Material Fatigue: Why Things Break Under Repeated Loading

Three stages of a fatigue failure

Fatigue proceeds in three stages. Initiation comes first: repeated cyclic slip at the surface or at sub-surface defects forms persistent slip bands that create microscopic intrusions and extrusions, providing nucleation sites for a crack — this stage alone can consume 60-90% of the total fatigue life. In crack propagation, a micro-crack grows a little further with each cycle, leaving a visible "beach mark" on the fracture surface; growth rates in metals typically run 10⁻⁸-10⁻³ mm per cycle. Final fracture happens abruptly once the crack reaches a critical size and the remaining cross-section can no longer carry the load — the classic post-fracture surface shows a smooth beach-marked fatigue zone next to a rough, granular overload zone.

S-N curves and the endurance limit

August Wöhler developed systematic fatigue testing in the 1860s on railway axles after several catastrophic failures, and his S-N diagram — stress amplitude against cycles to failure, on a log-log scale — remains the fundamental engineering tool. For a typical steel, stress amplitude might fall from ~800 MPa at 10³ cycles to ~350 MPa by 10⁷ cycles, where it levels off at the endurance limit: ferrous metals have a true fatigue limit, roughly 0.4-0.5 × their ultimate tensile strength, below which they can in principle survive forever. Aluminium alloys have no such floor — they will eventually fail at any stress level, so they are designed for a finite life instead.

The Paris law: predicting crack growth

Once a crack exists, Paul Paris's 1963 power law describes how fast it grows per cycle as a function of the stress intensity factor range ΔK:

da/dN = C · (ΔK)^m

ΔK = K_max − K_min = Δσ · Y · √(πa)
For many structural steels: C ≈ 10⁻¹², m ≈ 3
For aluminium alloys:       C ≈ 10⁻¹¹, m ≈ 3–4

Below a threshold ΔK_th the crack simply doesn't grow; above it, growth follows the Paris law until K reaches the material's fracture toughness K_IC and the part fails catastrophically. Integrating the Paris law from an initial detectable crack size to that critical size predicts remaining fatigue life — the basis of modern damage-tolerant design, where inspection intervals are scheduled before a crack can reach K_IC.

Notches, stress concentration and the Comet

Holes, fillets and surface defects amplify local stress — a circular hole in an infinite plate can raise it by a factor K_t = 3. The world's first commercial jet airliner, the de Havilland Comet, suffered three catastrophic fatigue failures in 1954: its square window corners acted as severe stress concentrations, and repeated cabin pressurisation cycles grew cracks from rivet holes near those corners until the fuselage failed. That accident established the modern practice of rigorous full-scale fatigue testing for aircraft certification, and it remains the textbook example of why generous fillet radii and polished surfaces — not sharp corners — are the first line of defence against fatigue.

Frequently asked questions

Try it live

Everything above runs in your browser — open Microcracks (Paris Law), pick a material preset, and watch a crack creep along its meandering path before snapping catastrophically once K_max reaches the fracture toughness K_IC.