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An Extended Rosenthal’s Model for Laser Powder-Bed Fusion Additive Manufacturing: Energy Auditing of Thermal Boundary Conditions

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Abstract

Laser Powder-Bed Fusions (LPBF), a class of additive manufacturing (AM), is a promising technique for producing components with complex geometry design. However, parts fabricated by LPBF suffer from residual stresses arising due to substantial temperature gradients inherent to the process. Numerical models are unable to provide a comprehensive thermal history of the built materials efficiently due to the mismatch between the characteristic length scales and infinitesimal time steps needed for complete simulations. In the present work, an extended Rosenthal’s model is presented by considering the effects of various heat dissipation/consumption mechanisms. The modeling results of energy auditing of thermal boundary conditions for stainless steel (SS17-4PH) laser melting indicated that the total energy losses by convection, radiation, and melting are less than 20% among which, radiation is the most dominant part. A comparison of the results obtained by the extended Rosenthal’s equation with finite element numerical predictions and experimental data shows a good agreement. Also, a parametric study has been conducted to identify the influence of laser scanning velocity, beam radius, and power on the overall temperature distributions and melt geometry. The present study can pave the way for the prospective use of this methodology to conduct further investigation such as microstructure analysis and thermo-mechanical modeling which are needed to predict residual stresses and distortions.

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Data Availability

The datasets used in the current study are available from the corresponding author on reasonable request.

Abbreviations

A :

Surface area [m2]

c P :

Heat capacity [J/kg.K]

D :

Melt pool depth [μm]

f :

Porosity

h :

Heat transfer coefficient [W/m2.K]

H :

Bed thickness under consideration [m, μm]

I :

Power density distribution [W/m2]

k :

Thermal conductivity [W/m.K]

L :

Length of bed/melt pool [m, μm]

P :

Power [W]

q" :

Heat flux [W/m2]

Q :

Volumetric heat source [W/m3]

Q v :

Heat flux distribution [W/m3]

Q 0 :

The highest value of heat intensity [W/m3]

Ra :

Convection Raleigh number

r e :

The upper radius of heat source [m]

r i :

The lower radius of heat source [m]

t :

Time [s]

T :

Temperature [°C, K]

V :

Laser velocity [m/s], Melt pool volume [μm3]

W :

Melt pool width [μm]

x, y, z :

Spatial directions [m]

z e :

The upper surface of the heat source in z-direction [m]

z i :

The lower surface of the heat source in z-direction [m]

α :

Thermal diffusivity [m2/s]

β :

Bed surface absorptivity

Δ :

Difference

ϵ :

Bed surface emissivity

ξ, η, ζ :

Moving coordinates [m]

ρ :

Density [kg/m3]

σ :

Stefan-Boltzmann coefficient [W/m2.K4]

λ :

Latent heat of flusion [kJ/kg]

A:

Argon

B :

Bed

C :

Chamber wall/shielding gas

Conv :

Convection

Evp :

Evaporation

f :

Film

i :

Individual volumes

L :

Laser

Loss :

Losses

m :

Mean/effective/melt pool

Melt :

Melt pool/Melting

Rad :

Radiation

Surf :

Bed surface

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Acknowledgments

This work was supported by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Federal Economic Development Agency for Southern Ontario (FedDev Ontario). Besides, the authors would like to appreciate Zhidong Zhang for his support in LPBF modeling and in providing experimental data.

Code Availability

Not applicable.

Funding

This work was supported by funding from the Natural Sciences and Engineering Research Council of Canada (NSERC), the Federal Economic Development Agency for Southern Ontario (FedDev Ontario).

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Authors and Affiliations

  1. Department of Mechanical and Mechatronics Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, N2L 3G1, Canada

    Shahriar Imani Shahabad & Ehsan Toyserkani

  2. Department of Chemical Engineering, Shiraz University, Shiraz, Iran

    Gholamreza Karimi

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  1. Shahriar Imani Shahabad
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Contributions

Gholamreza Karimi: Initiating the idea and working on the theoretical part of the manuscript, writing, review, and editing.

Shahriar Imani Shahabad: Conducting LPBF numerical analysis, writing, review, and editing.

Ehsan Toyserkani: Supervision, writing, review, and editing.

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Correspondence to Gholamreza Karimi.

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Imani Shahabad, S., Karimi, G. & Toyserkani, E. An Extended Rosenthal’s Model for Laser Powder-Bed Fusion Additive Manufacturing: Energy Auditing of Thermal Boundary Conditions. Lasers Manuf. Mater. Process. 8, 288–311 (2021). https://doi.org/10.1007/s40516-021-00148-0

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