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# How to Predict Fatigue Life of Welded Structures

January 30, 2015 By: Michael Bak

It is well known that structures with welds are susceptible to failure from repeated loadings, caused by the initiation and growth of cracks in the welds. There are several reasons why welds can be life-limiting:

1.    Weld material is more brittle than the parent material.
2.    Weld geometry contains local discontinuities that are sources of high local stress.
3.    Welds can contain voids and cracks that act as the initiation points for failure.
4.    High tensile residual stresses are present from the welding process.
5.    Welds are often located in locations of sharp section change.

Based on all of these factors, predicting the fatigue life of welded structures can be a challenge. However, a significant amount of research has been performed on this topic, and welding codes and standards have been developed that describe procedures to address the life prediction of welded structures. All of the welding standards describe two main steps:

1.    The weld stress calculation method.
2.    The associated S-N fatigue curve. (Stress range vs. cycles to failure, plotted on a log-log scale).

There are three main weld stress calculation methods, illustrated in the figure below. The nominal stress approach represents the simplest method and consists of dividing the far-field forces going through the welded joint by the representative weld area to provide a nominal, averaged stress. The structural stress or hot-spot stress approach extrapolates the near-field stresses to obtain the stress at the weld toe. The notch stress method uses specific, idealized weld geometry to obtain the local weld stress at the weld toe or root.

Note that the nominal stress method is often performed as a hand calculation, although finite element analyses can be used to extract far-field loads. The hot-spot stress method is usually performed using finite elements, with weld standards often specifying the locations where the stress should be obtained and linearized for extrapolation to the location of the weld toe. An example taken from weld specification EN-13445-3 is shown in the figure below. Note that the local weld geometry detail is not required in the nominal or hot-spot methods, i.e. smoothing out the sharp corners at the weld toe is not required. The notch stress approach requires more detailed modeling of the weld region by specifying fillet radii at the weld toe and root locations so that a non-singular local stress can be obtained.

Once the weld stresses have been determined, they can be used to estimate fatigue life.  Depending on the stress calculation method, correlated S-N curves are used.  For steel welds, the fatigue curves have the following characteristics:

1.    The S-N curve is assumed linear on the log-log plot, with a slope of -1/3.

2.    Based on the stress calculation method, this curve is shifted up or down, as specified by the weld standard.

3.    Typical designations of the weld curves are FATxxx, where xxx is the stress range in MPa that causes failure at a specified number of cycles, typically two million cycles.  The FAT225 curve, used in the notch stress method, is shown in the figure below.

4.    For cycles greater than two million, the curve can either flatten out (defining a true endurance limit), or a shallower slope is specified. In the example below, a slope of         -1/22 is used after ten million cycles.

5.    The stress range is used to predict life, and mean stress effects (i.e. cyclic loads that are not fully reversible) are typically ignored. Mean stress effects have been found to have little effect on the fatigue life of welds, most likely due to the high residual stresses in the welds that wash out this effect.

Look for future posts that will provide more detailed information on evaluation of life of welded structures in fatigue, including information on the individual methods, how to handle multiple cyclic loads, variations in S-N material data, and extension to weld fatigue from vibration. If you perform life prediction of welded structures and want to share some of your engineering analysis tips, please do so in the comments!