Casting Residual Stress Analysis

Prediction of residual stresses generated during solidification shrinkage and the cooling process. A thermo-structural coupled analysis using elastoplastic creep constitutive laws. Evaluation of deformation and cracking due to mold constraints.

Expressing this in a formula, it looks like this.

Norton's law creep:

Simulation of casting residual stress analysis is formulated as a coupled problem of thermodynamics, solid mechanics, and fluid mechanics. Since the physical phenomena of the manufacturing process 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, velocity, load, etc.) and product quality (dimensional accuracy, defects, mechanical properties).

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

Here, $T$ is temperature, $\mathbf{v}$ is the material's 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 in a formula, 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 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: