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Powder-scale multi-physics modeling of multi-layer multi-track selective laser melting with sharp interface capturing method

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Abstract

As a promising powder-based additive manufacturing technology, selective laser melting (SLM) has gained great popularity in recent years. However, experimental observation of the melting and solidification process is very challenging. This hinders the study of the physical mechanisms behind a variety of phenomena in SLM such as splashing and balling effects, and further poses challenges to the quality control of the products. Powder-scale computational models can reproduce the multi-physics process of SLM. In this study, we couple the Finite Volume Method (FVM) and Discrete Element Method to model the deposition of powder particles, and use the FVM to model the melting process, both with ambient air. In particular, a cutting-edge sharp surface capturing technique (iso-Advector) is incorporated into the Volume of Fluid Model to reconstruct the interface between different phases during the melting process. Iso-Advector is then used to capture and reconstruct the interface between molten material and ambient air, which is further used as a solid boundary for spreading the next powder layer. As such, 3D geometrical data is exchanged between these two stages repeatedly to reproduce the powder spreading-melting process of SLM incorporating different scan paths on multiple powder layers. To demonstrate the effectiveness of the powder-scale multi-physics modeling framework, typical scenarios with different fabrication parameters (Ti–6Al–4V powder) are simulated and compared with experimental observations available in literature.

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Acknowledgements

Z. K. Wang and M. B. Liu acknowledge the support by the Beijing Innovation Center for Engineering Science and Advanced Technology (BIC-ESAT), and the National Key Research Project (Grant No. 2018YFB0704000). W. K. Liu acknowledges the support by the National Science Foundation (NSF) Cyber-Physical Systems (CPS) under Grant No. CPS/CMMI-1646592. W. K. Liu, and W. Yan acknowledge the support by National Institute of Standards and Technology (NIST) and Center for Hierarchical Materials Design (CHiMaD) under Grant No. 70NANB14H012. The simulations have been conducted at Tianhe II Super Computer in the National Supercomputing Center in Guangzhou with the effective support from Beijing Paratera Technology Co., Ltd.

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Authors and Affiliations

  1. BIC-ESAT, College of Engineering, Peking University, Beijing, 100187, China

    Zekun Wang & Moubin Liu

  2. Department of Mechanical Engineering, Northwestern University, Evanston, IL, 60201, USA

    Wentao Yan & Wing Kam Liu

  3. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, Peking University, Beijing, 100871, China

    Zekun Wang & Moubin Liu

Authors
  1. Zekun Wang
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  2. Wentao Yan
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  3. Wing Kam Liu
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  4. Moubin Liu
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Corresponding author

Correspondence to Moubin Liu.

Appendices

Appendix A

Physical parameters used in the paper

Parameter

Value and units

Viscosity at melt point

\( \mu_{l} = 0.0052\;{\text{kg/m}}\,{\text{s}} \)

Density

\( \rho_{1} = 4510\;{\text{kg/m}}^{ 3} \)

Heat transfer coefficient

\( k_{10} = 8\;{\text{kg}}\,{\text{m/s}}^{3} \,{\text{K}} \)

Heat capacity

\( C_{10} = 411\;{\text{m}}^{ 2} / {\text{s}}^{ 2} \,{\text{K}} \)

Preheating temperature

T0 = 120 °C

Liquidus temperature

Tl = 1659 °C

Solidus temperature

Ts = 1200 °C

Latent heat

\( L = 2.88 \times 10^{5} \;{\text{m}}^{ 2} / {\text{s}}^{ 2} \)

Convective heat transfer coefficient

\( h = 19\;{\text{kg}}\;{\text{s}}^{3} \,{\text{K}} \)

Laser radius

R = 4.2 × 10−5 m

Laser absorptivity

η = 0.5

Surface tension coefficient

\( \kappa_{1} = 1.5\;{\text{kg/s}}^{2} \)

Rate of change of surface tension coefficient

\( \frac{\partial \kappa }{\partial T} = - 0.00026\;{\text{kg/s}}^{ 2} \,{\text{K}} \)

Viscosity of air

\( \mu_{2} = 1.5 \times 10^{ - 5} \;{\text{kg/m}}\,{\text{s}} \)

Air density

\( \rho_{2} = 1\;{\text{kg/m}}^{3} \)

Heat capacity of air

\( C_{2} = 1164\;{\text{m}}^{ 2} / {\text{s}}^{ 2} \,{\text{K}} \)

Appendix B

In order to show the performance of this surface capturing method in extremely complicated flow, two classical validation tests, Rudman–Zalesak solid rotation test and Rudman-shearing test [38, 39], are carried out and comparisons between iso-Advector and MULES (a multi-dimensional limiter for explicit solution for interface reconstruction), are provided. Figure 12 shows the original shape of the 2D Rudman-Zalesak solid rotation test together with the shape after the rotation simulated by MULES (Fig. 12a) and iso-Advector respectively (Fig. 12b) with the same structured grid (200 × 200). It is obvious that the obtained shape by MULES is severely distorted, while the shape obtained by iso-Advector preserves the original shape quite well.

Fig. 12
figure 12

Original shape of the 2D Rudman–Zalesak solid rotation test (marked as 1) together with the shape after the rotation (marked as 2 and 3 respectively) simulated by MULES (a) and by iso-Advector (b) respectively. The obtained shape by MULES deforms severely and becomes distorted. In contrast the shape obtained by iso-Advector preserves the shape quite well

Full size image

In the Rudman-shearing test, a disc is originally placed in a spiraling flow, and is sheared clockwise to form a long filament during the former half period, and then the filament is sheared anti-clockwise until the period finishes to re-form the original disk. This procedure is more complicated and can better test the performance of a surface capturing method. Figure 13 shows the original shape of the disc together with the final shape after the shearing obtained by MULES (Fig. 13a) and by iso-Advector (Fig. 13b) respectively. Again, the shape obtained by MULES severely deforms and become zigzagged. In contrast the shape obtained by iso-Advector preserves the shape much better.

Fig. 13
figure 13

Original shape (marked as 1) of the disc together with the final shape after the shearing (marked as 2 and 3 respectively) obtained by MULES (a) and by iso-Advector respectively (b). The shape obtained by MULES severely deforms and becomes zigzag

Full size image

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Wang, Z., Yan, W., Liu, W.K. et al. Powder-scale multi-physics modeling of multi-layer multi-track selective laser melting with sharp interface capturing method. Comput Mech 63, 649–661 (2019). https://doi.org/10.1007/s00466-018-1614-5

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  • DOI: https://doi.org/10.1007/s00466-018-1614-5

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