| 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
- T < 0.3 Tm: creep negligible (Tm = melting point [K])
- T = 0.3-0.5 Tm: primary creep significant
- T > 0.5 Tm: steady-state creep dominates; time-dependent design required
- Use LMP to select material: need t_r ≥ design life at operating σ, T
- 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.
