Injection Molding Filling Analysis

Flow analysis of the molten resin filling process into the mold cavity. Predicts flow front progression, weld line positions, and air traps using Hele-Shaw approximation or 3D analysis.

Expressing this with equations looks like this.

Cross-WLF viscosity model:

Injection molding filling analysis simulation is formulated as a coupled problem of thermodynamics, material mechanics, and fluid dynamics. 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, 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 within the extrapolation range 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'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 with equations looks like this.

Here, $L$ is the latent heat, and $f_l(T)$ is the liquid fraction (takes 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.