Heat source model calibration for thermal analysis of laser powder-bed fusion


Laser powder-bed fusion (LPBF) is one of the mainstream additive manufacturing (AM) processes, which has dominated the metal AM manufacturing market. LPBF has the capability to manufacture complex parts, which pose a manufacturing challenge by conventional methods. In this paper, an efficient numerical-experimental approach has been introduced to calibrate the parameters of a proposed three-dimensional (3D) conical Gaussian moving laser heat source model. For this purpose, several Hastelloy X single tracks are printed with various process parameters. The melt pool depth and width were measured experimentally, and results were used to calibrate and validate the heat source model. An empirical relationship between heat source parameters and laser energy density was also proposed. In addition, temperature gradients and cooling rates around the melt pool were extracted from the numerical model to be used towards microstructure prediction. Estimated microstructure cell spacing, calculated based on predicted cooling rate during solidification, was in good agreement with experimental measurements, indicating the validity of the heat source model.

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k e :

Effective thermal conductivity of powder

k g :

Thermal conductivity of the continuous gas phase

k s :

Thermal conductivity of skeletal solid

φ :

The porosity of powder bed

k R :

Thermal conductivity part of the powder bed owing to radiation


The flattened surface fraction of particle in contact with another particle

B :

Deformation parameter of the particle

k contact :

Contact conductivity between two particles according to the value of ∅

C p :

Specific heat

L :

Latent heat

ρ :


k :

Thermal conductivity

Q :

Internal heat generation

h c :

Heat transfer coefficient

ε :

Emissivity coefficient

σ sb :

Stefan-Boltzmann coefficient

q c :

Convective heat dissipation

q r :

Radiative heat dissipation

I :

Heat intensity distribution

q 0 :

The maximum value of heat intensity

r 0 :

The top radius of heat source

r d :

The bottom radius of heat source

z e :

Z coordinates of the top surface of heat source

z i :

Z coordinates of the bottom surface of heat source

H :

Height of heat source

α :

Absorption coefficient

P :

Laser power

V :

Scanning speed

\( \dot{T} \) :

Cooling rate

λ 1 :

Primary spacing


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The authors would like to appreciate the Federal Economic Development Agency for Southern Ontario (FedDev Ontario), Natural Sciences and Engineering Research Council of Canada (NSERC), and Siemens Canada Limited, for supporting financially. In addition, special thanks to Jerry Ratthapakdee and Karl Rautenberg for assisting in preparing the LPBF setup and printing the samples, National Research Council Canada (NRC) and Adhitan Rani Kasinathan for their contributions to the LPBF modeling.

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Correspondence to Ehsan Toyserkani.

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Shahabad, S.I., Zhang, Z., Keshavarzkermani, A. et al. Heat source model calibration for thermal analysis of laser powder-bed fusion. Int J Adv Manuf Technol 106, 3367–3379 (2020). https://doi.org/10.1007/s00170-019-04908-3

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  • Laser powder-bed fusion (LPBF)
  • Additive manufacturing
  • Heat source modeling
  • Temperature gradient
  • Cooling rate