Superplastic Forming (SPF) Tooling Vector Prepress Guide

Comprehensive engineering guide to superplastic hot gas blow forming, Backofen constitutive modeling, die radius design, and CAD/CAM vector prepress.

1. Superplastic Forming (SPF) Principles

Superplasticity is the capability of certain fine-grained polycrystalline metallic alloys (grain size $d < 10\text{ µm}$) to undergo extraordinarily high isotropic tensile elongations (300% to > 1,000%) without macroscopic localized necking when deformed at elevated homologous temperatures ($T > 0.5 T_{\text{melt}}$) within a specific strain rate regime ($10^{-4}$ to $10^{-2}\text{ s}^{-1}$).

In the SPF process, a sheet blank is clamped securely between heated tooling dies, and high-pressure inert argon gas is injected to blow the sheet into the female cavity geometry.

2. Constitutive Power-Law & Gas Pressure Equations

2.1 Backofen Strain Rate Sensitivity

The relationship between true flow stress $\sigma$ and true strain rate $\dot{\varepsilon}$ is expressed by the Backofen equation:

σ = K · (dε/dt)^m

Where:

• K = Material strength coefficient ($MPa·s^m$)
• m = Strain-rate sensitivity index ($m = \partial \ln \sigma / \partial \ln \dot{\varepsilon}$)

Superplastic behavior occurs when $m \ge 0.45$. High $m$ values suppress necking by work-hardening localized strain regions.

2.2 Dynamic Gas Pressure Cycle

Because the sheet thins and increases in curvature radius during forming, constant inlet gas pressure would cause exponential strain rate acceleration and rupture. The gas controller must modulate pressure dynamically:

P(t) = [4 · t_0 · K · (dε/dt)^m / R_0] · exp(-2 · (dε/dt) · t) · √[exp(2 · (dε/dt) · t) - 1]

3. Tooling Die Design & Vector DXF Requirements

4. CAM Prepress Vector Preparation Workflow

1. Unfolded Flat Blank Optimization: Utilize inverse finite element blank unfolding with non-linear thickness distribution to minimize edge trim waste.
2. Stop-off Masking Patterns: For combined Superplastic Forming / Diffusion Bonding (SPF/DB), generate precision Yttria ($Y_2O_3$) screen-printing vector masks to define internal honeycomb rib structures.