bolt-fatigue

name	bolt-fatigue
description	Bolt fatigue — VDI 2230 preloading, compliance ratio, alternating load on bolt, endurance limit for threaded fasteners, fatigue improvement (rolling, thread form, washer), joint separation.
metadata	{"priority":7,"promptSignals":{"phrases":["bolt fatigue","fastener fatigue","VDI 2230 fatigue","bolt endurance","bolted joint fatigue","preload fatigue","alternating bolt stress"],"minScore":3}}

Bolt Fatigue — Complete Skill

Bolted Joint Compliance Model (VDI 2230)

Compliance (flexibility) definitions: Bolt compliance: δ_b = L_b / (E_b × A_stress) [m/N] A_stress = tensile stress area [mm²] (ANSI B18/ISO 898 tables)

Clamped parts compliance (joint compliance): δ_j = Σ L_i / (E_i × A_effective_i) [sum over all clamped parts] A_effective = pressure cone area (frustum or Rotscher method; simplified: A_eff ≈ 1.5 × A_bolt_head)

Load sharing factor (compliance ratio): Φ = δ_j / (δ_b + δ_j)

Φ → 0: stiff joint (soft bolt or rigid flange); bolt sees very little of external load Φ → 1: compliant joint (stiff bolt, soft gasket); bolt sees full external load

Typical Φ values: All-metal joint, short bolt: Φ = 0.05–0.20 Soft gasket (compressed fiber): Φ = 0.60–0.90 Engine cylinder head (composite gasket): Φ ≈ 0.20–0.40

Bolt Force Under External Load (VDI 2230)

Pre-tension force F_M (preload): applied during assembly External axial force: F_A applied to joint

Bolt force at maximum load: F_b,max = F_M + Φ × F_A

Remaining clamp force: F_Kl = F_M - (1 - Φ) × F_A ≥ 0 [must stay positive for joint contact]

Joint separation condition: F_A > F_M / (1 - Φ) → separation (not allowed in fatigue service)

Alternating Bolt Load

Alternating axial load on bolt: F_a = Φ × (F_A,max - F_A,min) / 2

Mean bolt load: F_m = F_M + Φ × (F_A,max + F_A,min) / 2

Alternating bolt stress: σ_a = F_a / A_stress [MPa]

Mean bolt stress: σ_m = F_m / A_stress [MPa]

Fatigue Endurance of Bolts

Unmodified Bolts (Standard Thread)

Endurance limit (R = -1, fully reversed) for threaded fastener: σ_A_bolt ≈ 50 MPa (property class 8.8 and below; rolled threads) σ_A_bolt ≈ 60–80 MPa (property class 10.9–12.9; rolled threads)

Reason for low endurance: stress concentration at thread root K_t ≈ 4–7 at thread root (first thread engagement most critical) Actual notch sensitivity q < 1 → K_f = 1 + q(K_t - 1) < K_t

ASME chart endurance (for fasteners): σ_e ≈ 0.06–0.08 × S_u for machined threads σ_e ≈ 0.09–0.12 × S_u for rolled threads (30–40% improvement)

Modified Goodman for Bolts

σ_a / σ_e + σ_m / S_u ≤ 1/n [n = factor of safety]

For preloaded bolt (σ_m ≈ 0.7 × S_y typically from F_M = 0.7 × F_proof): n = (σ_e × S_u) / (σ_a × S_u + σ_e × σ_m)

Helical coil insert (wire insert): reduces K_t at first thread → σ_e increase 15–25%

Fatigue Failure Initiation Sites

1. Thread root at first engaged thread (most common; ~65% of failures)
2. Head-to-shank fillet (if sharp radius; 15%)
3. Shank under preload (if overtorqued; unusual)
4. Under bolt head (if bending moment)

Fatigue Improvement Methods

Thread Rolling (vs. Thread Cutting)

Rolled threads: plastic deformation during rolling → compressive residual stress in root σ_residual ≈ -200 to -500 MPa at root (compressive → reduces fatigue crack growth) σ_e improvement: 30–50% increase vs. cut threads Specification: threads rolled after heat treatment (ASTM F1941 for rolling; high-strength: class 10.9, 12.9)

Surface Rolling (Head Fillet and Thread Run-Out)

Roll the fillet under the head → compressive residual stress Improvement: 20–30% in fatigue life

Thread Form (UNJ, MJ, Whitworth)

UNJ thread (aerospace): larger root radius (r_t = 0.15/TPI vs. 0.108/TPI UNC) Reduces K_t → better fatigue; MIL-S-8879 (aerospace standard) ISO metric fine thread (MJF): metric equivalent; larger root radius

Washer Selection

Hardened washers (F436): distribute load; reduce brinelling Belleville washers: maintain preload under vibration; Nordlock system

Vibration Resistance

Thread locking: thread-locking adhesive (Loctite 243); prevents loosening Prevailing torque nuts: distorted thread or polymer insert; maintains preload Castle nut + cotter pin: positive locking; aerospace applications

Torque to Preload Relationship

Standard torque-preload relationship: T = K × d × F_M [Nm; K = nut factor; d = bolt diameter mm; F_M in kN]

K values (approximate): K = 0.20 (cadmium plate or lubricated) K = 0.15 (heavy lubricant, MoS₂) K = 0.22–0.30 (plain dry; zinc plate)

Scatter in preload: ±25–30% for torque method alone → use torque + angle or direct tension indicators for critical joints

Direct tension indicators (DTI): load cell washers; elongation measurement; ultrasonic measurement for critical bolts

Tensile stress area (metric, ISO 898): A_s = π/4 × ((d₂ + d₃)/2)² [mm²] d₂ = pitch diameter; d₃ = minor diameter

Standard values (M10 ×1.5): A_s = 58.0 mm²; (M12×1.75): 84.3; (M16×2): 157; (M20×2.5): 245

Fatigue Assessment (VDI 2230 Section 7)

Allowable alternating stress amplitude: σ_a,allow = σ_A_bolt / (SF × (1 + σ_m/σ_u))

SF = safety factor ≥ 1.2 (static), ≥ 1.5 (fatigue, well-defined loads), ≥ 2.0 (fatigue, poor load knowledge)

VDI 2230 Requirement: σ_a < σ_A_bolt → fatigue safe

If σ_a exceeds → increase preload (shift operating point), reduce Φ (stiffer joint), change bolt grade

Output

Provide: compliance ratio Φ, alternating bolt stress σ_a [MPa], mean bolt stress σ_m [MPa], comparison to endurance σ_e [MPa] with safety factor, joint separation check (F_Kl > 0), recommended preload F_M [kN] and tightening torque T [Nm] (with lubricant/dry state), thread form (UNF/UNJ/MJ), rolling specification (rolled vs. cut), locking method, and applicable standard (VDI 2230, ASME B18, ISO 898-1).