Global sensitivity analyses of a selective laser melting finite element model: influential parameters identification

  • Claire Bruna-RossoEmail author
  • Ali Gökhan Demir
  • Maurizio Vedani
  • Barbara Previtali


Selective laser melting, an additive manufacturing technique that allows 3D printing of metal components, has recently gained great interest. Despite its growing popularity, this technology continues to suffer from deficiencies in standards and qualifications, factors that limit wide industrial use. Numerical modeling is currently a standard tool in production engineering for both process optimization and a more comprehensive understanding of the process physics. However, inherent to any model implementation and computation are various sources of uncertainties and errors. It is of major importance to identify them and assess whether their influences on outputs is significant. This can be accomplished using sensitivity analysis. To determine the parameters that most influence variability in the computational results, global sensitivity analyses were performed using an in-house developed nonlinear finite element model of the selective laser melting process. The computational load was limited by utilizing a 2D model for a single-layer simulation. The studies were performed on 26 process parameters including material properties, their dependencies on temperature, laser-related parameters, and boundary conditions, among others. Computed maximal temperatures and melt pool widths and lengths were obtained. Two sensitivity analyses were performed using the elementary effect method: one included process parameters and the other excluded them. Among the 26 input parameters tested, 16 did not show significant effects in either study. By including process parameters, they were found to be the most influential. By excluding them, the significant influence of the emissivity coefficient on output variability was revealed. These results evidence the parameters that should be given higher priority in modeling, the sources of error to be considered during validation, and insights into which parameters should be prioritized for further studies, both experimental and computational.


Selective laser melting Finite elements Simulation Global sensitivity analysis 



Surface emittance


Convection coefficient [W m− 2 K]


Ambient temperature [K]


Latent heat of phase change [kJ kg− 1]

\(\rho _{l_{0}}\)

Constant of the liquid metal density model [kg m− 3]

\(\rho _{l_{1}}\)

First order coefficient of the liquid metal density model [kg m− 3 K− 1]

\(\rho _{s_{0}}\)

Constant of the solid metal density model [kg m− 3]

\(\rho _{s_{1}}\)

First order coefficient of the solid metal density model [kg m− 3 K− 1]


Constant of the heat capacity model [J kg− 1 K− 1]


First order coefficient of the heat capacity model [J kg− 1 K− 2]


Second order coefficient of the heat capacity model [J kg− 1 K− 3]


Constant of the thermal conductivity model [W m− 1 K− 1]


First order coefficient of the thermal conductivity model [W m− 1K− 2]


Power absorption


Solidus temperature [K]


Liquidus temperature [K]


Sintering temperature [K]


Powder porosity


Powder diameter [μ m]


Interstitial gas heat conductivity [W m− 1 K− 1]


Layer thickness [μ m]


Goldak heat source parameter [μ m]


Goldak heat source parameter [μ m]


Goldak heat source parameter [μ m]


Laser power [W]


Laser displacement speed [mms− 1]


Stefan-Boltzmann constant


Thermal conductivity of the powder bed resulting from radiation [W m− 1 K− 1]


Thermal conductivity of the bulk AISI316L stainless steel [W m− 1 K− 1]


Laser heat input density [W m− 3]


Nodal FEM powder fraction


Nodal FEM phase fraction


Number of starting point in the sensitivity analyses


Elementary effect of parameter i at starting point j


Mean of EEi over the r starting points


Standard deviation of EEi over the r starting points


Standard error of the mean of parameter i


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Funding information

This work was supported by Regione Lombardia (MADE4LO project) under the call “POR FESR 2014-2020 ASSE I - AZIONE I.1.B.1.3.


