# Modeling of Laser Beam Absorption in a Polymer Powder Bed

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## Abstract

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## 1. Introduction

## 2. Absorption Model

## 3. Implementation

## 4. Validation

#### 4.1. Plain Surface

#### 4.2. Polyamide 12 Powder Bed

## 5. Penetration Depth in a Powder Bed

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**The incoming ray $\overrightarrow{k}$ is divided into a reflected ${\overrightarrow{k}}_{R}$ and refracted ${\overrightarrow{k}}_{T}$ part at the interface of media A and B. $\alpha $ and $\beta $ are the reflection and refraction angle, respectively.

**Figure 2.**(

**Left**) Arbitrary geometry G. (

**Middle**) Volume of fluid (VOF) representation of G on a 5 × 5 grid. The exact surface is indicated by the dashed line. The grey scale shows the volume fraction of the geometry within one cell. (

**Right**) Reconstruction of the surface in one cell.

**Figure 3.**Relative intensity distribution of a laser irradiating onto a flat surface with two incident angles $\gamma $ of ${0}^{\circ}$ (upper row) and ${45}^{\circ}$ (lower row) for three different spatial resolutions $\Delta x=\left(\right)open="["\; close="]">40\phantom{\rule{4pt}{0ex}}\mathsf{\mu}\mathrm{m},\phantom{\rule{0.277778em}{0ex}}20\phantom{\rule{4pt}{0ex}}\mathsf{\mu}\mathrm{m},\phantom{\rule{0.277778em}{0ex}}5\phantom{\rule{4pt}{0ex}}\mathsf{\mu}\mathrm{m}$ (left to right).

**Figure 4.**Comparison of the analytical (Equation (15)) and numerical relative intensity distribution in the beam center along the normal direction for five resolutions and three incident angles.

**Figure 5.**Trace of a ray cast from the top of the simulation domain propagating towards a powder bed. From left to right, the number of rays is increased.

**Figure 7.**(

**Left**) Relative transmission in a thin foil of PA12 with different film thicknesses. (

**Right**) Comparison of the relative transmission and reflection in a PA12 powder bed between experimental data [15] and the simulation.

**Figure 8.**(

**Right**) Three powder beds with their relative absorbed intensity distributions. (

**Left**) The mean intensity ${I}_{m}$ over the powder bed depth for the corresponding relative densities with ${n}_{med}=1.7$ and ${\lambda}_{0}=100\phantom{\rule{0.277778em}{0ex}}\mathsf{\mu}$m.

**Figure 9.**The correlation between ${\lambda}_{eff}$ and ${\rho}_{rel}$ for three different refractive indices. The dot-dashed line indicates penetration depth ${\lambda}_{0}=100\phantom{\rule{0.277778em}{0ex}}\mathsf{\mu}$m in bulk material.

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## Share and Cite

**MDPI and ACS Style**

Osmanlic, F.; Wudy, K.; Laumer, T.; Schmidt, M.; Drummer, D.; Körner, C.
Modeling of Laser Beam Absorption in a Polymer Powder Bed. *Polymers* **2018**, *10*, 784.
https://doi.org/10.3390/polym10070784

**AMA Style**

Osmanlic F, Wudy K, Laumer T, Schmidt M, Drummer D, Körner C.
Modeling of Laser Beam Absorption in a Polymer Powder Bed. *Polymers*. 2018; 10(7):784.
https://doi.org/10.3390/polym10070784

**Chicago/Turabian Style**

Osmanlic, Fuad, Katrin Wudy, Tobias Laumer, Michael Schmidt, Dietmar Drummer, and Carolin Körner.
2018. "Modeling of Laser Beam Absorption in a Polymer Powder Bed" *Polymers* 10, no. 7: 784.
https://doi.org/10.3390/polym10070784