Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A pragmatic continuum level model for the prediction of the onset of keyholing in laser powder bed fusion

Abstract

Laser powder bed fusion (L-PBF) is a complex process involving a range of multi-scale and multi-physical phenomena. There has been much research involved in creating numerical models of this process using both high and low fidelity modelling approaches where various approximations are made. Generally, to model single lines within the process to predict melt pool geometry and mode, high fidelity computationally intensive models are used which, for industrial purposes, may not be suitable. The model proposed in this work uses a pragmatic continuum level methodology with an ablation limiting approach at the mesoscale coupled with measured thermophysical properties. This model is compared with single line experiments over a range of input parameters using a modulated yttrium fibre laser with varying power and line speeds for a fixed powder layer thickness. A good trend is found between the predicted and measured width and depth of the tracks for 316L stainless steel where the transition into keyhole mode welds was predicted within 13% of experiments. The work presented highlights that pragmatic reduced physics-based modelling can accurately capture weld geometry which could be applied to more practical based uses in the L-PBF process.

Abbreviations

ρ :

Density

C p :

Specific heat capacity

T :

Temperature

κ :

Thermal conductivity

α :

Thermal diffusivity

t :

Time

\(\hat {n}\) :

Unit normal to surface

q v :

Volumetric energy input

q :

Irradiated heat flux

P :

Laser power

σ :

Laser spot size

r x :

Local laser radius in x-direction

r y :

Local laser radius in y-direction

h :

Heat transfer coefficient

T 0 :

Ambient temperature

L t :

Layer thickness

τ L :

Optical thickness

τ Z :

Dimensionless local layer thickness

d p :

Particle diameter

β :

Extinction coefficient

ρ t :

Tap density

ρ s :

Sample density

Z :

Density of water

κ p :

Powder thermal conductivity

κ s :

Solid thermal conductivity

\(C_{p_{p}}\) :

Powder specific heat capacity

\(C_{p_{s}}\) :

Solid specific heat capacity

ρ p :

Powder density

ρ s :

Solid density

e t :

Exposure time

p d :

Point distance

ν :

Effective line speed

d :

Penetration depth

A :

Material absorptivity

T b :

Material boiling temperature

T m :

Material melting temperature

ΔH :

Enthalpy change

h s :

Enthalpy at melting

References

  1. 1.

    Wang X, Gong X, Chou K (2017) Review on powder-bed laser additive manufacturing of Inconel 718 parts. Proc Inst Mech Eng Part B J EngManuf 231(11):1890–1903. https://doi.org/10.1177/0954405415619883

  2. 2.

    Bourell DL (2016) Perspectives on additive manufacturing. Annu Rev Mater Res 46(1):1–18. https://doi.org/10.1146/annurev-matsci-070115-031606

  3. 3.

    Gao W, Zhang Y, Ramanujan D, Ramani K, Chen Y, Williams CB, Wang CC, Shin YC, Zhang S, Zavattieri PD (2015) The status, challenges, and future of additive manufacturing in engineering. Comput Des 69:65–89. https://doi.org/10.1016/j.cad.2015.04.001

  4. 4.

    Mindt HW, Megahed M, Lavery NP, Holmes MA, Brown SGR (2016) Powder bed layer characteristics: the overseen first-order process input. Metall Mater Trans A Phys Metall Mater Sci 47(8):1–12. https://doi.org/10.1007/s11661-016-3470-2

  5. 5.

    Cherry JA, Davies HM, Mehmood S, Lavery NP, Brown SGR, Sienz J (2014) Investigation into the effect of process parameters on microstructural and physical properties of 316L stainless steel parts by selective laser melting. Int J Adv Manuf Technol 76(5-8):869–879. https://doi.org/10.1007/s00170-014-6297-2

  6. 6.

    Sillars SA, Sutcliffe CJ, Philo AM, Brown SG, Sienz J, Lavery NP (2018) The three-prong method: a novel assessment of residual stress in laser powder bed fusion. Virtual Phys Prototyp 13(1):20–25. https://doi.org/10.1080/17452759.2017.1392682

  7. 7.

    Lavery NP, Cherry J, Mehmood S, Davies H, Girling B, Sackett E, Brown SG (2016) Sienz J (2017) Effects of hot isostatic pressing on the elastic modulus and tensile properties of 316L parts made by powder bed laser fusion. Mater Sci Eng A 693:186–213. https://doi.org/10.1016/j.msea.2017.03.100

  8. 8.

    Körner C, Bauereiß A, Attar E (2013) Fundamental consolidation mechanisms during selective beam melting of powders. Model Simul Mater Sci Eng 21(8):085011. https://doi.org/10.1088/0965-0393/21/8/085011

  9. 9.

