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Fatigue Analysis Calculator — Endurance Limit, S-N Life & Safety Factor (Shigley / ASME Goodman)

Governing standard: Shigley / ASME Goodman· Shigley DE-Goodman / Gerber / Soderberg · Marin factors · Miner's rule (ASTM E1049) · Coffin-Manson LCF (ASTM E606) · Peterson notch sensitivity

The MechanixCalc fatigue analysis calculator covers the full Shigley / ASME Goodman design workflow in one tool: enter the material (Sut, Sy), the alternating and mean stresses, and the surface, size, load, temperature and reliability correction factors, and the tool returns the corrected endurance limit Se, the Goodman (or Gerber or Soderberg) fatigue safety factor, the estimated S-N life, and the Haigh diagram — all in a single pass. A dedicated stress-concentration panel interpolates Peterson Kt and Neuber Kf for shoulder fillets, circular grooves, transverse holes and keyways; Miner's linear damage rule handles variable-amplitude spectra; and Coffin-Manson covers low-cycle strain-life regimes below about 10 000 cycles.

It is built for machine-design, structural and rotating-machinery engineers who need a defensible fatigue assessment — from a quick Goodman safety-factor check to a full variable-amplitude damage sum or a multiaxial Dang Van / Crossland critical-plane analysis — and who need to hand a reviewer a standards-cited, fully worked calculation rather than a spreadsheet.

What this calculator does

  • Goodman, Gerber and Soderberg fatigue safety factor with von Mises combined bending + torsion (σ_a_eq, σ_m_eq)
  • Marin endurance-limit correction factors ka (surface), kb (size), kc (load type), kd (temperature), ke (reliability) — 40+ built-in materials
  • S-N (Wöhler) curve with Basquin slope b and operating-point overlay on the log-log plot
  • Miner's linear damage rule for variable-amplitude loading — up to six stress-range levels with per-level di = n/Nf and cumulative damage D (ASTM E1049)
  • Coffin-Manson strain-life (LCF) for low-cycle fatigue below ~10 000 cycles, with elastic/plastic separation and transition-life Nt (ASTM E606)
  • Stress concentration factor Kt/Kf interactive interpolator (Peterson/Neuber) for shoulder fillets, grooves, transverse holes and keyways
  • Multiaxial fatigue via von Mises equivalent stresses and Dang Van / Crossland critical-plane criteria; Haigh diagram; branded PDF engineering report

Method & formulas

Marin corrected endurance limit and Goodman safety factor

The rotating-beam endurance limit Se_prime is estimated as 0.5·Sut for steels (up to the 1 400 MPa cap, above which Se_prime = 700 MPa). Marin correction factors then reduce it for the real part: ka (surface finish), kb (cross-section size), kc (loading mode — bending, axial or torsion), kd (operating temperature) and ke (reliability percentile). The corrected endurance limit is Se = ka·kb·kc·kd·ke·Se_prime.

The fatigue stress-concentration factor Kf (= 1 + q·(Kt − 1), where q is the Neuber notch sensitivity) is folded into the alternating stress component. The von Mises equivalent alternating and mean stresses combine the normal and shear contributions before the mean-stress criterion is applied, so torsion loading is handled without double-counting the √3 shear conversion.

Corrected endurance limit
Se = ka · kb · kc · kd · ke · Se_prime

where Se_prime = 0.5·Sut (≤ 700 MPa); ka = surface factor; kb = size factor; kc = load factor; kd = temperature factor; ke = reliability factor

Goodman fatigue safety factor
SF = 1 / (σ_a_eq / Se + σ_m_eq / Sut)

where σ_a_eq = von Mises alternating stress including Kf; σ_m_eq = von Mises mean stress; Se = corrected endurance limit; Sut = ultimate tensile strength

S-N curve and estimated fatigue life

The S-N curve is anchored at Sf(10³) = 0.9·Sut and Se at 10⁶ cycles. The Basquin slope b = −log(0.9·Sut / Se) / log(10⁶ / 10³) defines the finite-life segment. To account for a non-zero mean stress, the fully-reversed equivalent amplitude σ_ar is computed from the chosen criterion (Goodman: σ_ar = σ_a / (1 − σ_m/Sut); Gerber: σ_ar = σ_a / (1 − (σ_m/Sut)²); Soderberg: σ_ar = σ_a / (1 − σ_m/Sy)) before reading off the S-N curve — ignoring the mean stress when looking up N_life would be unconservative.

Basquin S-N relation
Sf(N) = a · N^b for 10³ ≤ N ≤ 10⁶

where a = 0.9·Sut / (10³)^b; b = −log(0.9·Sut / Se) / 3 (log base 10); Sf = fatigue strength at N cycles

Miner's damage rule and Coffin-Manson low-cycle fatigue

For variable-amplitude loading, each stress-range block contributes a partial damage fraction di = ni / Nf,i, where Nf,i is the S-N life at the amplitude σa,i = Δσ_i / 2. Total damage D = Σdi; failure is predicted when D ≥ 1 (Miner's rule, ASTM E1049). Cycles below Se accumulate zero damage.

