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Fatigue is failure under repeated cyclic loading at stresses well below the static yield or tensile strength. It accounts for the majority of in-service mechanical failures. The S-N (Wöhler) curve plots stress amplitude vs. cycles to failure; ferrous materials exhibit a fatigue limit (endurance limit) below which fatigue will not occur, while nonferrous alloys do not. Fatigue failure proceeds in three stages: crack initiation at surface stress concentrations, stable crack propagation governed by Paris's Law, and final sudden fracture when the crack reaches critical size. Surface finish, mean stress, and environmental factors all strongly influence fatigue life.
Analyze a fatigue fracture surface (beach marks indicating stable propagation, rough zone indicating final overload fracture) and trace the crack origin. Then use a Goodman diagram to account for mean stress when designing for fatigue.
From stress-strain behavior, you know that stresses below the yield strength cause only elastic — fully reversible — deformation. Fatigue seems to violate this intuition: a component loaded at half its yield strength can fracture after enough cycles, even though each individual loading event appears benign. The resolution is that microscopic damage accumulates cycle by cycle in a way that is invisible at the macroscopic level. Fatigue is not a single event but the cumulative consequence of thousands or millions of tiny, irreversible damage increments.
Stage 1 is crack initiation. Even when the nominal stress is well below yield, stress concentrations at the surface can drive local stresses above the yield point. Surface scratches, corrosion pits, machining marks, thread roots, and keyways all act as stress concentrators. At these locations, tiny irreversible slip bands form during each load cycle. Over time these slip bands develop into a surface microcrack — typically tens of micrometers long. This is why surface condition dominates early fatigue life: a mirror-polished surface has far fewer initiation sites than a rough machined one. Shot peening improves fatigue life by introducing compressive residual stresses at the surface that must be overcome before tensile fatigue cracks can open.
Stage 2 is stable crack propagation. Once initiated, the crack grows by a small, predictable amount with each load cycle as the crack tip plastically blunts and re-sharpens. From fracture mechanics, you know that the stress intensity factor K characterizes the stress field ahead of a crack. The crack growth rate follows Paris's Law: da/dN = C(ΔK)m, where ΔK is the stress intensity range per cycle, and C and m are material constants. This stage leaves beach marks on the fracture surface — visible concentric bands radiating outward from the crack origin like growth rings in a tree. The spacing between beach marks corresponds to the crack advance per load block, and forensic engineers can read these marks to reconstruct the failure history.
Stage 3 is final fracture. As the crack grows, the remaining uncracked cross-section (the ligament) must carry the full load. When the crack has grown large enough that the peak stress intensity K_max reaches the material's fracture toughness K_Ic, the ligament fails suddenly. The final fracture zone appears rough and granular on the fracture surface, contrasting sharply with the smooth, banded fatigue zone — this visual distinction is the first thing a failure analyst looks for.
The S-N curve (stress amplitude vs. cycles to failure) encodes the fatigue behavior of a material. Ferrous metals (steels) show a characteristic endurance limit — a stress amplitude below which the S-N curve flattens out, meaning the material can sustain infinite cycles without fatigue failure. Non-ferrous alloys (aluminum, titanium, copper) have no such plateau: they continue to weaken with increasing cycles, which is why aircraft with aluminum structures carry mandatory retirement lives based on total cycles regardless of apparent condition. Mean stress also matters: the Goodman diagram accounts for the fact that a tensile mean stress reduces fatigue life, while compressive mean stress (from shot peening or interference fits) extends it.