Fatigue Life Calculator

Applied Stress

Material

Goodman vs Gerber

The Goodman line is linear and conservative — it lies below the experimental scatter band for most ductile metals. Gerber passes through the middle of the data. For initial design, use Goodman. For weight-sensitive applications, verify with Gerber. Never use Gerber for cast iron or brittle materials.

Marin Factors for Corrected Se

Surface finish is usually the dominant factor. A forged part may have ka ≈ 0.5, meaning the corrected Se is half the test specimen value. Polishing, shot peening, or case hardening can increase ka toward 1.0.

Worked Example — Rotating Shaft, Steel 4340

More Worked Examples

Example 2 — Pressure vessel with pulsating internal pressure: A SA-516-70 steel vessel sees pressure cycles from 0 to 2.5 MPa roughly 10 times per day. At the head-to-shell junction, stress concentration drives alternating hoop stress from 10 to 180 MPa. σ_a = 85 MPa, σ_m = 95 MPa. Material Sut = 485 MPa, Se' = 243 MPa. Marin factors: ka = 0.85 (hot-rolled), kb = 0.9, kc = 1.0 (bending-like), ke = 0.868 (99.9%). Se = 161 MPa. Goodman n = 1 / (85/161 + 95/485) = 1.38 — marginal. Post-weld heat treatment and grinding at the junction can improve ka to 0.95, raising n to 1.53 and satisfying ASME Section VIII Division 2 fatigue check.

Example 3 — Aluminium aircraft wing spar: 7075-T6 aluminium (Sut = 572 MPa) sees 1g + gust cycles from 50 MPa to 250 MPa in flight. σ_a = 100 MPa, σ_m = 150 MPa. Aluminium has no true endurance limit — use Sf at 5×10⁸ cycles ≈ 160 MPa uncorrected. With ka = 0.75 (machined and anodised), kb = 0.95, kc = 1.0, ke = 0.814 (99.99% for flight-critical): Se ≈ 93 MPa. Goodman: n = 1 / (100/93 + 150/572) = 1 / 1.34 = 0.75 — UNSAFE. Design engineers retain 2× safety factor on top of this by reducing peak stress to 175 MPa (σ_a = 63 MPa), giving n = 1.41 but with known fatigue life only — no infinite-life assumption for aluminium.

Example 4 — Automotive connecting rod small-end, low-cycle fatigue: A 4340 steel rod small-end sees alternating tension-compression peaks of ±400 MPa for 250 million cycles over engine life. Sut = 1200 MPa, Se' = 600 MPa. ka (forged, not machined) = 0.45, kb = 0.85, kc = 1.0, ke = 0.868. Se = 199 MPa. Fully reversed: σ_a = 400, σ_m = 0. Goodman n = Se/σ_a = 199/400 = 0.50 — far UNSAFE under elastic assumption. Real connecting rods use shot-peening (ka improved to 0.85) and optimised geometry: Se rises to ~380 MPa, n = 0.95 — still requires supplemental nitriding and strict NDT. Connecting rods are a classic infinite-life application where the factor-by-factor improvements accumulate to push Se above applied stress.

Example 5 — Welded bridge connection, AASHTO Category D: A bridge girder splice welded with a partial-penetration fillet weld. For steel, AASHTO fatigue categories A through E' directly specify allowable stress range vs. cycles. Category D: for 2 million cycles, allowable Δσ = 48 MPa; for 10 million cycles, Δσ = 27 MPa. A bridge seeing 5,000 truck passes per day for 75 years sees 1.4×10⁸ cycles — past the finite-life threshold, use constant-amplitude fatigue threshold (CAFT) = 48/2 = 24 MPa. Design live-load stress range must stay below 24 MPa or the detail must be upgraded (e.g., grind-flush Category B: allowable rises to 110 MPa CAFT). This is why bridge designers obsess over fatigue-category detailing.

