Skip to main content
Log in

Prediction of molten pool height, contact angle, and balling occurrence in laser powder bed fusion

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

In this work, an analytical modeling method is proposed for the prediction of molten pool height, contact angle, and balling occurrence in laser powder bed fusion (LPBF) metal additive manufacturing. A closed-form temperature prediction model is employed to calculate the temperature distribution during melting process. The width and length of molten pool, and width of powder consumed band are then determined by comparing the temperature profile with the melting point of the material. The shape of the solidified cap of the molten pool is assumed to be a segmental cylinder. Per this assumption and mass conservation, the molten pool height, contact angle, and diameter of the cylindrical cap are then determined through geometrical relationships. The occurrences of balling defect are then predicted by checking the stability condition of scan tracks under different process conditions. The predicted results of molten pool width, height, and contact angle are compared with experimental results of Ti6Al4V, Inconel 625 in LPBF, and show acceptable accuracy. The predictions of balling occurrence are consistent with most experimental observations of SS316L. The sensitivities of contact angle to process conditions are discussed. In light of the fact that the temperature profiles are calculated based upon solutions in closed form, the presented computations of molten pool geometric characteristics and balling occurrence do not use any numerical iterations, which makes the proposed analytical modeling method computationally efficient. Thus, the proposed modeling method can be a fast and acceptable tool for the study of molten pool geometry and stability of single tracks in LPBF.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

Availability of data and material

Not applicable.

Code availability

Not applicable.

References

  1. Cunningham R, Zhao C, Parab N, Kantzos C, Pauza J, Fezzaa K, Sun T, Rollett AD (2019) Keyhole threshold and morphology in laser melting revealed by ultrahigh-speed x-ray imaging. Science 363(6429):849–852. https://doi.org/10.1126/science.aav4687

    Article  Google Scholar 

  2. Zhou X, Liu X, Zhang D, Shen Z, Liu W (2015) Balling phenomena in selective laser melted tungsten. J Mater Process Technol 1(222):33–42. https://doi.org/10.1016/j.jmatprotec.2015.02.032

    Article  Google Scholar 

  3. Wang D, Liu Y, Yang Y, Xiao D (2016) Theoretical and experimental study on surface roughness of 316L stainless steel metal parts obtained through selective laser melting. Rapid Prototyp J. https://doi.org/10.1108/RPJ-06-2015-0078

    Article  Google Scholar 

  4. Yadroitsev I, Gusarov A, Yadroitsava I, Smurov I (2010) Single track formation in selective laser melting of metal powders. J Mater Process Technol 210(12):1624–1631. https://doi.org/10.1016/j.jmatprotec.2010.05.010

    Article  Google Scholar 

  5. Hojjatzadeh SM, Parab ND, Yan W, Guo Q, Xiong L, Zhao C, Qu M, Escano LI, Xiao X, Fezzaa K, Everhart W (2019) Pore elimination mechanisms during 3D printing of metals. Nat Commun 10(1):1–8. https://doi.org/10.1038/s41467-019-10973-9

    Article  Google Scholar 

  6. Guo Q, Zhao C, Qu M, Xiong L, Hojjatzadeh SM, Escano LI, Parab ND, Fezzaa K, Sun T, Chen L (2020) In-situ full-field mapping of melt flow dynamics in laser metal additive manufacturing. Addit Manuf 1(31):100939. https://doi.org/10.1016/j.addma.2019.100939

    Article  Google Scholar 

  7. Miyagi M, Wang J (2020) Keyhole dynamics and morphology visualized by in-situ X-ray imaging in laser melting of austenitic stainless steel. J Mater Process Technol 1(282):116673. https://doi.org/10.1016/j.jmatprotec.2020.116673

    Article  Google Scholar 

  8. Bertoli US, Wolfer AJ, Matthews MJ, Delplanque JP, Schoenung JM (2017) On the limitations of volumetric energy density as a design parameter for selective laser melting. Mater Des 5(113):331–340. https://doi.org/10.1016/j.matdes.2016.10.037

    Article  Google Scholar 

  9. Li R, Liu J, Shi Y, Wang L, Jiang W (2012) Balling behavior of stainless steel and nickel powder during selective laser melting process. Int J Adv Manuf Technol 59(9):1025–1035. https://doi.org/10.1007/s00170-011-3566-1

    Article  Google Scholar 

  10. Guo C, Xu Z, Zhou Y, Shi S, Li G, Lu H, Zhu Q, Ward RM (2021) Single-track investigation of IN738LC superalloy fabricated by laser powder bed fusion: track morphology, bead characteristics and part quality. J Mater Process Technol 1(290):117000. https://doi.org/10.1016/j.jmatprotec.2020.117000

    Article  Google Scholar 

  11. Dilip JJ, Zhang S, Teng C, Zeng K, Robinson C, Pal D, Stucker B (2017) Influence of processing parameters on the evolution of melt pool, porosity, and microstructures in Ti-6Al-4V alloy parts fabricated by selective laser melting. Prog Addit Manuf 2(3):157–167. https://doi.org/10.1007/s40964-017-0030-2

