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


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.


ρ :


C p :

Specific heat capacity

T :


κ :

Thermal conductivity

α :

Thermal diffusivity

t :


\(\hat {n}\) :

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


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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.


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.

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Correspondence to A. M. Philo.

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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

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