Welded joints are particularly vulnerable to fatigue damage when subjected to repetitive loading. Fatigue cracks may initiate and grow in the vicinity of the welds during service life even if the dynamic stresses are moderate and well below the yield limit.

During welding process, residual stresses are created. The areas subjected to tensile residual stresses are more vulnerable to fatigue.

The relatively short fatigue life of welded joints is mainly due to three factors:

1) severe notch effect due to attachment and weld filler metal;

2) presence of non-metallic intrusions or micro-flaws or welding imperfections along the fusion line;

3) presence of large tensile residual stresses.

Fatigue of welded joints is a very complex problem. Simple calculation procedures for fatigue properties of joints cannot be formulated. This has led to fatigue life estimation procedures from fatigue test data of similar joints of the same material. This is a similarity approach. The S-N curves are obtained by numerous tests on different construction details. Statistical methods are employed to deal with scatter in experimental results. The S-N curves are classified by stress categories or detail categories. The notch effects are included in the test results in most design codes; therefore, there is no need for extra effort to handle these effects in such codes. Geometric stress concentration factors may or may not be included, depending on design codes and specific construction details.

The test results on welded specimens are usually drawn on a graph with the number of cycles N to failure on the abscissa and with the stress range delta S on the ordinate. This is why this kind of fatigue curves are called S-N curve.

### Stress Types

Different fatigue curves for different structural details require using different types of stresses. The figure below shows stress types commonly seen in fatigue life analysis for welded structures.

**Nominal stress** is the Stress in a structural member near the structural detail, obtained using simple elastic strength of material theory, i.e. beam theory. Influence of shear lag, or effective widths of sections shall be taken into account. Stress concentrators and residual stresses effects are excluded.

**Structural stress**, also known as **geometric stress**, is the value of stress on the surface of a structural detail, which takes into account membrane stresses, bending stress components and all stress concentrations due to structural discontinuities, but ignoring any local notch effect due to small discontinuities such as weld toe geometry, flaws, cracks, etc.

**Hot spot** is a point in the structure subjected to repeated cycling loading, where a fatigue crack is expected to initiate due to a combination of stress risers. **Hot spot stress** is the structural stress at the hot spot, which is the value of geometric stress at the weld toe used in fatigue verification. Its definition, and the related design fatigue curve, is not unique since different extrapolation methods exist.

**Notch stress** is the local peak stress concentration due to notch effect. **Effective notch stress** is the notch stress calculated for a notch with a certain effective notch radius.

### Fatigue Life Analysis Approaches

In practice there are three types of approaches for fatigue life analysis of welded structures:

1) Nominal stress approach. The procedure is to define one test population where the joints have very similar geometries with similar quality. The associated S-N curve for this population is then defined as a class or category.

2) Hot spot stress approach. This approach uses geometrical stress range as the key parameter to fatigue life for a given detail. This approach requires only a reference S-N curve, usually a butt weld between two plates. Other details are also applicable if influence of global geometry of the actual joint is explicitly accounted for by analytical formulas or FEA.

It should be noted that in both nominal stress and hot spot approaches, the S-N curves inherently manage the non-linear weld notch effects and statistical variability.

3) Weld notch stress approach. This is the most logical method but also the least practical approach. Due to large variances of weld toe profiles and highly localized nature of the stress concentration, the notch stresses are very hard to calculate at reasonable precision. Similar to hot spot stress approach, this method only needs a reference S-N curve of a butt welded joint between two plates where the weld bead is ground flush with the plates.

### Fatigue Curves

Fatigue resistance has been derived from an exponential relationship between the number of cycles to failure, N, and the stress range ΔS, called an S-N relationship, of the form

N = C٠ΔS^{-m}

where

N number of cycles of stress range ΔS

C constant representing the influence of the structural detail

ΔS constant amplitude stress range

m slope coefficient of the mean test results line

In the design codes, AISC 360 for example, the allowable stress range has been developed by adjusting the coefficient, C, so that a design curve is provided that lies two standard deviations of the standard error of estimate of the fatigue cycle life below the mean S-N relationship of the actual test data. These values of C correspond to a probability of failure of 2.5% of the design life.

The general relationship is often plotted as a linear log-log function

logN = logC – m٠log(ΔS)

The following is an example:

The lower limit of the line (corresponding to the low ΔS values) represents the constant amplitude fatigue limit (CAFL, or also endurance limit). This limit indicates that cyclic loading with ranges under this limit can be applied a very large number of times (>10^{8}) without resulting in a fatigue failure. For practical purposes, these numbers can be considered as infinity. Just keep in mind that infinity does not mean infinite fatigue life.

Note that CAFL does not always exist even for constant amplitude loading.

For variable amplitude loading, the CAFL no longer applies; the above fatigue curve becomes

Note that the slope, m, changed for the line segment greater than 10^{7} cycles. This is not always the case. For instance, for sea water with catholic protection a constant slope S-N curve should be used.

The most commonly adopted approach for the prediction of fatigue damage under variable amplitude loading is the use of the Palmgren-Miner summation law.

### Fatigue Improvement Techniques

Postweld fatigue improvement techniques may be used to improve fatigue life. Common techniques include grinding, TIG dressing, hammer peening, profiling, etc. These techniques improve fatigue life by improving local geometry at the weld toe, reducing stress concentrations and modifying residual stresses. Generally multiple improvement factors should not be considered for the same joint. If more than one technique is applied, only the one giving the highest improvement factor should be considered.

Weld improvement techniques may be considered as a last resort measure in new projects that can only be justified when the project is too far advanced to still enable changes to be introduced in a timely and practical manner.

### Size Effect

Fatigue performance is dependent on member thickness, the performance decreasing with increasing thickness for the same stress range.

### Weathering Steel

Weathering steel can be left unprotected in mild corrosive environments. The protective oxide layer developed on the surface of weathering steel is rougher than the surface of normal carbon steel, thus reduces fatigue strength. For this reason, EN 1993-1-9 reduces weathering steel plain member details in classes 160, 140 and 125 to the next lower category.

### Mean Stress Effect

Residual stresses in or around welds can be assumed to have magnitudes equal to the stress at which the material yields in tension. Stress variations in or around welds can hence be assumed to always range downwards from the yield strength in tension. Consequently, other than for plain steel, the mean stress and the stress ratio, R (the ratio of the minimum to the maximum stress during a cycle), of the applied stresses are inappropriate parameters to assess fatigue damage potential in welded components. For applied stresses that are less than or equal to half the yield strength, the local R value will always be greater than or equal to zero. Therefore, the stress range is universally accepted as the sole stress parameter that governs fatigue of welded components.

However, for welded connections that have been subject to post weld heat treatment or where correspondingly low residual stresses can be documented, the stress ranges may be reduced prior to the fatigue analysis depending on whether part of the stress range is tensile stress or compressive stress.

### Stress Analysis

Fatigue damage is a highly localized phenomenon. The local situation with respect to stress variations, and the local details of construction and workmanship during fabrication, have a profound effect on the fatigue life. All these features have to be taken into account in a fatigue assessment as accurately as possible if the results are to be reliable. Therefore, a fatigue analysis generally requires much more detailed models of the actions and of the structure, as well as much more refined analysis procedures than those of a strength analysis.

DN VGL-RP-C203 effective stress method uses an 1 mm radius at the weld toe to take account of statistical nature and scatter of weld shape parameters, as well as of nonlinear material behavior at the notch root. For structural steels with thickness t ≥ 5 mm, an effective notch root radius of r = 1.0 mm has been verified to give consistent results. For smaller wall thicknesses, the method has not been verified.