fatigue-testing

name	fatigue-testing
description	Fatigue testing — S-N curve generation (ASTM E466/E468), staircase method, strain-life (ASTM E606), load spectrum testing, Miner's rule validation, crack growth (ASTM E647).
metadata	{"priority":7,"promptSignals":{"phrases":["fatigue test","S-N curve","fatigue testing","staircase method","crack growth test","da/dN","ASTM E647","load spectrum"],"minScore":4}}

Fatigue Testing — Complete Skill

Test Types and Loading

Uniaxial Fatigue (ASTM E466 — Force-Controlled, S-N)

Constant amplitude: F_max and F_min constant; R = F_min/F_max Typical R ratios: R = -1 (fully reversed), R = 0 (zero-to-tension), R = 0.1, R = 0.5 Frequency: 1-100 Hz (servo-hydraulic); 100-1000 Hz (resonance fatigue machine) Run-out: 10⁷ cycles (steel, cast iron), 10⁸ cycles (Al, Ti, no endurance limit)

Specimen types: Round (smooth): diameter d = 6-10 mm; gauge length 3d Hourglass (notched): Kt controlled notch for notch sensitivity testing Flat (sheet): 1-3 mm; for thin-wall structures Welded specimens: plate + weld bead for structural fatigue (IIW categories)

Strain-Life Testing (ASTM E606 — Strain-Controlled, ε-N)

Servo-hydraulic with clip gauge or extensometer (strain feedback) Strain amplitude ε_a controlled; measure force response Better for low-cycle fatigue (N_f < 10⁴) Outputs: Coffin-Manson parameters ε_f', c, σ_f', b → ε-N curve

Rotating Bending (R.R. Moore)

R = -1 (fully reversed bending); simple, fast, no hydraulics 4-point loading: uniform bending moment → surface stress fully reversed Historically most fatigue data was generated this way Cost: 1/10th of servo-hydraulic; Limitation: fixed R = -1, surface failure only

Staircase Method (Dixon-Mood) — Endurance Limit

Procedure

1. Start at estimated endurance limit S_e
2. If specimen fails: reduce stress by step d (typically 0.05-0.10 × S_e)
3. If runout (10⁷): increase stress by step d
4. Continue for 20-30 specimens
5. Analyze: S_e_mean = A_0 + d(A/F ± 0.5) where A,F from tabulated results

Statistics: σ_S = 1.62 × d × √(FB - A²)/F² [standard deviation of endurance limit] Design: S_e_design = S_e_mean - z × σ_S (z = 1.65 for 95% reliability)

Minimum specimens: 15 for ±15% accuracy on S_e; 30 for ±8%

S-N Curve Construction (ASTM E468)

Data Collection

At least 3 stress levels (4-6 preferred) 6-10 specimens per stress level (for statistical scatter) Include at least one runout level (stress below expected Se)

Statistical Analysis

Log-normal distribution: log(N) ~ Normal(μ, σ) at each stress level Mean S-N curve: 50% probability of survival Design S-N: 97.7% survival = mean - 2σ (AISC fatigue uses mean minus 2 std dev) Weibull distribution: sometimes used for probability-of-failure plots

Basquin Law (High Cycle)

S_a = S_f' × (2N_f)^b log(S_a) = log(S_f') + b × log(2N_f) b ≈ -0.05 to -0.12 (fatigue strength exponent, from slope of S-N in log-log)

ASTM E739: Statistical Analysis of S-N Data

Regression: log(N) = A + B × log(S) — B negative Confidence interval on regression "Runouts" handled as censored data (maximum likelihood estimation)

Variable Amplitude (Spectrum) Fatigue Testing

Standardized Load Spectra

FALSTAFF (fighter aircraft wing root), TWIST (transport wing), CARLOS (car body) WISPER/WISPERX (wind turbine blade) ALOHA (offshore structures) Each represents one flight/trip/year at stated severity level

Rainflow Cycle Counting (ASTM E1049)

Converts arbitrary load-time history → set of (σ_a, σ_m) cycles Algorithm: "rainflow" down sides of σ-t signal mountains Output: range-mean matrix or amplitude-mean matrix

Miner's Rule Validation

Apply known spectrum loading, measure actual N_f Compare to: N_predicted = N_f(σ_a1)/n₁ + N_f(σ_a2)/n₂ + ... Miner's constant at failure: M_f = Σ(n/N_f) If M_f ≠ 1: use modified Miner (allow for sequence effects, mean stress scatter) Typical: M_f = 0.6-1.5 for metals under random loading

Crack Growth Rate Testing (ASTM E647)

Specimen

Compact Tension (CT) or Middle-Crack Tension (M(T)) Pre-cracked by fatigue cycling at ΔK below test range Crack length measured: compliance method (automated), optical (periodic)

Data Reduction

ΔK = ΔF × Y(a/W) / (B × √(πa)) Y = geometry correction function (from ASTM E647 Tables) a = crack length, W = specimen width, B = thickness, ΔF = force range

Compute da/dN from consecutive a-measurements vs. N: da/dN = Δa/ΔN [7-point polynomial incremental method, ASTM E647 recommended]

Results Presentation

Log-log plot: da/dN vs. ΔK Paris region: da/dN = C × ΔK^m [linear on log-log] C = Paris constant, m = Paris exponent (m = 2-4 for metals)

R-ratio effect: R = K_min/K_max; higher R → faster crack growth at same ΔK Walker correction: da/dN = C₀ × [ΔK/(1-R)^(1-γ)]^m

K-calibration for Standard Specimens

CT: K = F/(B√W) × [0.886 + 4.64(a/W) - 13.32(a/W)² + 14.72(a/W)³ - 5.6(a/W)⁴] × √(πa/W)/(1-a/W)^(3/2)

Threshold ΔK_th (ASTM E647 Annex)

Load shedding: gradually reduce ΔK until no crack growth (da/dN < 10⁻⁷ mm/cycle) ΔK_th typically 2-6 MPa√m for steels (increases with R decreasing)

Fretting Fatigue Testing

Fretting motion (small oscillatory slip at contact) + bulk fatigue stress Specialized fixture to apply contact load + bending Reduces fatigue life significantly (factor 2-10×) Relevant for: bolted joints, shrink fits, dovetail joints in turbines

Testing at Temperature and Environment

Elevated temperature: oven + servo-hydraulic, high-temp extensometer (ceramic) Cryogenic: LN₂ bath, usually increases fatigue life (higher Sy at low T) Corrosive environment: SCC fatigue, corrosion fatigue (accelerated by cycling) Salt spray: ASTM B117 (accelerated corrosion), then fatigue → corrosion fatigue S-N

Output

Provide: test type (S-N/ε-N/crack growth), R ratio, frequency, number of specimens, statistical method, S-N parameters (S_f', b or C, m), endurance limit S_e_design [MPa], threshold ΔK_th [MPa√m].