Injection Molding Warpage Analysis

It predicts the warpage deformation that occurs during demolding after cooling. It calculates the warpage amount from residual stresses caused by non-uniform cooling, molecular orientation, and crystallinity distribution.

Expressing this in a formula, it looks like this.

Warpage of thin-walled parts:

Injection molding warpage 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, velocity, load, etc.) and product quality (dimensional accuracy, defects, mechanical properties).

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 the solidification process, 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:

All physical models have their assumptions and applicable ranges. The governing equations we discussed are based on continuum mechanics and thermodynamics assumptions. They may not accurately represent phenomena at extremely small scales (below micrometers) or under extreme conditions (ultra-high pressure, ultra-high temperature, high-speed deformation). Additionally, material properties like thermal conductivity and viscosity are temperature- and pressure-dependent, and simplified constant-value assumptions can lead to significant errors. When applying these models, you must carefully verify that the assumptions match your specific problem.