Fatigue

Bend a metal paperclip back and forth a few dozen times and it snaps — even though a single bend, however hard, would barely mark it. That's fatigue: a component can fail after enough repeated loading even though it would never fail under the same peak stress applied just once.

Failure below the static strength

Fatigue is the progressive weakening and eventual failure of a material subjected to repeated (cyclic) loading, at stress levels that can be significantly below the material's static ultimate tensile stress — or even below its yield stress. This is the central, counter-intuitive fact this lesson exists to teach: everything covered so far in this topic (Young modulus, elastic and plastic deformation, the stress-strain graph, ductility) describes how a material responds to a load applied once. Fatigue shows that repeatedly applying and removing a load — even one well within the range the material can comfortably withstand statically — can eventually cause failure anyway.

How fatigue failure develops

Fatigue failure develops in stages, driven by microscopic crack growth rather than uniform overload of the whole cross-section:

• Crack initiation. A microscopic crack begins to form, almost always starting at a point of stress concentration — a surface scratch, a sharp corner, a small manufacturing flaw, a hole, or any other geometric feature where stress is locally much higher than the average stress across the component (the physics of why this happens is covered in the next lesson, on fracture).
• Crack growth. With each subsequent loading cycle, the crack grows very slightly — often by a barely measurable amount per cycle — as the repeated stress at the crack tip pulls the material apart microscopically, cycle after cycle.
• Sudden final failure. As the crack lengthens over many cycles, the remaining unfractured cross-section carrying the load steadily shrinks. Eventually, that remaining cross-section becomes too small to support the applied load, and the component fails suddenly — often abruptly, even in a material that would otherwise be considered ductile, since the crack has already done much of the work of separating the material before final failure occurs.

The fatigue (S-N) curve

A material's fatigue behaviour is typically characterised using an S-N curve: the number of cycles to failure ($N$) plotted against the applied stress amplitude ($S$). In general, these curves show that fewer cycles are needed to cause failure as the stress amplitude increases — a component cycled at high stress fails after relatively few cycles, while one cycled at lower stress can withstand many more before failing.

Some materials, notably many steels, show a fatigue limit (or endurance limit): a stress amplitude below which the material can withstand an extremely large — for practical engineering purposes, effectively unlimited — number of cycles without fatigue failure. Below this stress, the S-N curve flattens out to a roughly horizontal line. Other materials, notably most aluminium alloys, show no true fatigue limit: their S-N curve continues to slope gradually downward indefinitely, meaning that, in principle, fatigue failure will eventually occur at any non-zero cyclic stress amplitude given enough cycles, however small that stress is.

Real engineering context

Fatigue is a dominant design consideration wherever components experience continuous or repeated cyclic loading over their working life:

• Aircraft structures — wings and fuselage panels flex with every takeoff, landing, and gust of turbulence, accumulating loading cycles throughout the aircraft's operational life.
• Engine components — crankshafts and connecting rods in an engine undergo millions of loading cycles as the engine runs, making fatigue resistance central to their design.
• Bridges — repeated traffic loading, cycle after cycle over decades, subjects bridge structures to fatigue conditions quite different from a single static load test.
• Rotating machinery — shafts, gears, and bearings in continuous rotational service experience constant cyclic stress as they turn.

All of these are specifically designed and routinely inspected with fatigue life in mind — using S-N data, careful attention to avoiding stress concentrations, and scheduled inspection for the microscopic cracks that fatigue produces long before final failure would otherwise occur.

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