    Körner C, Attar E, Heinl P (2011) Mesoscopic simulation of selective beam melting processes. J Mater Process Technol 211(6):978–987. https://doi.org/10.1016/j.jmatprotec.2010.12.016

  10. 10.

    Contuzzi N, Campanelli SL, Ludovico AD (2011) 3D finite element analysis in the Selective Laser Melting process. Int J Simul Model 10(3):113–121. https://doi.org/10.2507/IJSIMM10(3)1.169

  11. 11.

    Fu CH, Guo YB (2014) Three-Dimensional Temperature gradient mechanism in selective laser melting of Ti-6Al-4V. J Manuf Sci Eng 136(6):061004. https://doi.org/10.1115/1.4028539

  12. 12.

    Gusarov AV, Smurov I (2010) Radiation transfer in metallic powder beds used in laser processing. J Quant Spectrosc Radiat Transf 111(17-18):2517–2527. https://doi.org/10.1016/j.jqsrt.2010.07.009

  13. 13.

    Wits WW, Bruins R, Terpstra L, Huls RA, Geijselaers HJM (2016) Single scan vector prediction in selective laser melting. Addit Manuf 9:1–6. https://doi.org/10.1016/j.addma.2015.12.001

  14. 14.

    Boley CD, Khairallah SA, Rubenchik AM (2015) Calculation of laser absorption by metal powders in additive manufacturing. Appl Opt 54(9):2477–82. https://doi.org/10.1364/AO.54.002477

  15. 15.

    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 108:36–45. https://doi.org/10.1016/j.actamat.2016.02.014

  16. 16.

    Wits W, Becker JJ (2015) Laser beam welding of titanium additive manufactured parts. Procedia CIRP 28:70–75. https://doi.org/10.1016/j.procir.2015.04.013

  17. 17.

    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

  18. 18.

    Tolochko NK, Mozzharov SE, Yadroitsev IA, Laoui T, Froyen L, Titov VI, Ignatiev MB (2004) Balling processes during selective laser treatment of powders. Rapid Prototyp J 10(2):78–87. https://doi.org/10.1108/13552540410526953

  19. 19.

    Yadroitsev I, Smurov I (2010) Selective laser melting technology: From the single laser melted track stability to 3D parts of complex shape. Phys Procedia 5(PART 2):551–560. https://doi.org/10.1016/j.phpro.2010.08.083

  20. 20.

    Fabbro R (2010) Melt pool and keyhole behaviour analysis for deep penetration laser welding. J Phys D Appl Phys 43(44):445501. https://doi.org/10.1088/0022-3727/43/44/445501

  21. 21.

    Fabbro R, Slimani S, Doudet I, Coste F, Briand F (2006) Experimental study of the dynamical coupling between the induced vapour plume and the melt pool for Nd–Yag CW laser welding. J Phys D Appl Phys 39(2):394–400. https://doi.org/10.1088/0022-3727/39/2/023

  22. 22.

    Assuncao E, Williams S, Yapp D (2012) Interaction time and beam diameter effects on the conduction mode limit. Opt Lasers Eng 50(6):823–828. https://doi.org/10.1016/j.optlaseng.2012.02.001

  23. 23.

    Kumar N, Dash S, Tyagi AK, Raj B (2011) Melt pool vorticity in deep penetration laser material welding. Sadhana - Acad Proc Eng Sci 36(2):251–265. https://doi.org/10.1007/s12046-011-0017-5

  24. 24.

    Zhang Y, Li L, Zhang G (2005) Spectroscopic measurements of plasma inside the keyhole in deep penetration laser welding. J Phys D Appl Phys 38(5):703–710. https://doi.org/10.1088/0022-3727/38/5/007

  25. 25.

    Aalderink BJ, Lange DFD, Aarts RGKM, Meijer J (2007) Keyhole shapes during laser welding of thin metal sheets. J Phys D Appl Phys 40(17):5388–5393. https://doi.org/10.1088/0022-3727/40/17/057

  26. 26.

    Sundar M, Nath aK, Bandyopadhyay D, Chaudhuri S, Dey P, Misra D (2007) Numerical simulation of melting and solidification in laser welding of mild steel. Int J Comput Mater Sci Surf Eng 1(6):717. https://doi.org/10.1504/IJCMSSE.2007.017926

  27. 27.

    Otto A, Schmidt M (2010) Towards a universal numerical simulation model for laser material processing. Physics Procedia 5(November):35–46. https://doi.org/10.1016/j.phpro.2010.08.120

  28. 28.

