creep-relaxation

name	creep-relaxation
description	Creep and stress relaxation — Norton power law, Larson-Miller parameter, creep rupture, stress relaxation in bolts, high-temperature design, creep-fatigue interaction.
metadata	{"priority":6,"promptSignals":{"phrases":["creep","stress relaxation","high temperature","Norton law","Larson-Miller","creep rupture","tertiary creep"],"minScore":4}}

Creep & Stress Relaxation — Complete Skill

Creep Stages

Primary creep: decreasing strain rate (work hardening > thermal softening) Secondary (steady-state) creep: constant minimum strain rate ε̇_min (work hardening = recovery) Tertiary creep: accelerating strain rate → necking → rupture

Typical: secondary creep dominates design life

Norton Power Law (Steady-State Creep)

ε̇ = A × σⁿ × exp(-Q/RT)

Where:

• ε̇ = steady-state creep rate [s⁻¹]
• σ = stress [MPa or psi]
• n = stress exponent (n = 3-8 for metals; n ≈ 5 typical)
• Q = activation energy [J/mol]
• R = 8.314 J/(mol·K)
• T = absolute temperature [K]
• A = material constant

Simplified form (at constant T): ε̇ = B × σⁿ

Log-log plot of ε̇ vs. σ → straight line with slope n

Larson-Miller Parameter (LMP)

LMP = T(C + log t_r) × 10⁻³ [T in °R or K]

Where:

• T = temperature [°R (°F + 460) or K]
• t_r = rupture life [hours]
• C = Larson-Miller constant (C ≈ 20 for most steels in °R; C ≈ 10-45 range)

Usage: From material rupture data, plot LMP vs. σ → single master curve For a given σ and T: find LMP → solve for t_r

Example (ferritic steel, C = 20): LMP = 38,000 at σ = 100 MPa At T = 760°C = 1400°F → T°R = 1860°R 1860 × (20 + log t_r) × 10⁻³ = 38.0 20 + log t_r = 20.43 → t_r = 10^0.43 = 2.7 hr → low

Creep Rupture Strength

σ_r(t) = stress at which rupture occurs after time t at temperature T Reported as: "100 MPa at 538°C for 10,000 hr" (ASME Sec II D)

Design allowable (ASME Boiler Code): S = min(Sy/1.5, Su/3.5, 1% creep in 100,000 hr / 1.0, rupture at 100,000 hr / 1.5)

Stress Relaxation

Definition: stress decreases over time at CONSTANT strain (creep strain replaces elastic strain)

Governing equation: dσ/dt = -E × ε̇_c = -E × B × σⁿ (total strain = const → d(σ/E)/dt + dε_c/dt = 0)

Solution (n ≠ 1): σ(t) = σ₀ / [1 + (n-1) × E × B × σ₀^(n-1) × t]^(1/(n-1))

For n = 1 (linear viscous): σ(t) = σ₀ × exp(-E×B×t)

Application — bolt preload loss: Initial preload σ₀ → after time t at elevated T → remaining σ(t) Must recheck joint integrity at service condition

Creep Deformation (Total strain after time t)

Bailey-Norton: ε(σ,T,t) = ε₀ + ε̇_min × t (secondary only) Primary: ε_primary ≈ A × σᵐ × t^r (r ≈ 0.3 for metals)

Full tertiary (Omega method, API 579-1/ASME FFS-1): ε(t) = ε_c × exp(Ω × ε̇_min × t) / (Ω) t_r = 1/(Ω × ε̇_min)

Materials — Creep Resistance

Material	Max Temp (creep-limited)	Notes
Carbon steel	370°C (700°F)	Below this: negligible creep
Cr-Mo steel (9Cr-1Mo)	580°C	Power plant piping
Austenitic SS 304/316	650°C	Chemical, food
Inconel 625	870°C	Gas turbine components
Inconel 718	980°C (short)	Aerospace
ODS alloys	1100°C	Experimental
Ceramics (SiC)	1400°C	Nozzles, refractories

Creep-Fatigue Interaction (ASME III, Subsection NH)

When creep and cyclic loading coexist: Interaction rule: D_f + D_c ≤ 1

D_f = Σ(n/N_f) — fatigue damage fraction (Miner's rule) D_c = Σ(Δt/t_r) — creep damage fraction (Robinson's rule)

Failure envelope in D_f vs. D_c space (bilinear for most materials): Conservative: D_f + D_c = 1 (no interaction credit) Code: ASME TRD-700 or French RCC-MRx creep-fatigue envelope

Design Rules

1. T < 0.3 Tm: creep negligible (Tm = melting point [K])
2. T = 0.3-0.5 Tm: primary creep significant
3. T > 0.5 Tm: steady-state creep dominates; time-dependent design required
4. Use LMP to select material: need t_r ≥ design life at operating σ, T
5. Ductility at temperature ≥ 5% elongation preferred (creep ductility exhaustion)

Output

Provide: creep rate ε̇ [%/hr], rupture life t_r [hr], LMP value, σ_remaining after relaxation [MPa], damage D_f + D_c.