    Article  Google Scholar 

  12. Li C, Guo YB, Zhao JB (2017) Interfacial phenomena and characteristics between the deposited material and substrate in selective laser melting Inconel 625. J Mater Process Technol 1(243):269–281. https://doi.org/10.1016/j.jmatprotec.2016.12.033

    Article  Google Scholar 

  13. Tian Y, Yang L, Zhao D, Huang Y, Pan J (2020) Numerical analysis of powder bed generation and single track forming for selective laser melting of SS316L stainless steel. J Manuf Process 1(58):964–974. https://doi.org/10.1016/j.jmapro.2020.09.002

    Article  Google Scholar 

  14. Tang C, Tan JL, Wong CH (2018) A numerical investigation on the physical mechanisms of single track defects in selective laser melting. Int J Heat Mass Transf 1(126):957–968. https://doi.org/10.1016/j.ijheatmasstransfer.2018.06.073

    Article  Google Scholar 

  15. Tang C, Le KQ, Wong CH (2020) Physics of humping formation in laser powder bed fusion. Int J Heat Mass Transf 1(149):119172. https://doi.org/10.1016/j.ijheatmasstransfer.2019.119172

    Article  Google Scholar 

  16. Khairallah SA, Anderson AT, Rubenchik A, King WE (2016) Laser powder-bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Mater 15(108):36–45. https://doi.org/10.1016/j.actamat.2016.02.014

    Article  Google Scholar 

  17. Ge W, Han S, Na SJ, Fuh JY (2021) Numerical modelling of surface morphology in selective laser melting. Comput Mater Sci 1(186):110062. https://doi.org/10.1016/j.commatsci.2020.110062

    Article  Google Scholar 

  18. Ning J, Mirkoohi E, Dong Y, Sievers DE, Garmestani H, Liang SY (2019) Analytical modeling of 3D temperature distribution in selective laser melting of Ti-6Al-4V considering part boundary conditions. J Manuf Process 1(44):319–326. https://doi.org/10.1016/j.jmapro.2019.06.013

    Article  Google Scholar 

  19. Tang M, Pistorius PC, Beuth JL (2017) Prediction of lack-of-fusion porosity for powder bed fusion. Addit Manuf 1(14):39–48. https://doi.org/10.1016/j.addma.2016.12.001

    Article  Google Scholar 

  20. Wang W, Ning J, Liang SY (2021) Prediction of lack-of-fusion porosity in laser powder-bed fusion considering boundary conditions and sensitivity to laser power absorption. Int J Adv Manuf Technol 112(1):61–70. https://doi.org/10.1007/s00170-020-06224-7

    Article  Google Scholar 

  21. Promoppatum P, Yao SC, Pistorius PC, Rollett AD (2017) A comprehensive comparison of the analytical and numerical prediction of the thermal history and solidification microstructure of Inconel 718 products made by laser powder-bed fusion. Engineering 3(5):685–694. https://doi.org/10.1016/J.ENG.2017.05.023

    Article  Google Scholar 

  22. Vastola G, Pei QX, Zhang YW (2018) Predictive model for porosity in powder-bed fusion additive manufacturing at high beam energy regime. Addit Manuf 1(22):817–822. https://doi.org/10.1016/j.addma.2018.05.042

    Article  Google Scholar 

  23. Carslaw HS, Jaeger JC (1959) Conduction of heat in solids. Clarendon Press

  24. Wang YM, Kamath C, Voisin T, Li Z (2018) A processing diagram for high-density Ti-6Al-4V by selective laser melting. Rapid Prototyp J. https://doi.org/10.1108/RPJ-11-2017-0228

    Article  Google Scholar 

  25. Trapp J, Rubenchik AM, Guss G, Matthews MJ (2017) In situ absorptivity measurements of metallic powders during laser powder-bed fusion additive manufacturing. Appl Mater Today 1(9):341–349. https://doi.org/10.1016/j.apmt.2017.08.006

    Article  Google Scholar 

  26. Ye J, Khairallah SA, Rubenchik AM, Crumb MF, Guss G, Belak J, Matthews MJ (2019) Energy coupling mechanisms and scaling behavior associated with laser powder bed fusion additive manufacturing. Adv Eng Mater 21(7):1900185. https://doi.org/10.1002/adem.201900185

    Article  Google Scholar 

  27. Zhang S, Lane B, Whiting J, Chou K (2019) On thermal properties of metallic powder in laser powder bed fusion additive manufacturing. J Manuf Process 1(47):382–392. https://doi.org/10.1016/j.jmapro.2019.09.012

    Article  Google Scholar 

  28. Zhang Y, Zhang J (2019) Modeling of solidification microstructure evolution in laser powder bed fusion fabricated 316L stainless steel using combined computational fluid dynamics and cellular automata. Addit Manuf 1(28):750–765. https://doi.org/10.1016/j.addma.2019.06.024

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Wenjia Wang or Steven Y. Liang.

Ethics declarations

Ethics approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Conflict of interest

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, W., Liang, S.Y. Prediction of molten pool height, contact angle, and balling occurrence in laser powder bed fusion. Int J Adv Manuf Technol 119, 6193–6202 (2022). https://doi.org/10.1007/s00170-021-08633-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00170-021-08633-8

Keywords

Navigation