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Numerical Model for Simulation of Melting and Microstructure Evolution during a Multi-layered Laser Melting Process

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Abstract

In this paper, a numerical model is presented for the simulation of melting and microstructure formation during a layer-by-layer laser melting process. The model couples the solution of thermal and species transport with a sharp-interface enthalpy-based phase change model to track the melting and solidification in each layer. The effect of the moving laser energy source is implemented through a transient moving heat flux boundary condition. Transition from the completion of a layer to the start of a new layer is implemented using a domain translation technique, kee** the size of the computational domain constant. The model captures the remelting of a previous layer during the formation of a new layer. Simulations are performed to predict the segregation and grain structure formation during multi-layered laser melting of Al-10%Cu alloy. It is seen that the laser scan direction governs the grain orientation with grains growing in the direction of laser travel. Also, the remelting of the previously formed grains in the adjacent layer affects the species concentration and grain structure in the subsequent layer. Higher power, lower laser scan speed, and smaller laser radius leads to the formation of longer grains with larger aspect ratio spanning multiple layers.

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Data Availability

The raw/processed data will be available on request.

Abbreviations

A :

Absorptivity

a, b :

Constants

C :

Volume-averaged concentration

C p :

Specific heat (J/kgK)

C m :

Mean concentration

C 0 :

Initial concentration

C ck :

Coefficient of flow resistance source term

D :

Solute diffusivity (m2/s)

f l :

Liquid fraction

h :

Enthalpy (J/kg)

k :

Effective thermal conductivity (W/mK)

k p :

Partition coefficient

L :

Latent heat of fusion (J/kg)

m :

Equilibrium slope of the liquidus line for binary alloy

n :

Nucleation density

n max :

Maximum number of nuclei

p :

Pressure (N/m2)

P :

Laser power (W)

S :

Flow resistance source (N/m3)

S b :

Buoyancy source term in momentum equation (N/m3)

S cr :

Volumetric source term in energy equation (W/m3)

T :

Temperature (K)

T m :

Melting temperature (K)

T i :

Interface temperature (K)

t :

Time (s)

\(\overrightarrow{u}\) :

Velocity (m/s)

v l :

Laser travel speed (m/s)

r 0 :

Laser spot radius (m)

V :

Concentration potential

g :

Acceleration due to gravity (m/s2)

x, y :

Domain axes

\({\beta }_{\mathrm{T}}\) :

Thermal expansion coefficients (K−1)

\({\beta }_{\mathrm{S}}\) :

Solutal expansion coefficients

\(\gamma \) :

Surface tension (N/m)

\(\epsilon \) :

Porosity

\(\theta \) :

Interface angle

\(\theta \) r :

Crystallographic orientation of dendrite

\(\kappa \) :

Curvature (m−1)

\(\mu \) :

Dynamic viscosity (Pa.s)

ρ :

Density (kg/m3)

Δ T :

Undercooling (K)

Δ T m :

Mean undercooling for nucleation (K)

Δ T σ :

Standard deviation of undercooling for nucleation (K)

σ :

Surface tension coefficient (N/mK)

σ t :

Surface tension (N/m)

l :

Liquid phase

s :

Solid phase

x, y :

With respect to x-axis and y-axis, respectively

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Funding

This work has been funded and supported by DST (Department of Science and Technology) SERB Project no. ECR/2017/002440.

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Authors and Affiliations

  1. School of Mechanical Sciences, IIT Bhubaneswar, Argul, Jatni District, Khurda, Odisha, 752050, India

    Aurabinda Swain, M. Jegatheesan, Prasenjit Rath & Anirban Bhattacharya

  2. Department of Mechanical Engineering, Chandigarh University, Ajitgarh, 140413, India

    Amman Jakhar

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  1. Aurabinda Swain
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Swain, A., Jegatheesan, M., Jakhar, A. et al. Numerical Model for Simulation of Melting and Microstructure Evolution during a Multi-layered Laser Melting Process. J. of Materi Eng and Perform (2023). https://doi.org/10.1007/s11665-023-08519-8

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