Sheet Metal Press Forming Simulation

Analysis of the thin sheet press forming process using explicit FEM. Crack prediction using the Forming Limit Diagram (FLD), wrinkle occurrence prediction, and springback evaluation. Essential for automotive body panel die design.

Expressing this in a formula, it looks like this.

FLD (Forming Limit Diagram):

Sheet metal press forming simulation is formulated as a coupled problem of thermodynamics, solid mechanics, and fluid mechanics. 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, 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 mechanics, 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 in a formula, it looks like this.

Here, $L$ is latent heat, and $f_l(T)$ is the liquid fraction (taking a value between 0 and 1 in the solid-liquid coexistence region).

Metal plastic deformation 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.