Common Pitfalls

• Assuming all steels have an endurance limit. Only ferrous steels and titanium show a true knee in the S-N curve. Aluminium, copper, magnesium, and most plastics have no endurance limit — stress-life decreases continuously, and designs must specify both σ and N.
• Ignoring stress concentrations. Holes, fillets, keyways, and thread roots multiply local stress by Kt = 2 to 4 typically. Fatigue notch factor Kf < Kt but is still typically 1.5 to 3. The nominal stress in the calculator must be multiplied by Kf before checking against Se, or Se must be divided by Kf.
• Forgetting mean stress effects on compression. Compressive mean stress (σ_m < 0) actually improves fatigue life (closes cracks). Goodman conservatively ignores this by stopping at σ_m = 0. For shot-peened surfaces with residual compression, use more accurate models like Smith-Watson-Topper.
• Applying Goodman to cast iron. Cast iron is brittle and shows scatter that makes linear Goodman overly optimistic for some combinations. Use Modified Goodman only with a higher safety factor (n ≥ 2), or apply Smith-Watson-Topper or strain-life approaches.
• Neglecting variable amplitude. Real loading rarely has constant amplitude. Miner's linear damage rule (Σn_i/N_i = 1) estimates cumulative damage, but is only accurate to factor of 2 or 3. Critical fatigue designs use rainflow counting and full spectrum analysis with block-loading tests.
• Using laboratory Se without Marin corrections. The uncorrected Se' = 0.5 Sut is for polished rotating-beam specimens at room temperature. Real parts have rough surfaces, larger size, different load type, temperature elevation, and reliability requirements — all of which reduce the effective endurance limit.
• Assuming infinite life means forever. Even stresses below Se accumulate damage from occasional overloads, corrosion, and minor stress concentrations. Infinite-life design requires Se-plus-safety-factor, not just Se ≥ σ_a at the nominal.

Frequently Asked Questions

What is the difference between high-cycle and low-cycle fatigue? High-cycle fatigue (HCF) occurs above ~10⁴ cycles where stresses remain elastic and S-N curves apply. Low-cycle fatigue (LCF, < 10⁴ cycles) involves plastic deformation each cycle and is characterised by strain-life ε-N curves (Coffin-Manson). Bolted joints and bridge girders are HCF; pressure vessels with thermal cycling or automotive crankshafts during each start often fall into LCF.

Why does surface finish matter so much? Fatigue cracks initiate at surface imperfections — machining marks, forging scale, mill oxide, or tool chatter. A polished specimen (ka &approx; 1.0) can have 3× the fatigue life of a forged-as-received specimen (ka &approx; 0.4 for Sut = 700 MPa). Shot-peening introduces compressive residual stress and can raise ka above the machined baseline.

How many cycles does a typical machine see in 20 years? A 1,800 RPM motor running 8 hours/day, 250 days/year for 20 years sees 1,800 × 60 × 8 × 250 × 20 = 4.3×10⁹ cycles — deep in infinite-life territory where Se governs. A 10 Hz structural component seeing intermittent loading sees on the order of 10⁶ to 10⁷ cycles — finite-life regime where the S-N curve above Se is relevant.

What safety factor should I target? For static design, n = 1.5 to 2 is common. Fatigue adds uncertainty (scatter in S-N data, mean stress effects, spectrum effects), so typical design safety factors on fatigue are n = 1.5 to 2.5 on endurance, and n = 3 to 10 on life itself. Flight-critical and code-regulated vessels often mandate n ≥ 2 on Goodman.

Can welding be infinite-life? Welded joints have residual tensile stress at the weld toe equal to yield, so mean stress is effectively Sy regardless of applied load. For welds, fatigue design uses nominal stress range (Δσ) and weld-category S-N curves (AWS D1.1, AASHTO, Eurocode EN 1993-1-9) rather than Goodman analysis on parent-metal Se. Even for Category B (best detail), constant-amplitude threshold is only 110 MPa range.

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Disclaimer

This calculator is provided for educational and informational purposes only. Fatigue analysis for safety-critical components (aerospace, pressure vessels, bridges, medical) must be performed by a qualified engineer per the applicable code (ASME, AWS, AASHTO, Eurocode, FAA). While we strive for accuracy, users should verify all calculations independently. We are not responsible for any errors, omissions, or damages arising from the use of this calculator.