Superplastic Cavitation Growth Calculator
Aerospace Structural Integrity: Compute cavity volume fraction ($C_v$), growth parameter ($\eta$), and minimum hydrostatic gas back-pressure to suppress voids.
Alloy & Stress State
Void Fraction & Suppression Analysis
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Mechanics of Cavitation & Hydrostatic Suppression
While superplastic forming yields remarkable geometric elongation, alloys with hard intermetallic dispersoids (particularly 5xxx and 7xxx series aluminum alloys) are prone to internal intergranular cavitation.
1. The Stowell Cavity Growth Model
The accumulation of cavity volume fraction $C_v$ as a function of true strain $\varepsilon$ is given by:
C_v = C_v0 · exp(η · ε)
where $\eta$ is the cavity growth rate parameter governed by strain rate sensitivity $m$ and stress triaxiality $(\sigma_m / \bar{\sigma})$:
η = [3(m + 1) / (2m)] · sinh[2(2 - m)/(2 + m) · (σ_m / σ̄)]
2. The Role of Stress Triaxiality
Stress triaxiality $(\sigma_m / \bar{\sigma})$ depends strongly on forming mode:
- Uniaxial Tension: $\sigma_m / \bar{\sigma} = 1/3 \approx 0.333$
- Plane Strain: $\sigma_m / \bar{\sigma} = 1 / \sqrt{3} \approx 0.577$
- Equibiaxial Free Bulging: $\sigma_m / \bar{\sigma} = 2/3 \approx 0.667$ (most severe cavitation rate)
Frequently Asked Questions
What causes cavitation in superplastic forming and why is it dangerous?
Cavitation occurs when grain boundary sliding (GBS) creates stress concentrations at grain boundary triple junctions and hard secondary phase particles (e.g. $\text{MnAl}_6$ in AA5083). If local diffusion or dislocation accommodation is too slow, micro-voids nucleate, grow, and coalesce into planar fissures, drastically degrading post-forming tensile strength, fatigue life, and ductility.
How does gas back-pressure suppress cavity growth?
Superimposing a positive hydrostatic gas back-pressure ($P_{\text{back}}$) in the lower die cavity reduces the positive mean hydrostatic tensile stress: $\sigma_m = \frac{\sigma_1 + \sigma_2 + \sigma_3}{3} - P_{\text{back}}$. When $P_{\text{back}} \ge 0.5\text{ to }0.7 \times \sigma_{\text{eff}}$, the hydrostatic stress becomes neutral or compressive, halting void expansion completely.
What is the aerospace allowable limit for cavity volume fraction ($C_v$)?
Critical aerospace structural specifications (e.g. for airframe fuselage panels and nacelle skins) strictly cap post-formed internal cavity volume fraction at $C_v < 1.0\%$, with components exhibiting $C_v > 2\text{ to }3\%$ subjected to mandatory scrapping due to fatigue knockdown.