Most parts that fail in service don't break from a single overload — they break from fatigue, cracking slowly under loads well below their static strength, cycle after cycle. A shaft happily carrying its load can crack after a few million rotations. Designing against fatigue is a different mindset from designing against yield.
Alternating vs mean stress
Split any cyclic load into two parts: the steady mean stress σ_m and the fluctuating alternating stress σ_a. Fatigue is driven mostly by σ_a — the back-and-forth is what grows cracks — while σ_m has a smaller, secondary effect. This is why a preloaded bolt (high mean, low alternating) survives so well.
The endurance limit
For steels there's a stress below which the part can, in principle, cycle forever: the endurance limit, roughly half the ultimate tensile strength for a polished lab specimen. Real parts are worse, so we knock it down with Marin factors for surface finish, size, load type, temperature and reliability. Aluminium, notably, has no true endurance limit — it keeps weakening, so it's designed to a finite life. Run the numbers on the Fatigue tool.
Stress concentrations start the crack
Fatigue cracks almost always begin at a stress raiser — a hole, a fillet, a sharp corner, a keyway, even a machining mark. A plain round hole triples the local stress. The geometric factor is K_t (see the Stress Concentration tool); the fatigue notch factor K_f is a bit lower but still punishing. The single best fatigue improvement you can make is usually to round off a sharp corner.
Designing against it
Use a mean-stress criterion — Goodman (common), Soderberg (conservative) or Gerber — to get a safety factor from σ_a, σ_m and the corrected endurance limit. Generous fillets, good surface finish, compressive residual stress (shot peening) and keeping stress raisers out of high-stress regions all buy fatigue life cheaply.