# Experimental and Numerical Investigations of In Situ Alloying during Powder Bed Fusion of Metals Using a Laser Beam

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## Abstract

**:**

## 1. Introduction and State of the Art

#### 1.1. Problem Statement

#### 1.2. Approach

## 2. Numerical Modeling of the In Situ Alloying

#### Alloy Species Transport

## 3. Experiments

#### 3.1. Experimental Setup

#### 3.1.1. Calibration of the Thermographic Imaging System

#### 3.1.2. Experimental Approach

#### 3.2. Simulation Setup

## 4. Results and Discussion

## 5. Conclusions and Outlook

- The powder blends consisting of 316L and AlSi10Mg were successfully simplified with an Fe-Al system using curve-fitted material parameters.
- The simulation results were validated with a novel experimental setup. High-speed thermographic imaging provided validation data of the melt pool cross-section on a small spatial scale. The global validation quantity was the melt pool length. For both simulation and experiment, the same trend of increasing melt pool dimensions with higher amounts of additives was found.
- The simulation results show a good agreement with the experimental SEM-EDS results for the concentration profile of a single AlSi10Mg powder particle.
- The presented framework is a suitable basis for the simulation of in situ alloying during PBF-LB/M.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

316L | Property | Temperature Range | Value | Units | References |
---|---|---|---|---|---|

${T}_{\mathrm{s}}$ | Solidus temperature | − | 1633 | K | [42] |

${T}_{\mathrm{l}}$ | Liquidus temperature | − | 1683 | K | [42] |

${T}_{\mathrm{b}}$ | Boiling temperature | − | 3073 | K | [43] |

k | Thermal conductivity | $T<{T}_{\mathrm{l}}$ | $9.59+141\times {10}^{-4}\xb7{\mathrm{K}}^{-1}\xb7T$ | $\frac{\mathrm{W}}{\mathrm{K}\phantom{\rule{4pt}{0ex}}\mathrm{m}}$ | [44] |

${T}_{\mathrm{l}}>T>{T}_{\mathrm{s}}$ | $355.93-196.90\times {10}^{-3}\xb7{\mathrm{K}}^{-1}\xb7T$ | $\frac{\mathrm{W}}{\mathrm{K}\phantom{\rule{4pt}{0ex}}\mathrm{m}}$ | [44] | ||

$T>{T}_{\mathrm{l}}$ | $6.60+121.40\times {10}^{-4}\xb7{\mathrm{K}}^{-1}\xb7T$ | $\frac{\mathrm{W}}{\mathrm{K}\phantom{\rule{4pt}{0ex}}\mathrm{m}}$ | [44] | ||

H | Specific enthalpy | $T<1132\phantom{\rule{0.166667em}{0ex}}\mathrm{K}$ | $-138,595.00+458.93\xb7{\mathrm{K}}^{-1}\xb7T$ | $\frac{\mathrm{J}}{\mathrm{kg}}$ | [45] |

$1132\phantom{\rule{0.166667em}{0ex}}\mathrm{K}<T<{T}_{\mathrm{l}}$ | −374,150.00 + $714.29\xb7{\mathrm{K}}^{-1}\xb7T$ | $\frac{\mathrm{J}}{\mathrm{kg}}$ | [45] | ||

${T}_{s}<T<{T}_{\mathrm{l}}$ | −8,181,263.00 +$5494.51\xb7{\mathrm{K}}^{-1}\xb7T$ | $\frac{\mathrm{J}}{\mathrm{kg}}$ | [45] | ||

$T>{T}_{\mathrm{l}}$ | −336,177.97 + $847.46\xb7{\mathrm{K}}^{-1}\xb7T$ | $\frac{\mathrm{J}}{\mathrm{kg}}$ | [45] | ||

c | Specific heat capacity | $T<{T}_{\mathrm{l}}$ | 492 | $\frac{\mathrm{J}}{\mathrm{kg}\phantom{\rule{4pt}{0ex}}\mathrm{K}}$ | [42] |

