fea-fatigue-analysis

name	fea-fatigue-analysis
description	FEA fatigue analysis — stress-life (S-N), strain-life (ε-N), critical plane approaches, rainflow counting, Miner's rule, Goodman mean stress correction, FE-SAFE/nCode integration, multiaxial fatigue, notch effects.
metadata	{"priority":7,"promptSignals":{"phrases":["FEA fatigue","fatigue analysis FEA","stress life","strain life","FE-Safe","multiaxial fatigue"],"minScore":3}}

FEA Fatigue Analysis — Complete Skill

Fatigue Analysis Methods

1. Stress-Life (S-N) Approach — High Cycle Fatigue

Applicable: N > 10⁵ cycles; nominally elastic; fatigue dominated by crack initiation Input: stress amplitude σ_a vs. life N from S-N curve

Basquin equation: σ_a = σ_f' × (2N_f)^b [MPa; σ_f' = fatigue strength coefficient; b = fatigue strength exponent (typically -0.05 to -0.12)] For steel: σ_f' ≈ σ_u + 345 MPa (Morrow approximation); b ≈ -0.09

Mean stress correction (Goodman): σ_a / S_e + σ_m / σ_u = 1 → equivalent zero-mean: σ_a_equivalent = σ_a / (1 - σ_m/σ_u)

Endurance limit (S_e): S_e = S_e_corrected = k_a × k_b × k_c × k_d × k_f × S'_e S'_e = 0.5 × σ_u (for σ_u < 1400 MPa); k_a = surface finish; k_b = size; k_c = loading; k_d = temp; k_f = stress concentration

Stress life from FEA: Extract principal stresses σ₁, σ₂, σ₃ per element from multiple load steps Compute σ_a and σ_m per element → enter modified Goodman → find N_f per element Minimum N_f = fatigue life of structure

2. Strain-Life (ε-N) Approach — Low-High Cycle Fatigue

Applicable: N < 10⁵ cycles; local plasticity at notch; total life (initiation + short crack) Coffin-Manson + Basquin: Δε_total / 2 = σ_f' / E × (2N_f)^b + ε_f' × (2N_f)^c Δε_total = elastic strain range + plastic strain range ε_f' = fatigue ductility coefficient; c = fatigue ductility exponent (typically -0.5 to -0.7)

Neuber notch correction (elastic FEA to local plastic): At stress concentration: (K_t σ_nominal)² / E = σ_local × ε_local [Neuber hyperbola] Intersect with σ-ε curve → find local σ_local and ε_local at notch → use in ε-N

ESED method (Energy Strain Energy Density): Similar to Neuber but equates strain energy; more accurate for multi-axial

3. Critical Plane Approaches — Multiaxial Fatigue

Fatigue cracks initiate on specific planes:

Findley criterion (shear-based): f_Findley = τ_a + k × σ_n_max [k = material constant ≈ 0.2–0.3; τ_a = shear amplitude; σ_n = normal stress on same plane] Maximize over all planes → critical plane → compare to τ_a_allow = τ_f' (2N_f)^b'

Smith-Watson-Topper (SWT — tension-based): SWT = σ_max × Δε_total / 2 [kJ/m³; maximize over all planes] Find plane maximizing SWT → N_f from SWT vs. N material data

von Mises equivalent (conservative for proportional loading): σ_eq_a = √(Δσ₁² + Δσ₂² - Δσ₁Δσ₂) [for biaxial; similar to von Mises] Enter into uniaxial S-N → non-conservative for non-proportional loading (rotating principal axes)

FEA Fatigue Workflow

Step 1: Stress extraction Linear elastic FEA for each load case (unit loads or actual amplitude) Store stress tensors at all elements/nodes For variable amplitude: extract stress time history at critical locations

Step 2: Load superposition σ(t) = Σ [L_i(t) × σ_unit_i(x)] [L_i = load history; σ_unit_i = FEA stress for unit load i] Produces stress tensor time history at each location

Step 3: Rainflow counting Count cycles from stress history: amplitude and mean for each counted cycle ASTM E1049: standard rainflow counting algorithm Half-cycles and full-cycles; range, mean, number of cycles per bin

Step 4: Damage accumulation (Miner's rule) D = Σ (n_i / N_fi) [n_i = counted cycles; N_fi = life at σ_ai from S-N curve] Failure when D ≥ 1.0 (conservative); actual failure: D = 0.7–2.3 (scatter)

Step 5: Life prediction N_f = 1 / D_per_block × N_repetitions_per_block [total life in blocks] Display fatigue life contour map

Software Integration

FE-SAFE (Simulia): Reads ABAQUS .odb; applies S-N or ε-N approach; multiaxial fatigue; probabilistic life Post-process: log₁₀(N_f) contour; damage contour; safety factor

nCode DesignLife: Reads FEA from ABAQUS, ANSYS, Nastran; full multiaxial; critical plane; rainflow Standards compliance: automotive (E8 duty cycle), aerospace fatigue spectra

ANSYS Fatigue (Mechanical): Built-in fatigue tool; stress-life only (no strain-life); zero-mean or mean correction options Quick integration; less powerful than FE-SAFE

Fatigue software inputs: Material: σ_u [MPa], S_e [MPa], S-N curve (R = -1 fully reversed); or ε-N constants Loading: stress tensor time history or unit loads + load history Surface finish: k_a factor (from Shigley surface finish chart) Surface treatment: shot-peened → k_a > 1 (beneficial compressive RS)

Notch Effects

Theoretical stress concentration K_t: from geometry Fatigue notch factor K_f: K_f = 1 + q × (K_t - 1) [q = notch sensitivity, 0.7–0.95 for steel] Effective fatigue stress: σ_eff = K_f × σ_nominal → use in S-N instead of nominal

Fatigue in FEA: FEA already captures local stress concentration (if mesh is fine enough at notch) Do NOT apply K_f again → will be double-counting Only apply K_f if using nominal stress from FEA at section away from notch

Weld Fatigue (Structural Stress Approach — IIW)

Hot-spot stress method (IIW): Structural stress at weld toe by linear extrapolation from 0.5t and 1.5t away from weld σ_hs = 1.67 × σ_0.5t - 0.67 × σ_1.5t [t = plate thickness; σ from FEA] Enter structural stress into FAT class from IIW tables (e.g., FAT90 for butt weld)

Master S-N curve for welds (Dong structural stress): σ_s = E × t_s × κ / (1 + l/t_s) [structural stress; l = loading type parameter] Universal master curve (no scatter across different weld joint types)

Standards

Standard	Scope
ASTM E1049	Rainflow counting for fatigue
ASTM E466	Fatigue testing (load control)
ASTM E606	Strain-controlled fatigue
IIW-2259-15	Recommendations for fatigue design of welded joints
FKM Guidelines	German fatigue assessment of machine components
SAE HS-784	Statistical aspects of fatigue

Output

Provide: fatigue approach (S-N/ε-N/multiaxial), critical location (element/node), maximum principal stress amplitude σ_a [MPa] and mean σ_m [MPa], modified Goodman factor, equivalent stress ratio R = σ_min/σ_max, equivalent S-N curve (S_e [MPa], σ_f', b), Miner damage D per load block, fatigue life N_f [cycles or blocks], safety factor on life (N_f/N_required), log₁₀(N_f) contour map minimum value, Findley parameter or SWT parameter (if multiaxial), hot-spot stress σ_hs [MPa] and FAT class (if weld), and applicable standard (ASTM E1049, IIW, FKM).