laser Powder Bed Fusion Process of 316L Stainless Steel. *Materials*. 2024; 17(4):946.
https://doi.org/10.3390/ma17040946

**Chicago/Turabian Style**

Shan, Xiuyang, Zhenggao Pan, Mengdi Gao, Lu Han, Joon-Phil Choi, and Haining Zhang.
2024. "Multi-Physics Modeling of Melting-Solidification Characteristics in Laser Powder Bed Fusion Process of 316L Stainless Steel" *Materials* 17, no. 4: 946.
https://doi.org/10.3390/ma17040946