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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
ORIGINAL ARTICLE
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Abstract

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.

Keywords

Selective laser melting Finite elements Simulation Global sensitivity analysis 

Nomenclature

𝜖

Surface emittance

h

Convection coefficient [W m− 2 K]

Tamb

Ambient temperature [K]

L

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]

c0

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

c1

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

c2

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

k0

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

k1

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

α

Power absorption

TS

Solidus temperature [K]

TL

Liquidus temperature [K]

Tsint

Sintering temperature [K]

ϕpow

Powder porosity

Dpow

Powder diameter [μ m]

kg

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

hPB

Layer thickness [μ m]

afront

Goldak heat source parameter [μ m]

arear

Goldak heat source parameter [μ m]

c

Goldak heat source parameter [μ m]

P

Laser power [W]

v

Laser displacement speed [mms− 1]

σ

Stefan-Boltzmann constant

kR

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

kbulk

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

Q

Laser heat input density [W m− 3]

ϕ

Nodal FEM powder fraction

φ

Nodal FEM phase fraction

r

Number of starting point in the sensitivity analyses

\(E{E_{i}^{j}}\)

Elementary effect of parameter i at starting point j

μi

Mean of EEi over the r starting points

σi

Standard deviation of EEi over the r starting points

SEMi

Standard error of the mean of parameter i

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Notes

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.

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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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