| name | shape-memory-alloys |
| description | Shape memory alloys — NiTi (Nitinol), one-way/two-way SME, pseudoelasticity, transformation temperatures, stress-strain, actuator design, biomedical applications, Tanaka model. |
| metadata | {"priority":7,"promptSignals":{"phrases":["shape memory alloy","SMA","Nitinol","NiTi","pseudoelasticity","superelastic","shape memory effect"],"minScore":3}} |
Shape Memory Alloys — Complete Skill
Phase Transformation
SMA undergoes thermoelastic martensitic transformation between:
- Austenite (A): high-temperature phase; ordered cubic (B2 for NiTi)
- Martensite (M): low-temperature phase; monoclinic/rhombohedral; twin structure
Transformation temperatures (on heating/cooling):
M_f → M_s → A_s → A_f (characteristic temperatures for specific composition)
Transformation temperatures depend on composition:
NiTi: 1 at% increase in Ni → M_s decreases ~10°C
Biomedical NiTi: A_f ≈ 37°C (body temperature activation)
High-temperature SMA (NiTiPd, NiTiHf): A_f up to 400°C
Transformation Behavior
Cooling: A → M_s (start) → M_f (finish); martensite formed
Heating: M → A_s (start) → A_f (finish); austenite recovered
Transformation is irreversible in temperature sense; hysteresis typically 20–60°C width
Shape Memory Effects
One-Way SME
- Deform in martensite phase (below M_f); apply strain up to εr = 6–8%
- Strain appears permanent in martensite; detwinning of martensite variants
- Heat above A_f → reverts to austenite; original shape recovered
Strain recovery: up to 8% for NiTi; 4% for Cu-Zn-Al
Two-Way SME
SMA "remembers" both hot and cold shapes; repeatable cycling
Requires training (thermomechanical cycling to create permanent martensite texture)
Recovery strain: typically 1–4% (less than one-way)
Pseudoelasticity (Superelasticity)
Above A_f: stress-induced martensitic transformation
Apply load → martensite forms → remove load → spontaneously reverts to austenite
Recoverable strain: 8–10% (NiTi); fully elastic apparent behavior but with hysteresis
Stress-strain curve:
Forward plateau: σ_Ms → transformation (constant stress, increasing strain)
Reverse plateau: σ_As → recovery on unloading
Typical: forward plateau σ = 400–500 MPa; hysteresis = 200 MPa; max strain = 8%
Tanaka Constitutive Model
σ - σ₀ = E(ξ)(ε - ε₀) - Ω(ξ)(ξ - ξ₀) + θ(T - T₀)
ξ = martensite volume fraction (0 = austenite, 1 = martensite)
E(ξ) = ξ E_M + (1-ξ) E_A (rule of mixtures; E_M ≈ 40 GPa, E_A ≈ 75 GPa for NiTi)
Ω = transformation tensor (related to max transformation strain)
θ = thermoelastic modulus
Martensite evolution:
Cooling (M formation): ξ = 1 - exp[a_M(M_s - T) + b_M σ]
Heating (A formation): ξ = exp[a_A(A_s - T) + b_A σ]
Actuator Design
SMA actuator force:
F = σ_recovery × A_wire [N]
σ_recovery typically 200–500 MPa for NiTi
Spring back required:
Bias spring or antagonist SMA returns actuator when cooled
Bias spring stiffness: k_bias × δ_stroke = F_SMA × (1 - R) where R = work output ratio
Frequency:
Heating: direct current (Joule heating) or convection
Cooling: convection (air/water); limits frequency to 0.1–5 Hz
Power for Joule heating:
Q = I² × R_wire × t = m × c_p × ΔT + latent heat
Latent heat of transformation: L ≈ 20–30 kJ/kg (NiTi)
Resistance: ρ_A ≈ 80 μΩ·cm; ρ_M ≈ 100 μΩ·cm
Fatigue
Thermomechanical cycling: degradation of transformation strain
High-cycle fatigue (pseudoelastic): > 10⁷ cycles at σ < 250 MPa (NiTi wires)
Low-cycle (<1000 cycles): higher stress/strain; common for actuators
Training-induced degradation: two-way strain decreases with cycles
Biomedical Applications (FDA-Regulated)
Stents: pseudoelastic; crimped for delivery; expands to body temperature in vessel
Orthodontic wires: constant force over large deflection → better tooth movement
Bone staples: compressed cold → body temp → expand → compress fracture
Guidewires: superelastic → thread through curved anatomy
Commercial Alloys
| Alloy | A_f range | Notes |
|---|
| NiTi (equiatomic) | -100 to +100°C | Most common; biomedical |
| NiTiCu | Narrower hysteresis | Better stability |
| Cu-Zn-Al | -200 to +150°C | Lower cost; brittle |
| Cu-Al-Ni | -200 to +200°C | High-temperature capable |
| NiTiHf, NiTiPd | 100–400°C | HTSMA; actuators |
Output
Provide: transformation temperatures M_s, M_f, A_s, A_f [°C], recovery strain ε_r [%], actuator force [N], wire diameter [mm], heating current/power [W], estimated actuation frequency [Hz], fatigue life estimate for given stress.
