Knowledge / Shipyards and production

Welded-hull fatigue: stress range, hot spots and cycle damage

Separate static strength from fatigue endurance, and read nominal stress, hot-spot stress, S–N curves and cumulative damage through worked examples.

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Fatigue in a welded hull is the initiation and growth of cracks under repeated stress changes. Remaining below yield in one load condition does not establish adequate endurance under years of cycling. Assessment combines the stress range at the correct structural detail, the cycles the vessel is expected to experience and fatigue data compatible with that stress definition.

How does hull loading reach the detail?

Wave-induced hull bending, local pressures and vibration can produce repeated loading on different time scales. Where a longitudinal member terminates at a bracket or stiffness changes sharply, the load path concentrates stress. An apparently small geometric difference can produce a different local stress fluctuation under the same overall hull load.

TWI’s fatigue explanation highlights geometric concentrations and small initiating features in welded joints. A weld accepted by non-destructive examination does not acquire unlimited fatigue life. Inspection assesses the present condition within the selected method and coverage; it does not measure the number of future loading cycles.

Stress range and amplitude are different quantities

If stress varies between 20 MPa and 80 MPa, its range Δσ is 60 MPa, its amplitude 30 MPa and its mean 50 MPa. TWI’s testing explanation describes relating endurance to cycles at a specified stress range. Entering amplitude into a curve that expects range halves the quantity the model requires.

Welding residual stresses affect the local cycle. TWI’s second fatigue note explains why nominal mean stress and higher parent-material strength do not translate into a simple endurance improvement for a welded detail. This does not make every improvement method ineffective; an improved joint needs the relevant test evidence and assessment method.

Nominal, structural hot-spot and notch stress

Nominal stress is defined from a chosen section and its overall loading. Structural hot-spot stress includes the effect of the joint’s structural geometry while excluding the very local notch peak at the weld toe. A notch approach represents that local geometry separately. The three approaches can produce different numbers; selecting the largest number for any available curve is not a guarantee of a valid conservative assessment.

TWI’s 2001 FPSO research examines matching stress definition and S–N curve for weld-toe cracking. Its dated recommendations for particular curves are not adopted here as current vessel acceptance criteria. Root cracking and plate-edge mechanisms are not automatically within the scope of a method appropriate to a weld toe on a plate surface.

Do not simply read the largest finite-element value

The ABS offshore-fatigue guide dated June 2020 describes extrapolating stress components from specified distances near the weld toe with an appropriate mesh. The highest nodal value at an idealised sharp corner can rise as the mesh is refined. A changing numerical peak does not establish an equivalent change in the physical structure’s fatigue behaviour.

To illustrate only the mathematics, take two linear stress values in the same direction and at the same load phase: 90 MPa at x = 0.5t and 70 MPa at x = 1.5t, where t is plate thickness. Linear extrapolation to x = 0 gives 1.5 × 90 − 0.5 × 70 = 100 MPa. This is not a multiaxial analysis and does not justify combining principal-stress maxima occurring at different times.

One wave does not represent a ship’s service life

A load spectrum specifies how many cycles are expected at different stress ranges. Loading condition, route, wave direction and encounter frequency affect the result. Extracting cycles from a time record and estimating them spectrally from a sea-state distribution are different evidence paths. Both must explain how external loading becomes stress at the detail.

ABS’s marine-analysis overview identifies dynamic loading and spectral fatigue as a dedicated vessel-assessment field. The service description does not validate a particular ship’s endurance. If a sea-state distribution is adopted, its relevance to the vessel’s intended service needs a separate justification.

An illustrative S–N curve and Miner calculation

Assume the teaching curve N = 2 000 000 × (60 MPa / Δσ)³, where N is cycles and the stress ratio is dimensionless. This is not a classification detail category. It gives N = 2 000 000 at a 60 MPa range and approximately 592 593 cycles at 90 MPa.

Now assume 500 000 cycles in the first range and 120 000 in the second. The linear Miner sum D = Σ(n_i/N_i) gives D = 0.25 + 0.2025 = 0.4525. D is a dimensionless model damage sum, not a 45.25% failure probability or proof of 54.75% remaining physical life. Load sequence, crack size and test scatter are not fully represented by this one number.

If every stress range increases by 10% while remaining on the same curve branch, the exponent m = 3 multiplies calculated damage by 1.1³ = 1.331. The new D is approximately 0.6023. A 10% stress change producing a 33.1% damage change illustrates why the stress definition and load model deserve careful attention.

Finding a crack changes the question

Once a crack is detected, rewriting the original S–N calculation is insufficient. Crack size and direction, potential growth, remaining section and the area accessible to inspection become important. Fracture mechanics addresses growth of an existing crack, whereas a detail-based S–N method relates cyclic endurance to a defined experimental starting condition.

An inspection interval is not a universal time from the first visible mark to inevitable fracture. Detectable crack size and subsequent loading enter the decision. A repair can also change the load path and create a new concentration nearby. Rewelding a connection does not automatically remove the effects of its geometry and service loading.

What a meaningful fatigue result must identify

A report should connect the detail location, crack mechanism, stress definition, selected curve and corrections, cycle spectrum and design duration. Numerical sensitivity should be distinguished from physical uncertainty: changing the mesh and changing the route answer different questions.

A fatigue calculation evaluates a model under stated assumptions. Acceptance needs the applicable rule, material, detail category, corrosion environment and relevant safety approach. Without those inputs, the illustrative D value neither accepts nor rejects a vessel. It shows which inputs can strongly change the calculated outcome.

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