$T>{T}_{\mathrm{l}}$ | 736 | $\frac{\mathrm{J}}{\mathrm{kg}\phantom{\rule{4pt}{0ex}}\mathrm{K}}$ | [42] | ||

$\eta $ | Dynamic viscosity | $T>{T}_{\mathrm{l}}$ | $-180.76\xb7{\mathrm{e}}^{-1.95/T}+180.68$ | $\frac{\mathrm{kg}\phantom{\rule{4pt}{0ex}}\mathrm{s}}{{\mathrm{m}}^{2}}$ | [46] |

$\alpha $ | Surface tension coefficient | ${T}_{\mathrm{l}}<T<2166$ | 1.82 | $\frac{\mathrm{N}}{\mathrm{m}}$ | [47] |

$T>2166$ | $1.84-0.11\times (T-2000\phantom{\rule{0.166667em}{0ex}}\mathrm{K})\times {10}^{-3}$ | $\frac{\mathrm{N}}{\mathrm{m}}$ | [47] | ||

M | Molar mass | - | $57.96\times {10}^{-3}$ | $\frac{\mathrm{kg}}{\mathrm{mol}}$ | |

a | Absorptivity | 0.4 | − | [43] |

AlSi10Mg | Property | Temperature Range | Value | Units | References |
---|---|---|---|---|---|

${T}_{\mathrm{s}}$ | Solidus temperature | − | 816 | K | [48] |

${T}_{\mathrm{l}}$ | Liquidus temperature | − | 853 | K | [48] |

${T}_{\mathrm{b}}$ | Boiling temperature | − | 2737 | K | [49] |

k | Thermal conductivity | $T<{T}_{\mathrm{l}}$ | 155 | $\frac{\mathrm{W}}{\mathrm{K}\phantom{\rule{4pt}{0ex}}\mathrm{m}}$ | [50] |

$T>{T}_{\mathrm{l}}$ | 120 | $\frac{\mathrm{W}}{\mathrm{K}\phantom{\rule{4pt}{0ex}}\mathrm{m}}$ | [51] | ||

H | Specific enthalpy | $T<{T}_{\mathrm{l}}$ | − 230,136.36 +$909.09\xb7{\mathrm{K}}^{-1}\xb7T$ | $\frac{\mathrm{J}}{\mathrm{kg}}$ | [42] |

$T<{T}_{\mathrm{l}}$ | −8,243,682.40 + $10,729.61\xb7{\mathrm{K}}^{-1}\xb7T$ | $\frac{\mathrm{J}}{\mathrm{kg}}$ | [42] | ||

${T}_{\mathrm{s}}<T<{T}_{\mathrm{l}}$ | 140,209.01 +$909.09\xb7{\mathrm{K}}^{-1}\xb7T$ | $\frac{\mathrm{J}}{\mathrm{kg}}$ | [42] | ||

c | Specific heat capacity | $T<{T}_{\mathrm{l}}$ | 920 | $\frac{\mathrm{J}}{\mathrm{kg}\phantom{\rule{4pt}{0ex}}\mathrm{K}}$ | [52] |

$T>{T}_{\mathrm{l}}$ | 1050 | $\frac{\mathrm{J}}{\mathrm{kg}\phantom{\rule{4pt}{0ex}}\mathrm{K}}$ | [51] | ||

$\eta $ | Dynamic viscosity | $T>{T}_{\mathrm{l}}$ | $-163.16\xb7{\mathrm{e}}^{-1.78/T}+163.12$ | $\frac{\mathrm{kg}\phantom{\rule{4pt}{0ex}}\mathrm{s}}{{\mathrm{m}}^{2}}$ | [53] |

$\alpha $ | Surface tension coefficient | $T>{T}_{\mathrm{l}}$ | 0.88 | $\frac{\mathrm{N}}{\mathrm{m}}$ | [54] |

M | Molar mass | - | $332.14\times {10}^{-3}$ | $\frac{\mathrm{kg}}{\mathrm{mol}}$ | |

a | Absorptivity | 0.09 | − | [55] |

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**Figure 1.**The verification case (

**a**) and the comparison of the analytical solution with the numerical solution for $t=1.0$ s (

**b**).

**Figure 4.**The initial powder bed (

**a**) and the steady-state melt pool (

**b**) for 316L blended with 5 wt.% AlSi10Mg.

**Figure 5.**Comparison of the melt pool length between the steady-state simulation results and the experimental results in dependence of the amount of AlSi10Mg additives.

