superplastic-forming

name	superplastic-forming
description	Superplastic forming (SPF) — superplastic conditions (fine grain < 10 μm, high T > 0.5 Tm, low strain rate 10⁻⁴ to 10⁻²/s), flow stress and strain rate sensitivity m-value (m > 0.5), SPF tooling (die, argon pressure), SPF of titanium (Ti-6Al-4V at 900–950°C) and aluminum (5083-SPF at 500°C), diffusion bonding (DB/SPF combined), thickness distribution prediction (area ratio), grain growth during SPF, and aerospace applications (fuselage frames, fan blades).
metadata	{"priority":7,"promptSignals":{"phrases":["superplastic forming","SPF","superplastic","diffusion bonding","DB/SPF","superplasticity"],"minScore":3}}

Superplastic Forming (SPF) — Complete Skill

Superplasticity Fundamentals

Definition and Requirements

Superplasticity: materials exhibiting elongations of 200–2,000% without failure under specific conditions

Three essential conditions:

1. Fine grain size: d < 10 μm (grain boundary sliding dominates at fine grain)
2. High temperature: T > 0.5 T_m (homologous; enables grain boundary mobility)
3. Low strain rate: ε̇ = 10⁻⁴ to 10⁻² s⁻¹ (optimal window for GBS mechanism)

Grain boundary sliding (GBS): dominant mechanism; grains slide over each other at grain boundaries Accommodated by: grain boundary diffusion + limited dislocation activity GBS requires clean, migrating boundaries → impurity control important

Constitutive Behavior

Strain Rate Sensitivity

Flow stress for superplastic metals: σ = K × ε̇^m [K = material constant at given T; m = strain rate sensitivity exponent; ε̇ = strain rate]

m-value (strain rate sensitivity): m = ∂(ln σ) / ∂(ln ε̇) |_T,ε [logarithmic slope of log σ vs. log ε̇] For superplasticity: m ≥ 0.5 (typically 0.5–0.8) Normal metals (cold): m ≈ 0; warm: m ≈ 0.1–0.2 (not superplastic)

Physical significance of high m: High m → load capacity of necked region increases as ε̇ increases → stable deformation (no necking) Considère criterion: σ_neck > σ_unnecked → neck grows slower than surrounding material → elongation without failure

Measuring m: Strain rate jump test: change ε̇ by factor 10; measure Δσ → m = log(σ₂/σ₁)/log(ε̇₂/ε̇₁) Or: strain rate history test at constant temperature; fit log-log plot

Superplastic Materials

Titanium Ti-6Al-4V

Most commercially important SPF material: Grain size requirement: d ≤ 10 μm (typical fine-grained Ti-6Al-4V: 5–7 μm) SPF temperature: 900–950°C (T_m = 1,670°C → T/T_m = 0.56–0.59) Optimal strain rate: ε̇ = 10⁻⁴ to 2×10⁻³ s⁻¹ m-value at 927°C: m ≈ 0.7–0.85 → excellent superplastic Elongation achievable: 500–1,200%

Flow stress at SPF conditions: σ = K × ε̇^m; K ≈ 350–500 MPa at ε̇ = 10⁻³ s⁻¹; σ_flow ≈ 3–10 MPa (very low → low forming forces) Pressure required for SPF: p = 4 × σ_flow × t / r [membrane equation; r = local radius of curvature; t = wall] Typical: 1–5 MPa argon gas pressure for Ti-6Al-4V

Aluminum 5083-SPF

5083 superplastic grade: special processing to achieve d < 10 μm; extra Fe, Mn for pinning SPF temperature: 500–520°C (T/T_m = 0.87–0.90) m-value: 0.45–0.55 (lower than Ti; less superplastic; elongation 150–400%) Forming pressure: 0.5–2 MPa (lower than Ti)

Other SPF alloys: 2004 (Al-Cu-Zr): m ≈ 0.55 at 460°C; high strength after T6; aerospace structural 7475-T7351: SPF grade; m ≈ 0.8 at 516°C; skin panels Al-Li 8090: SPF grade; lower density; m ≈ 0.7 at 530°C

Other SPF Materials

Zinc-Aluminum (Zn-22Al): very superplastic at room temperature; T_m = 400°C; m = 0.5 at T_room Duplex stainless: 2205 type at 975°C; m ≈ 0.4; SPF of complex shapes Nickel superalloy (IN-718): superplastic at 950–1,000°C; m ≈ 0.5 (limited elongation)

SPF Process

Forming Setup

Die and tooling: Die: ceramic, INCO 718 or H-13 steel (for Ti); die surface must accommodate thermal expansion Seal: metal gasket seals blank at peripheral groove → argon pressure applied above blank Blank: sheet of SPF material; thickness t₀; area A₀

Argon atmosphere: Inert gas (argon, sometimes nitrogen): prevents oxidation; acts as forming pressure medium Pressure profile: controlled ramp rate → controls local strain rate → maintains m ≥ 0.5

