Fatigue Failure: Causes, S-N Curve and Prevention

Most mechanical failures in service are caused by fatigue. Rotating shafts, axles, crankshafts, springs, aircraft wings, bridges, offshore structures, pressure vessels under cyclic pressure and welded frames all experience fluctuating stresses. A part that is perfectly safe under a single static load can crack after millions of smaller cycles.

Cyclic stress parameters

For a stress cycling between σ_max and σ_min:

$$\sigma_a = \frac{\sigma_{max} - \sigma_{min}}{2} \qquad \sigma_m = \frac{\sigma_{max} + \sigma_{min}}{2} \qquad R = \frac{\sigma_{min}}{\sigma_{max}}$$

where σ_a is the stress amplitude, σ_m the mean stress and R the stress ratio. A rotating shaft under bending sees fully reversed stress (R = −1, σ_m = 0). Mean tensile stress reduces fatigue life.

Stages of fatigue failure

1. Crack initiation: cyclic slip in favourably oriented grains forms tiny intrusions and extrusions at the surface, or a crack starts at an existing defect: a notch, scratch, inclusion, weld toe or corrosion pit.
2. Crack propagation: the crack grows a small distance with each cycle, perpendicular to the main tensile stress. Growth rate follows the Paris law, da/dN = C(ΔK)^m, where ΔK is the stress intensity factor range.
3. Final fracture: when the crack reaches a critical size, the remaining ligament fails suddenly by ductile overload or brittle fracture.

The fracture surface typically shows a smooth region with beach marks radiating from the origin, and a rougher final fracture zone. The relative size of the zones indicates the stress level: a small final zone means low nominal stress.

The S-N curve

Download diagram (WebP)

Fatigue tests apply constant amplitude cycles to specimens at several stress levels and record cycles to failure. The resulting S-N (Wöhler) curve is usually plotted on log scales.

• Low cycle fatigue (below about 10³ to 10⁴ cycles) involves plastic strain and is analysed with strain based methods.
• High cycle fatigue (above about 10⁴ cycles) is mostly elastic and analysed with stress based S-N methods.
• For many steels, the endurance limit S_e′ for polished specimens is roughly half the ultimate tensile strength, up to about 700 MPa for UTS up to 1400 MPa.

The polished specimen limit is reduced for real parts by Marin factors for surface finish, size, loading type, temperature and reliability:

$$S_e = k_a k_b k_c k_d k_e \, S_e'$$

Effect of mean stress: the Goodman line

When mean stress is present, the modified Goodman criterion gives a safety factor n:

$$\frac{\sigma_a}{S_e} + \frac{\sigma_m}{S_{ut}} = \frac{1}{n}$$

Factors that reduce fatigue life

• Stress concentrations: holes, keyways, fillets, threads and abrupt changes in section raise local stress by the factor K_t.
• Surface condition: rough machining, scratches, decarburisation and corrosion pits act as crack starters.
• Size: larger parts contain more potential flaws.
• Welds: weld toes have sharp geometry and tensile residual stresses; welded joints are designed with dedicated detail categories from codes such as IIW and Eurocode 3.
• Environment: corrosion fatigue removes the endurance limit of steels; high temperature reduces strength.
• Tensile residual stress from welding or grinding.

Variable amplitude loading and Miner’s rule

Real components rarely see constant amplitude cycles. Wind, waves, traffic, machine start-ups and road roughness produce a spectrum of stress ranges. Engineers count cycles with rainflow counting and combine damage with the Palmgren-Miner rule: each block of n_i cycles at a stress level with life N_i uses a fraction n_i/N_i of the life, and failure is predicted when the fractions add up to 1. The rule is simple and widely used in codes, although load sequence effects mean real damage sums at failure can range from well below to above 1, so design codes include safety margins.

Preventing fatigue failure

• Design: generous fillet radii, gradual section changes, avoid notches in high stress areas, place holes and welds in low stress zones.
• Lower stress ranges: stiffen the structure, reduce vibration and dynamic loads, add damping.
• Surface improvements: polishing, grinding weld toes, avoiding sharp machining marks.
• Compressive residual stress: shot peening, rolling of fillets and threads, nitriding and induction hardening, discussed in heat treatment of steel.
• Materials: clean steels with few inclusions, higher strength materials where stress concentrations are controlled.
• Corrosion protection to avoid pits, as in types of corrosion.
• Inspection: periodic NDT methods to find cracks before they reach critical size, the basis of damage tolerant design in aircraft.

Fatigue failure in practice

Famous fatigue failures, from early railway axles in the 1840s to the de Havilland Comet aircraft in the 1950s, shaped modern engineering. Today, fatigue design combines S-N data, finite element stress analysis such as FEA, and realistic load spectra, applying an appropriate factor of safety. Good detailing and inspection remain the most effective defences against fatigue failure in real structures and machines.