**Figure 6.**SEM image of a longitudinal microsection with a superimposed EDS mapping of AlSi10Mg showing a single AlSi10Mg powder particle after single-track melting; the laser scanning direction was in the positive y-direction.

**Figure 7.**Comparison of the simulation and the experimental results of the mixing behavior for a single AlSi10Mg powder particle after single-track melting in two spatial directions.

Symbol | Property | Value | Unit |
---|---|---|---|

l | Height of the domain (z-direction) | 100 | µm |

b | Width of the domain (x-direction) | 40 | µm |

${x}_{1}$ | Position of the stripe in x-direction | 20 | µm |

${z}_{1}$ | Position of the stripe in z-direction | 44 | µm |

${z}_{2}$ | Position of the stripe in z-direction | 55 | µm |

${C}_{0}$ | Solute concentration | 100 | % |

${C}_{1}$ | Solvent concentration | 0 | % |

${\rho}_{0}$ | Solute density | 1000 | $\mathrm{kg}/{\mathrm{m}}^{3}$ |

${\rho}_{1}$ | Solvent density | 1000 | $\mathrm{kg}/{\mathrm{m}}^{3}$ |

${D}_{0}$ | Diffusivity | $1\times {10}^{-4}$ | ${\mathrm{m}}^{2}/\mathrm{s}$ |

$\Delta x$ | Particle size | 1 | µm |

Symbol | Property | Value | Unit |
---|---|---|---|

d | Powder layer thickness | 20 | µm |

- | Amount of AlSi10Mg additives in the powder blend | 0 | wt.% |

1 | wt.% | ||

5 | wt.% | ||

P | Laser power | 175 | $\mathrm{W}$ |

r | Laser beam radius | 40 | µm |

${v}_{\mathrm{b}}$ | Laser beam velocity | 0.375 | $\frac{\mathrm{m}}{\mathrm{s}}$ |

Symbol | Property | Value | Unit |
---|---|---|---|

${\rho}_{0}$ | Reference density | 7763 | kg/m${}^{2}$ |

- | Kernel type | Quintic spline | - |

${h}_{0}$ | Particle spacing | 2.0 | µm |

g | Gravity | 9.81 | m/s${}^{2}$ |

t | Exposure time (${v}_{b}$ = 0.375 m/s) | $10.4\times {10}^{-4}$ | s |

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## Share and Cite

**MDPI and ACS Style**

Wimmer, A.; Yalvac, B.; Zoeller, C.; Hofstaetter, F.; Adami, S.; Adams, N.A.; Zaeh, M.F.
Experimental and Numerical Investigations of In Situ Alloying during Powder Bed Fusion of Metals Using a Laser Beam. *Metals* **2021**, *11*, 1842.
https://doi.org/10.3390/met11111842

**AMA Style**

Wimmer A, Yalvac B, Zoeller C, Hofstaetter F, Adami S, Adams NA, Zaeh MF.
Experimental and Numerical Investigations of In Situ Alloying during Powder Bed Fusion of Metals Using a Laser Beam. *Metals*. 2021; 11(11):1842.
https://doi.org/10.3390/met11111842

**Chicago/Turabian Style**

Wimmer, Andreas, Baturay Yalvac, Christopher Zoeller, Fabian Hofstaetter, Stefan Adami, Nikolaus A. Adams, and Michael F. Zaeh.
2021. "Experimental and Numerical Investigations of In Situ Alloying during Powder Bed Fusion of Metals Using a Laser Beam" *Metals* 11, no. 11: 1842.
https://doi.org/10.3390/met11111842