For low-cycle fatigue (plastic strain is significant, typically N < 10 000 cycles) the Coffin-Manson relation separates elastic and plastic strain contributions. The transition life Nt marks the cross-over from predominantly elastic to predominantly plastic failure; the total strain amplitude at 2Nf reversals is fitted by bisection.

Coffin-Manson strain-life
ε_a = (σ'_f / E) · (2Nf)^b + ε'_f · (2Nf)^c

where ε_a = total strain amplitude; σ'_f = fatigue strength coefficient; E = elastic modulus; b = fatigue strength exponent; ε'_f = fatigue ductility coefficient; c = fatigue ductility exponent; 2Nf = reversals to failure

Worked example

A machined 1040 steel shaft (Sut = 600 MPa, Sy = 450 MPa) is loaded in bending. Use fully idealized Marin factors (ka = kb = kc = kd = ke = 1.0) and no notch (Kf = 1). Alternating bending stress σ_a = 100 MPa, mean bending stress σ_m = 50 MPa. Find the Goodman fatigue safety factor.

Given

  • Ultimate tensile strength Sut600 MPa
  • Alternating stress σ_a100 MPa
  • Mean stress σ_m50 MPa
  • Marin factors ka·kb·kc·kd·ke1.0 (all idealized)
  • Fatigue stress-concentration factor Kf1.0 (no notch)

Result

  • Corrected endurance limit Se300 MPa
  • Goodman fatigue safety factor SF2.40
  1. Estimate the rotating-beam endurance limit: Se_prime = 0.5 × 600 = 300 MPa.
  2. Apply Marin factors: Se = 1.0 × 1.0 × 1.0 × 1.0 × 1.0 × 300 = 300 MPa.
  3. Apply Goodman criterion: SF = 1 / (σ_a/Se + σ_m/Sut) = 1 / (100/300 + 50/600).
  4. Evaluate each term: 100/300 = 1/3; 50/600 = 1/12.
  5. Sum: 1/3 + 1/12 = 4/12 + 1/12 = 5/12.
  6. Safety factor: SF = 12/5 = 2.40.

Illustrative example with fully idealized Marin factors (all = 1.0) and no notch. Real components have surface, size and loading corrections that reduce Se and therefore reduce SF. Verify against your actual geometry, surface finish, material certificate and load history.

Frequently asked questions

Which standard does this fatigue calculator use?

The headline Goodman / Gerber / Soderberg safety factor follows the Shigley DE-Goodman method (Shigley's Mechanical Engineering Design, §6). Marin endurance-limit correction factors follow the same framework. Miner's linear damage rule is per ASTM E1049; Coffin-Manson strain-life is per ASTM E606. Stress concentration is from Peterson's Stress Concentration Factors (3rd ed.) with Neuber notch sensitivity. The governing method and all factor values are shown in the generated PDF report.

How does the calculator handle stress concentration (notches)?

A dedicated Stress Concentration panel interpolates the geometric concentration factor Kt from Peterson chart fits for shoulder fillets, circular grooves, transverse holes and keyways. The Neuber notch sensitivity factor q (a function of Sut and notch radius r) reduces Kt to the fatigue factor Kf = 1 + q(Kt − 1). Kf is then folded into the alternating stress component before computing the safety factor, so a notched component is never reported as passing on its nominal stress alone.

What is Miner's rule and when should I use it?

Miner's linear damage rule predicts cumulative fatigue life when a component sees more than one stress amplitude — for example, a vehicle axle experiencing different load levels over its service life. Each amplitude σa,i contributes a partial damage fraction di = ni/Nf,i (where ni = applied cycles and Nf,i = S-N life at that amplitude); failure is predicted when the sum D = Σdi reaches 1.0. It is simple and widely used for preliminary design, but it assumes no load-sequence effects and no damage below the endurance limit — both are conservative approximations.

When should I use Coffin-Manson instead of the S-N approach?

The Basquin S-N curve is calibrated for high-cycle fatigue (typically N > 10 000 cycles), where strains are predominantly elastic. Below about 10 000 cycles — for example, in pressure-vessel thermal cycling, forging tools or earthquake loading — plastic strain is significant and the S-N approach over-predicts life. The Coffin-Manson strain-life relation separates elastic and plastic contributions and gives much more accurate life estimates in the low-cycle regime. In the calculator, enter the fatigue strength and ductility coefficients (σ'f, ε'f, b, c) from your material test data or look-up tables.

Is the fatigue analysis calculator free?

You can run a full calculation during a free 30-minute preview with no sign-up required. A free 14-day account trial unlocks every calculator with no credit card. The branded PDF engineering report and saved calculations are part of a paid plan.

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