Fatigue Life Estimator

Estimate fatigue life (cycles to failure) using Basquin's equation from stress amplitude and material constants.

Calculator

Reference Values

Typical Fatigue Exponent (b)

Steel: -0.05 to -0.12

Aluminum: -0.07 to -0.14

Fatigue Strength Coefficient (σ'f)

For steel: σ'f ≈ 1.75 × UTS

Fatigue Regimes

Low Cycle: N < 10³

High Cycle: 10³ < N < 10⁶

Infinite Life: N > 10⁶

How to Use

  1. 1
    Enter the Applied Stress Amplitude and Mean Stress

    Provide the cyclic stress amplitude (σ_a) and mean stress (σ_m), or alternatively enter the maximum and minimum stresses from which these are computed as (σ_max−σ_min)/2 and (σ_max+σ_min)/2.

  2. 2
    Select the Alloy and Surface Condition

    Choose the alloy and specify surface finish (ground, machined, hot-rolled, as-cast) and any stress concentration factor Kf, which the tool uses to compute the effective fatigue notch factor.

  3. 3
    Read the Estimated Fatigue Life

    The tool outputs the estimated number of cycles to failure using the S-N (Wöhler) curve, adjusted for mean stress via the Goodman or Morrow correction, with a safety factor assessment.

About

Fatigue is responsible for the majority of in-service fractures of metal components — it is estimated that 50–90% of all mechanical failures in service originate as fatigue cracks. Unlike static overload, fatigue failure can occur at stress levels well below the yield strength, often after years of apparently successful service, making it one of the most challenging failure modes to predict and prevent.

The AlloyFYI Fatigue Life Estimator implements classical S-N curve analysis with Goodman mean stress correction and surface finish, size, and reliability correction factors as recommended by Shigley's Mechanical Engineering Design and ASME design standards. The tool is appropriate for high-cycle fatigue (HCF) life estimation in the 10⁵ to 10⁹ cycle regime. For low-cycle fatigue analysis (below approximately 10⁴ cycles) where significant plasticity occurs, the strain-based Coffin-Manson approach is more appropriate. Engineering judgment and component testing remain essential complements to any analytical fatigue life estimate.

FAQ

What is the endurance limit and do all metals have one?
The endurance limit (S_e) is the stress amplitude below which a material can theoretically withstand infinite cycles without fatigue failure. Plain carbon and low-alloy steels exhibit a distinct endurance limit at approximately 40–50% of their ultimate tensile strength, making it a useful design target. Aluminum alloys, austenitic stainless steels, and most non-ferrous metals do not exhibit a true endurance limit — their S-N curves continue to slope downward at high cycle counts. For these materials, a fatigue strength at a specific number of cycles (typically 10⁸ or 10¹) is quoted instead of an endurance limit.
How does mean stress affect fatigue life?
A tensile mean stress reduces fatigue life by pre-tensioning the material and assisting crack opening during the tensile part of the stress cycle. The Goodman criterion accounts for this: S_a/S_e + S_m/S_u = 1, where S_a is the allowable stress amplitude, S_e the endurance limit, S_m the mean stress, and S_u the ultimate tensile strength. The Gerber parabola and Morrow relation are alternative (less conservative) mean stress corrections. Compressive mean stress is generally beneficial and can be introduced through surface treatments such as shot peening and cold rolling.
What surface treatments improve fatigue life?
Shot peening, roller burnishing, nitriding, and case hardening all induce compressive residual stresses in the surface layer, counteracting the tensile stresses that drive fatigue crack initiation. Shot peening of steel springs and connecting rods routinely doubles or triples fatigue life. Surface grinding without subsequent stress relief can introduce harmful tensile residual stresses and should be avoided in fatigue-critical components. Electroplating (hard chrome, cadmium) introduces tensile residual stresses and reduces fatigue strength; post-plating baking is mandatory for high-strength steel components to restore some of the lost fatigue performance.
What is Paris's law for fatigue crack growth?
Paris's law describes the rate of fatigue crack propagation in the stable growth regime: da/dN = C(ΔK)ᵐ, where da/dN is the crack growth per cycle, ΔK is the stress intensity factor range (ΔK = Δσ√(πa) for a through crack), and C and m are material constants. For steels, m is typically between 2 and 4. Paris's law is used in damage-tolerant design to estimate the number of cycles for a flaw to grow from an initial detected size to a critical size, establishing inspection intervals for aircraft structures, pressure vessels, and rotating machinery.
How does fretting fatigue differ from plain fatigue?
Fretting fatigue occurs when two surfaces in nominally static contact (bolted joints, press fits, splines) undergo small-amplitude relative microslip due to cyclic bulk loading. This microslip removes the protective oxide layer, generates debris, creates surface damage (fretting damage), and introduces stress concentrations from pitting and small crack nucleation at the contact edges. Fretting fatigue strength can be as low as 20–40% of plain fatigue strength. Mitigation strategies include increasing clamping force to prevent slip, applying solid film lubricants, introducing compressive residual stresses via shot peening, or using compliant inserts (e.g., rubber or copper shims) to distribute the contact stress.
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