    Mościcki T, Hoffman J, Szymański Z (2006) Modelling of plasma plume induced during laser welding. J Phys D Appl Phys 39:685–692. https://doi.org/10.1088/0022-3727/39/4/014

  29. 29.

    Zhou J, Tsai HL, Lehnhoff TF (2006) Investigation of transport phenomena and defect formation in pulsed laser keyhole welding of zinc-coated steels. J Phys D Appl Phys 39(24):5338–5355. https://doi.org/10.1088/0022-3727/39/24/036

  30. 30.

    Rońda J, Siwek A (2011) Modelling of laser welding process in the phase of keyhole formation. Arch Civ Mech Eng 11(3):739–752. https://doi.org/10.1016/S1644-9665(12)60113-7

  31. 31.

    Zhou J, Tsai HL, Wang PC (2006) Transport phenomena and keyhole dynamics during pulsed laser welding. Trans Am Soc Mech Eng 128(July):680–690. https://doi.org/10.1115/1.2194043

  32. 32.

    Svenungsson J, Choquet I, Kaplan AF (2015) Laser welding process - a review of keyhole welding modelling. Physics Procedia 78(August):182–191. https://doi.org/10.1016/j.phpro.2015.11.042

  33. 33.

    Gladush GG, Smurov I (2011) Physics of laser materials processing. Springer, Berlin

  34. 34.

    Sandvik (2018) Austenitic Stainless Steel Metal Powder. https://www.materials.sandvik/en/products/metal-powder/list-of-materials/austenitic-stainless-steels/, Accessed 30-08-2018

  35. 35.

    Cowan RD (1963) Pulse method of measuring thermal diffusivity at high temperatures. J Appl Phys 34(4):926–927

  36. 36.

    Smakula A, Sils V (1955) Precision density determination of large single crystals by hydrostatic weighing. Phys Rev 99(6):1744–1746

  37. 37.

    ASTM (2015) Standard terminology for additive manufacturing - general principles. Part 1: Terminology. ISO/ASTM Stand 52792, ASTM

  38. 38.

    (1994) DIN 51007 Thermal analysis; differential thermal analysis; principles. STANDARD by Deutsches Institut Fur Normung E.V. (German National Standard)

  39. 39.

    Mills K (2002) Recommended values of thermophysical properties for selected commercial alloys. Woodhead publishing limited, Cambridge. https://doi.org/10.1016/B978-1-84569-990-1.50021-1

  40. 40.

    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 9:341–349. https://doi.org/10.1016/j.apmt.2017.08.006

  41. 41.

    King WE, Barth HD, Castillo VM, Gallegos GF, Gibbs JW, Hahn DE, Kamath C, Rubenchik AM (2014) Observation of keyhole-mode laser melting in laser powder-bed fusion additive manufacturing. J Mater Process Technol 214(12):2915–2925. https://doi.org/10.1016/j.jmatprotec.2014.06.005

  42. 42.

    Hann DB, Iammi J, Folkes J (2011) A simple methodology for predicting laser-weld properties from material and laser parameters. J Phys D Appl Phys 44(44):1–9. https://doi.org/10.1088/0022-3727/44/44/445401

  43. 43.

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

Download references

Acknowledgements

The authors would like to thank the Welsh Government A4B funded Centre for Advanced Materials Characterisation (MACH1) and Advanced Sustainable Manufacturing Technologies (ASTUTE 2020) and EPSRC funded Centre for Innovative Manufacturing in Laser-based production Processes (EP/K030884/1) for the Innovation Project which allowed some of the preliminary development of the WELD-AM models, as well as Professor Stewart Williams and Dr Wojciech Suder from Cranfield University for their helpful insights.

Funding

This study received funding from the Additive Manufacturing Products Division at Renishaw Plc., the Engineering and Physical Sciences Research Council (ESPRC), funded Engineering Doctoral Training (EDT), Manufacturing Advances Through Training Engineering Researchers (MATTER) scheme, the Welsh European Funding Office (WEFO), the Materials and Manufacturing Academy (M2A) and the European Social Fund through the Welsh European Funding Office.

Author information

Correspondence to A. M. Philo.

Additional information

Publisher’s Note

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

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Philo, A.M., Mehraban, S., Holmes, M. et al. A pragmatic continuum level model for the prediction of the onset of keyholing in laser powder bed fusion. Int J Adv Manuf Technol 101, 697–714 (2019). https://doi.org/10.1007/s00170-018-2770-7

Download citation

Keywords

  • Additive manufacturing
  • Laser powder bed fusion
  • Modelling
  • Keyhole-mode laser melting
  • 316L stainless steel