  1. 1.
    Frazier WE (2014) Metal additive manufacturing: a review. J Mater Eng Perform 23(6):1917–1928CrossRefGoogle Scholar
  2. 2.
    Demir AG, Colombo P, Previtali B (2017) From pulsed to continuous wave emission in SLM with contemporary fiber laser sources: effect of temporal and spatial pulse overlap in part quality. Int J Adv Manuf Technol 91:2701–2714CrossRefGoogle Scholar
  3. 3.
    Demir AG, Previtali B (2017) Investigation of remelting and preheating in SLM of 18Ni300 maraging steel as corrective and preventive measures for porosity reduction. Int J Adv Manuf Technol 93CrossRefGoogle Scholar
  4. 4.
    Markl M, Körner C (2016) Multiscale modeling of powder bed-based additive manufacturing. Annu Rev Mater Res 46(1): 93–123CrossRefGoogle Scholar
  5. 5.
    King WE, Anderson AT, Ferencz RM, Hodge NE, Kamath C, Khairallah SA, Rubenchik AM (2015) Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges. Appl Phys Rev 4:2Google Scholar
  6. 6.
    Lopez F, Witherell P, Lane B (2016) Identifying uncertainty in laser powder bed fusion additive manufacturing models. J Mech Des 138(11):114502CrossRefGoogle Scholar
  7. 7.
    Hu Z, Mahadevan S (2017) Uncertainty quantification and management in additive manufacturing: current status, needs, and opportunities. Int J Adv Manuf Technol 93:2855–2874CrossRefGoogle Scholar
  8. 8.
    Kamath C (2016) Data mining and statistical inference in selective laser melting. Int J Adv Manuf Technol 86(5):1659–1677CrossRefGoogle Scholar
  9. 9.
    Asserin O, Loredo A, Petelet M, Iooss B (2011) Global sensitivity analysis in welding simulations—what are the material data you really need? Finite Elem Anal Des 47(9):1004–1016CrossRefGoogle Scholar
  10. 10.
    Saltelli A, Ratto M, Andres T, Cariboni J, Gatelli D, Saisana M, Tarantola S (2008) Global sensitivity analysis: the primer. Wiley, New YorkzbMATHGoogle Scholar
  11. 11.
    Criales LE, Arısoy YM, Özel T (2016) Sensitivity analysis of material and process parameters in finite element modeling of selective laser melting of Inconel 625. Int J Adv Manuf Technol 86:2653–2666CrossRefGoogle Scholar
  12. 12.
    Pianosi F, Beven K, Freer J, Hall JW, Rougier J, Stephenson DB, Wagener T (2016) Sensitivity analysis of environmental models: a systematic review with practical workflow. Environ Model Softw 79:214–232CrossRefGoogle Scholar
  13. 13.
    Bogaard RH, Desai PD, Li HH, Ho CY (1993) Thermophysical properties of stainless steels. Thermochim Acta 218:373–393CrossRefGoogle Scholar
  14. 14.
    Bangerth W, Davydov D, Heister T, Heltai L, Kanschat G, Kronbichler M, Maier M, Turcksin B, Wells D (2016) The deal.II library, version 8.4. J Numer Math 24:135–141MathSciNetCrossRefGoogle Scholar
  15. 15.
    Bruna-Rosso C, Demir AG, Previtali B, Vedani M (2016) Selective laser melting high performance modeling. In: Drstvenšek I, Drummer D, Schmidt M (eds) Proceedings of 6th international conference on additive technologies. Interesansa - zavod, Ljubljana, pp 252–259Google Scholar
  16. 16.
    Bruna-Rosso C, Demir A, Previtali B (2018) Selective laser melting finite element modeling: validation with high-speed imaging and lack of fusion defects prediction. Mater Des 156:143–153CrossRefGoogle Scholar
  17. 17.
    Goldak J, Chakravarti A, Bibby M (1984) A new finite element model for welding heat sources. Metall Trans B 15(2):299–305CrossRefGoogle Scholar
  18. 18.
    Denlinger ER, Jagdale V, Srinivasan GV, El-Wardany T, Michaleris P (2016) Thermal modeling of Inconel 718 processed with powder bed fusion and experimental validation using in situ measurements. Addit Manuf 11:7–15CrossRefGoogle Scholar
  19. 19.
    Parry L, Ashcroft IA, Wildman RD (2016) Understanding the effect of laser scan strategy on residual stress in selective laser melting through thermo-mechanical simulation. Addit Manuf 12:1–15CrossRefGoogle Scholar
  20. 20.
    Mills KC (2002) Fe - 316 Stainless steel. In: Recommended values of thermophysical properties for selected commercial alloys, Woodhead Publishing Series in Metals and Surface Engineering. Woodhead Publishing, pp 135–142Google Scholar
  21. 21.
    Sih SS, Barlow JW (2004) The prediction of the emissivity and thermal conductivity of powder beds. Part Sci Technol 22(4):427–440CrossRefGoogle Scholar
  22. 22.
    Panayiotis JK, Marc-Jean B (1997) Thermal and structural properties of fusion related materials.
  23. 23.
    Pianosi F, Sarrazin F, Wagener T (2015) A Matlab toolbox for global sensitivity analysis. Environ Model Softw 70:80–85CrossRefGoogle Scholar
  24. 24.
    Campolongo F, Saltelli A, Cariboni J (2011) From screening to quantitative sensitivity analysis. A unified approach. Comput Phys Commun 182(4):978–988CrossRefGoogle Scholar
  25. 25.
    Vanrolleghem PA, Mannina G, Cosenza A, Neumann MB (2015) Global sensitivity analysis for urban water quality modelling: terminology, convergence and comparison of different methods. J Hydrol 522:339–352CrossRefGoogle Scholar
  26. 26.
    Delgado J, Ciurana J, Rodríguez C A (2012) Influence of process parameters on part quality and mechanical properties for DMLS and SLM with iron-based materials. Int J Adv Manuf Technol 60(5):601–610CrossRefGoogle Scholar
  27. 27.
    Bai X, Zhang H, Wang G (2013) Improving prediction accuracy of thermal analysis for weld-based additive manufacturing by calibrating input parameters using IR imaging. Int J Adv Manuf Technol 69:1087–1095CrossRefGoogle Scholar
  28. 28.
    Romano J, Ladani L, Razmi J, Sadowski M (2015) Temperature distribution and melt geometry in laser and electron-beam melting processes—a comparison among common materials. Addit Manuf 8:1–11CrossRefGoogle Scholar
  29. 29.
    Ladani L, Romano J, Brindley W, Burlatsky S (2017) Effective liquid conductivity for improved simulation of thermal transport in laser beam melting powder bed technology. Addit Manuf 14(Supplement C):13–23CrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Ltd., part of Springer Nature 2018

Authors and Affiliations

  • Claire Bruna-Rosso
    • 1
    Email author
  • Ali Gökhan Demir
    • 1
  • Maurizio Vedani
    • 1
  • Barbara Previtali
    • 1
  1. 1.Dipartimento di MeccanicaPolitecnico di MilanoMilanItaly

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