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Semi-analytical formulation for single-track laser powder-bed fusion process to estimate melt-pool characteristics considering fluid-flow and marangoni effect

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Abstract

The Laser-Based Powder Bed Fusion (LPBF) process is an additive manufacturing (AM) technique used to fabricate intricate 3D metallic components from fine powder particles. This study presents a 2D semi-analytical model, an algorithm developed by incorporating multiple physical phenomena of the process, i.e., heat transfer, fluid flow, and Marangoni effect for computing temperature and velocity distribution, to estimate the melt-pool characteristics for the single-track melting. The laser input energy has been modelled as a moving Gaussian volumetric heat source, and the fluid flow phenomenon has been formulated by ‘Semi-Implicit Method for Pressure Linked Equations’ (SIMPLE) method. A set of two-dimensional transient conservation of mass, momentum, and energy equations are discretized as co-located mesh by Finite Volume Method (FVM) and iteratively solved by Alternating Direction Implicit (ADI) scheme to obtain temperature and velocity field. The Pressure Weighted Interpolation Method (PWIM) is incorporated to avoid pressure oscillation and allow the use of co-located mesh for fluid flow, making the model computationally efficient. The model is validated for Ti6Al4V and Inconel 718 alloy with the experimental findings from the literature. The obtained results are in good agreement with an average deviation of 5.78% and 20.07% for Ti6Al4V , whereas for Inconel 718, 7.87 and 19.53% for melt-pool depth and width, respectively, were observed. Subsequently, the melt-pool growth and characteristics influenced by various process parameters are also studied.

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Abbreviations

A :

Fractional energy absorption

A P ,A E ,A W ,A N ,A S :

Advection diffusion coefficients

C :

Specific heat capacity

D :

Hatch distance

G :

Permeability

K :

Thermal conductivity

K p :

Thermal conductivity of powder

K s :

Thermal conductivity of solid phase

P :

Laser power

Q :

Internal heat generation

δQ conv :

Convective heat loss

Q eff :

Heat density

T :

Temperature

\(\Delta T\) :

Increment in temperature

T f :

Base-plate temperature

T L :

Liquidus temperature

T S :

Solidus temperature

T 0 :

Initial temperature

T ∞ :

Ambient temperature

V :

Scan velocity

\(a,b,c\) :

Laser parameters of semi-ellipsoid volumetric heat source

\(d\) :

Computational constant

h :

Heat transfer coefficient

\(l\) :

Layer thickness

\(p\) :

Pressure

t :

Time instant

t f :

Time counter for computation of front view

t s :

Time counter for computation of side view

\(\Delta t\) :

Time interval

u :

X-direction molten material velocity component

v :

Y-direction molten material velocity component

w :

Z-direction molten material velocity component

\(\Delta x\) :

Grid spacing

\(x,y,z\) :

Global co-ordinates

\({x}{\prime},{y}{\prime},z{\prime}\) :

Moving co-ordinates

α :

Thermal diffusivity

ε:

Liquid fraction

\(\mu \) :

Viscosity

\(\varphi \) :

Fractional porosity

ρ :

Mass density

ρ p :

Local mass density of powder phase

ρ s :

Local mass density of solid phase

\(\sigma \) :

Surface tension

\(\tau \) :

Time steps to achieve quasi steady state

\({\tau }_{x}\) :

Marangoni shear stress along x-direction

\({\tau }_{y}\) :

Marangoni shear stress along y-direction

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  1. Dattatraya Bombe and Rakesh Kumar have equally contributed to this work.

Authors and Affiliations

  1. Advanced Manufacturing Technology Lab, Department of Mechanical Engineering, Indian Institute of Technology Ropar, Punjab, 140001, India

    Dattatraya Bombe, Rakesh Kumar & Anupam Agrawal

  2. Department of Metallurgy and Materials Engineering, Indian Institute of Technology Kharagpur, West Bengal, Kharagpur, 721302, India

    Shubhra Kamal Nandi

  3. Department of Materials, University of Manchester, Manchester, M13 9PL, UK

    Shubhra Kamal Nandi

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Bombe, D., Kumar, R., Nandi, S.K. et al. Semi-analytical formulation for single-track laser powder-bed fusion process to estimate melt-pool characteristics considering fluid-flow and marangoni effect. Int J Interact Des Manuf (2023). https://doi.org/10.1007/s12008-023-01593-1

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