Spot Welding Simulation

It's a coupled electrical-thermal-structural analysis of resistance spot welding. It models contact resistance, nugget formation process, and predicts indentation and expulsion. It's essential for evaluating the joining quality of automotive body structures.

This can be expressed mathematically like this.

Temperature dependence of contact resistance:

Spot welding 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's 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 the validity within the extrapolation range is verified. Thermodynamic databases like 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 heat, latent heat, frictional heat, etc.).

During solidification, 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.

The flow of molten metal or resin follows the Navier-Stokes equations, but high viscosity and non-Newtonian fluid characteristics must be considered. For injection molding, the Cross-WLF model is standard: