LPBF (Laser Powder Bed Fusion) Simulation

LPBF (Laser Powder Bed Fusion), also known as SLM, is a metal 3D printing technology. It simulates the transient thermal process of powder melting and solidification by laser to predict residual stress, deformation, and defects.

This can be expressed mathematically like this.

Gaussian heat source model:

LPBF (Laser Powder Bed Fusion) simulation is formulated as a coupled problem of thermodynamics, solid mechanics, and fluid dynamics. The physical phenomena of the manufacturing process span multiple time and spatial scales, requiring an appropriate combination of macro-scale continuum models and meso/micro-scale material models. The goal is to quantitatively predict the causal relationship between process parameters (temperature, velocity, load, etc.) and product quality (dimensional accuracy, defects, mechanical properties).

The accuracy of manufacturing process simulation heavily depends on the fidelity of the material model. It is necessary to properly define elastoplastic constitutive laws, creep laws, phase transformation models, etc., as functions of temperature and strain rate. Data obtained from material testing (tensile, compression, torsion) is fitted, and validity in extrapolation ranges is verified. Thermodynamic databases such as JMatPro and Thermo-Calc are also utilized.

Manufacturing process simulation is formulated as a coupled problem of thermodynamics, fluid dynamics, and solid mechanics.

Here, $T$ is temperature, $\mathbf{v}$ is the material velocity field, $k$ is thermal conductivity, and $Q$ is internal heat generation (Joule heating, latent heat, frictional heat, etc.).

During the solidification process, the release/absorption of latent heat significantly affects the temperature field. Formulation using the enthalpy method:

This can be expressed mathematically like this.

Here, $L$ is the latent heat, and $f_l(T)$ is the liquid fraction (taking a value between 0 and 1 in the solid-liquid coexistence region).

Plastic deformation of metals is described by constitutive laws such as the Johnson-Cook model:

$A$: Initial yield stress, $B$: Hardening coefficient, $n$: Hardening exponent, $C$: Strain rate sensitivity, $m$: Thermal softening exponent.