Welded-Joint Fatigue Calculator

Estimate constant-amplitude fatigue life for a welded steel detail using either a stress-amplitude S–N model or a Eurocode-style stress-range model.

Engineering screening tool—verify inputs and results independently. Use at your own risk.

Inputs

Choose the model that matches your stress convention and detail parameter.

Fatigue strength parameter KMPaPositive S–N reference stress at Nₖ = 10⁷ cycles; use the classified weld-detail value.Fully reversed stress amplitude SᵢMPaPositive alternating amplitude, not peak-to-peak range. Tension/compression sign is removed after amplitude formation.

Estimated fatigue life

Cycles to model limit—— million cycles

S–N slope m—dimensionless

Regime—selected branch

Threshold—MPa

Reference—cycles

Convention check: for a fully reversed uniaxial cycle, stress range is normally twice stress amplitude. Do not enter the same number in both modes unless that is physically intended.

Stress-cycle interpretation

The selected detail curve maps one constant stress measure to an estimated cycle count. Weld toe geometry, residual stress, quality, thickness, environment, and spectrum loading require separate engineering treatment.

How to use

Select Stress-amplitude S–N only when the available cyclic stress is a fully reversed amplitude Sᵢ and the weld-detail parameter is K. Select Eurocode stress-range when the available value is the maximum-minus-minimum range ΔσR and the classified detail is ΔσC.
Enter each required positive stress in MPa. Accepted input is greater than 0 and no more than 10,000 MPa; this software range does not make an unrealistic stress valid.
Confirm the stress convention, weld-detail classification, nominal/hot-spot method, and any required code corrections before calculation.
Press Calculate or edit a field to update the result. Press Reset to restore the stress-amplitude example K = 45 MPa and Sᵢ = 100 MPa.
Read the canonical result as cycles to the model limit. The slope, branch, and threshold values show which S–N segment produced it.
Treat Not finite only as “below this simplified model’s endurance/cutoff threshold.” It is not proof of unlimited life and does not remove corrosion, defects, variable loading, inspection, or fracture risk.
Do not use this calculator for load spectra, cumulative Miner damage, low-cycle strain fatigue, multiaxial weld assessment, crack-growth/fracture mechanics, or code certification.

Worked example

Choose Eurocode stress-range.
Enter ΔσC = 80 MPa and ΔσR = 50 MPa.
The model gives ΔσD = 58.94 MPa, ΔσL = 32.38 MPa, m = 5, and NR = 11.385 million cycles.
Interpretation: 50 MPa lies between the constant-amplitude and cutoff limits, so the m = 5 branch controls. A design assessment must still apply the governing edition’s factors and detail rules.

Equations used

Stress-amplitude S–N mode

Inputs are fatigue strength parameter K [MPa] and positive fully reversed stress amplitude Sᵢ [MPa]. The endurance threshold and fixed reference counts are:

Sₑ = 0.55K; Nₖ = 10⁷ cycles; Nₑ = 2 × 10⁸ cycles.

The implemented branch slope is m = 3 for Sᵢ ≥ K, m = 5 for Sₑ ≤ Sᵢ < K, and not finite for Sᵢ < Sₑ. For either finite branch:

Nᵢ = Nₖ(K/Sᵢ)ᵐ.

Eurocode stress-range mode

Inputs are positive detail category ΔσC [MPa] and applied nominal stress range ΔσR [MPa]. The intermediate limits are:

ΔσD = (2/5)^(1/3) ΔσC; ΔσL = (5/100)^(1/5) ΔσD.

With ND = 5 × 10⁶ cycles and NL = 100 × 10⁶ cycles, m = 3 for ΔσR ≥ ΔσD, m = 5 for ΔσL ≤ ΔσR < ΔσD, and not finite for ΔσR < ΔσL. For either finite branch:

NR = ND(ΔσD/ΔσR)ᵐ.

Calculations use unrounded intermediates. In the Eurocode mode, the two stress limits are displayed to whole MPa and life to 0.001 million cycles.

Theory and method

These equations describe idealized piecewise S–N curves: a log–log straight line with slope m = 3 above the knee and m = 5 below it, followed by a threshold branch. K and ΔσC are classification parameters, not measured material ultimate strengths. Sᵢ is an amplitude; ΔσR is a range. All values are positive magnitudes, so tensile/compressive sign is resolved when the amplitude or range is formed.

The calculation assumes one constant-amplitude stress measure and a correctly selected weld-detail class. It omits mean-stress and residual-stress corrections, thickness and size effects, stress concentration/hot-spot derivation, variable-amplitude damage, weld quality and inspection reliability, environmental degradation, thermal cycling, multiaxial loading, plastic strain, and crack propagation. The threshold branch must therefore be treated as a model limit—not guaranteed infinite service life.

References: EN 1993-1-9, Eurocode 3: Design of steel structures — Fatigue; NEN 2063 as cited with the stress-amplitude relation. Confirm the current governing edition and national annex. See the European Commission JRC Eurocode 3 overview.

Continue in TriboSolver when the stress history, geometry, contact loads, or coupled simulation should be refined and independently checked.