Ask a steel fabricator how long a welded frame will last and you get a shrug. Ask a fatigue specialist the same question and you get an S-N curve, a weld class, a mean stress correction, and a lecture on why your calculation is wrong. The truth, on the machines I have worked on, is that welded fatigue is the difference between a frame that rattles harmlessly for a decade and one that develops a crack at the foot of a gusset after a season. This article is about estimating weld fatigue life with S-N curves the way they actually behave in non-standard machinery, without pretending the numbers are exact.
1. Why Welds Fail Before the Parent Metal
A welded joint is a stress raiser with a built-in defect: the weld toe. The geometry of the weld toe, the transition from the weld metal to the parent plate, concentrates the stress with a factor that depends on the weld profile, the plate thickness, and the loading direction. The parent metal rarely sees the full fatigue story; the toe sees a local stress several times the nominal, and that is where cracks start.
My blunt description for a young designer: a weld toe is a scribe mark the parent metal promises to fail along. You are not designing the weld, you are designing the geometry that keeps the toe stress low.
The other factor is the residual stress. Welding leaves the joint in tension at the toe, so the local mean stress is already high even when the applied load is completely reversed. That is why welded joints are so bad in fully reversed loading and why the S-N approach for welds is built on stress range rather than amplitude.
This changes the entire analysis philosophy. For unwelded metal you track the alternating stress and mean stress separately. For welds you track the stress range delta sigma, because the mean stress is dominated by the residual state and you cannot reliably separate it at the toe.
2. S-N Curves and the Weld Class System
The S-N curve for a weld family is a line on a log-log plot that relates the nominal stress range to the number of cycles to failure, and the family is identified by its FAT class, the fatigue class number at two million cycles. A higher FAT number means a better detail: a longitudinal fillet loaded along its length might be FAT 100, while a transverse attachment weld on a plate edge can drop to FAT 40 or less. These classes come from a century of test data, codified in standards like the IIW recommendations, and they are the honest basis for life estimation.
The slope of the S-N line for welded joints is typically near 3 in the high cycle region, meaning if you double the stress range the life drops by roughly a factor of eight. That steep sensitivity is the reason weld fatigue feels unforgiving, and it is also the reason small changes in weld detail have a huge effect on life. Improving the toe radius or grinding the weld toe is often worth more than switching to a higher grade steel.
| Detail / Weld Type | FAT Class (IIW) | Remarks |
|---|---|---|
| Longitudinal fillet weld | About 100 | Loaded along weld length |
| Transverse butt weld | About 80 | Full penetration, dressed |
| Attachment weld (loaded) | 50 to 70 | Gusset on loaded member |
| Cover plate end weld | About 40 | Sharp toe, high stress |
The table is a rough memory aid, not a design standard, but it gets the scale right, and the scale is what most newcomers miss. People imagine the welds are all similar because they all look the same in the shop. They are not, and the FAT class captures how different they are.
3. The Stress You Actually Need: Nominal, Hot Spot, Notch
Before you multiply anything, decide which stress you are going to feed into the S-N curve, because the fatigue method changes the required stress definition. The nominal stress method takes the stress in the parent plate away from the weld, applies a mechanical stress concentration factor, and uses the FAT class for the detail. It works for simple joints where the nominal stress is well defined.
The hot spot stress method is the one I reach for on real fabrications where the load path is three dimensional. You extrapolate the surface stress from two points close to the weld toe back to the toe, capture the local geometry effect, and compare against a hot spot FAT class around 90 to 100. It needs a fine enough mesh and a disciplined extraction procedure, and it gives a fairer result on complicated frames than the nominal method ever will.
sigma_hs = extrapolated surface stress at the weld toe, compared against a hot spot FAT class of about 90 to 100 for butt welds, with a mesh refinement check before you trust the number.
The notch stress method resolves the weld toe radius explicitly with a reference radius, typically 1 mm for steel, and gives the most accurate but by far the most demanding result. On non-standard machinery I use it rarely, only when a critical joint is right at the edge of the acceptance band and the cost of being wrong is a recall. For everything else, hot spot stress with a fine local mesh is the working tool.
Honestly, the biggest error I see is meshing the whole frame with 5 mm shells and then quoting a hot spot stress number. The number is meaningless if the mesh cannot resolve the stress gradient at the toe. Check the two-poster regression against converged values before you build anything on the result.