Optimal strain rate control: p(t) = 4 × K × ε̇_opt^m × t₀/(R(t)) × (A₀/A(t))^... [complex; pressure depends on evolving thickness and geometry] Simplified constant-strain-rate SPF: pressure increases as sheet thins (resistance increases) Target: maintain ε̇ = ε̇_opt = 10⁻³ s⁻¹ throughout forming to maximize m

Thickness Distribution

Area ratio method: For SPF under pressure, sheet stretches → area increases → thickness decreases t_local / t₀ = A₀_local / A_local [volume conservation; local area ratio to initial area] Non-uniform thinning: regions that contact die first stop thinning; corners thin most

Worst case thinning: For hemisphere: t_min / t₀ = 1/4 (80% thinning at pole; for hemisphere with D/t₀ = 100) More accurately: t_min / t₀ depends on tooling geometry and lubrication

Failure criterion: t_min ≥ t_design (minimum required wall); if not → increase t₀ or redesign geometry

Stop-off patches: apply ceramic paste (stop-off) at mating surfaces for DB areas → prevents bonding there; ensures pressure forming everywhere else

Diffusion Bonding Combined with SPF (DB/SPF)

Concept

DB/SPF: simultaneous or sequential diffusion bonding of sheet stack + superplastic forming Creates hollow structures with internal ribs/webs → high specific stiffness/strength

Process sequence (typical multi-sheet DB/SPF):

1. Stack 2 or 3 sheets; apply stop-off (ceramic paste) in non-bond areas; vacuum seal periphery
2. Apply high pressure (10–20 MPa) at high temperature: bonds selected areas (metallurgical bond at stop-off-free areas)
3. Reduce pressure; apply internal argon pressure → SPF of non-bonded areas (internal cavities open up)
4. Cool; inspect

Typical DB parameters (Ti-6Al-4V): T = 900–930°C; P = 10–20 MPa (mechanical press); time = 2–4 hours; oxide-free surfaces (HF etch or laser clean) Bond strength: approaches parent material (grain growth across interface)

Three-sheet structures: Core sheet perforated or grooved → forms internal truss or honeycomb web Produces hollow panel with specific stiffness better than solid Applications: fan blades (Rolls-Royce Trent), hollow fuselage frames

Grain Growth During SPF

Problem: long SPF cycles (hours) at high temperature → grain coarsening → m decreases → risk of failure Grain growth: d² = d₀² + K_g × t × exp(-Q_g / RT) [Q_g = grain growth activation energy; K_g = constant] For Ti-6Al-4V at 927°C: grain doubles from 5 to 10 μm after ~2–4 hours → m drops below 0.5

Mitigation: Minimize forming time (high ε̇ within SPF window → faster forming) Grain pinning with second-phase particles (Y₂O₃ in ODS; TiB₂ in Ti alloys) Post-SPF HIP to close voids from grain boundary separation (micro-cavitation at strain > 300%)

Cavitation

Void formation at grain boundaries during high SPF strain: Nucleation at triple junctions, inclusions; growth by diffusion and plasticity Cavitation starts at ε > 100–200%; severe above ε > 400% Post-SPF HIP: 900°C / 100 MPa / 2 h → closes cavities → restores ductility

Cavitation measurement: Metallographic section; count void area fraction; limit: < 0.5% for structural; < 0.1% for critical aerospace

Standards and References

Standard	Scope
AMS 4928	Titanium 6-4 bar and billet (for SPF stock)
AMS 4935	Ti-6Al-4V SPF sheet
ASTM B265	Titanium and titanium alloy strip, sheet, and foil
ASM Handbook Vol. 14B	Metalworking: sheet forming — SPF chapter
Pilling & Ridley "Superplasticity in Crystalline Solids"	Reference text

Output

Provide: material (alloy; grade; grain size d [μm]; m-value at T and ε̇; elongation capacity [%]), forming conditions (T [°C]; T/T_m; ε̇_opt [s⁻¹]; argon pressure range [MPa]; die material), flow stress (σ_flow = K×ε̇^m [MPa] at forming conditions; pressure calculation p = 4σ_flow×t₀/R_max), part geometry (final shape: D_max [mm]; depth h [mm]; minimum t_design [mm]), blank sizing (t₀ [mm] to achieve t_min; area ratio calculation for worst-case location), thickness distribution (prediction at 3–5 critical locations; t_min/t₀ at pole/corner; comparison with t_design), forming time estimate (from ε̇_opt and total strain ε_max ≈ ln(t₀/t_min); t_form = ε_max/ε̇_opt [s]), grain growth check (d after t_form at T [μm]; m at final d; verify m > 0.5), cavitation (strain at worst location [%]; HIP post-processing: T [°C]/P [MPa]/time [h]; required?), DB/SPF (if multi-layer: bond areas; stop-off pattern; DB pressure [MPa]; time [h]; expected internal structure), tooling (die material; thermal expansion compensation; seal type; argon supply system), and applicable standard (AMS 4935 for Ti sheet; ASM HB 14B; AMS 2801 for inspection).