Arc Welding Simulation

It uses Goldak's double ellipsoid model as the heat source model for TIG/MIG/MAG arc welding to predict weld pool shape, HAZ range, and temperature history. It is used for optimizing parameters like welding speed, current, and voltage.

Expressing this with equations, it looks like this.

Heat input:

Arc welding simulation is formulated as a coupled problem of thermodynamics, solid mechanics, and fluid dynamics. Since the physical phenomena of manufacturing processes span multiple time and spatial scales, an appropriate combination of macro-scale continuum models and meso/micro-scale material models is required. The goal is to quantitatively predict the causal relationship between process parameters (temperature, speed, 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 like JMatPro or 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 solidification, the release/absorption of latent heat significantly affects the temperature field. Formulation using the enthalpy method:

Expressing this with equations, it looks 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 like Johnson-Cook:

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

Flow analysis for manufacturing processes like casting and injection molding is governed by the Navier-Stokes equations. For incompressible flow with phase change, the equations include mass, momentum, and energy conservation, often coupled with a volume-of-fluid (VOF) method to track the free surface. Key phenomena include mold filling, turbulence, heat transfer with solidification, and potential defects like air entrapment or cold shuts. The simulation predicts flow patterns, pressure distribution, temperature fields, and final part quality.