4. Life Estimation for Welds: A Simple Working Sequence
Here is the sequence I actually use on a welded frame, and it fits on one page. First, get a reasonable stress range for the detail from the FE model or from hand calc at the critical cross section. Second, pick the appropriate FAT class from the standard for the weld detail and loading direction. Third, with the S-N slope m near 3, compute the life for the constant amplitude case.
For a non-constant spectrum, and every real machine has a spectrum, you can apply the Miner linear damage rule. Break the stress range history into bins of stress range and cycle count, compute the damage fraction for each bin with the S-N curve, and sum the fractions. When the total reaches one, the detail is at the end of its estimated life.
D = sum_i ( n_i / N_i ), and the detail is spent when D reaches 1.0. n_i is the number of cycles at stress range bin i, and N_i is the allowable cycles from the S-N curve at that range.
The sequence sounds simple, and the hard parts are the three assumptions nobody writes down. The stress range must include the full dynamic range, not the amplitude, because welds track range. The FAT class must reflect the actual weld quality, so if the workshop grinds the toe or leaves it ragged, the class changes. And the spectrum you measure today must represent the future operation, which on a machine that is repurposed every six months is a guess with a long tail.
I double the calculated damage for the worst-case detail as a practical safety factor and misalign it slightly to see if the ranking of critical details changes. If the ranking is stable, the design is healthy; if a small perturbation moves the critical joint somewhere else, the frame has several details all at the same risk, and that is worth knowing early.
5. Improving the Detail Instead of Arguing With the Curve
The most valuable direction in weld fatigue is not a more accurate calculation, it is a better detail. Once you understand S-N behavior, a whole list of practical improvements opens up. Grinding the weld toe to a smooth radius moves the geometry up a FAT class; peening the toe introduces beneficial compression; and changing a transverse attachment to a longitudinal one can double the life. On machines I have built, toe grinding has fixed more fatigue problems than any plate upgrade.
The detail design starts on the drawing. Avoid welding a stiffener across the tension face of a loaded member, keep weld starts and stops away from the highest stressed region, and let the load path run long and straight instead of through a cluster of gussets. When you must attach, aim the load along the weld, not across its toe.
If the boss will not approve a toe-grinding allowance on the drawing, buy a bigger mop or expect a phone call when the first crack turns up. The geometry is decided at the drafting table, not in the fatigue report.
6. A Shop-Floor Case: The Gusset That Cracked at 12 Million Cycles
Let me put numbers on it. A conveyor support frame, S355 plate, had a gusset welded at the end of an 80 mm wide flange carrying a reversing load with a measured nominal stress range of about 40 MPa at the attachment. The weld detail was a plain transverse fillet, and the first inspection plan expected about 20 million cycles before any crack was a concern, which several people on the project accepted because the load was low and the steel was structural.
The frame cracked at the gusset toe just past 12 million cycles on the fatigue rig, and the test report proved what the class table would have told us earlier. For a transverse loaded attachment, FAT 63 for a poorly dressed fillet puts the allowable stress range at two million cycles well below 40 MPa, so running the full range for twelve million cycles was asking the toe to survive well past its class. Verify the class before you promise the inspector a life, and the multiplier in a nameplate years figure hides the class reality underneath.
We fixed it by grinding the toe, moving a second gusset back from the corner, and adding a small radius. The follow-up test passed at 25 million cycles with the same load, and the change cost an afternoon in the shop. That, more than any formula, is the story of weld fatigue: it is managed with geometry, not surprised with calculations.
7. The Practical Takeaways I Hand Out
Summing up what I actually carry out of a fatigue meeting, there are five lines that I give to the draftsmen and the welding engineer, and they fit on the back of an envelope. Count cycles in stress range, not amplitude, because that is what the weld class responds to. Do not bless a detail onto the pad of paper until you can name its FAT class from the standard, because if nobody can, it is likely worse than you hope. Keep the weld toe out of the highest loaded corner by moving attachments and adding radii before the analysis ever runs.
And the last two are about people. Tell the workshop which joints are critical and why, because a good welder will gladly grind a toe if they know it is the difference between a call-back and a clean field test. Then treat a fatigue crack as data, not a failure: every crack on a welded machine carries the message of which detail drew the load, and logging the cracks instead of hiding them turns the whole fleet into a fatigue test you never paid for. The S-N curve does the math; the habit loop is what actually protects the machine.
