shape-memory-alloys

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

1. Deform in martensite phase (below M_f); apply strain up to εr = 6–8%
2. Strain appears permanent in martensite; detwinning of martensite variants
3. 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.