Design for Fatigue

Designing against fatigue

Fatigue is progressive damage under repeated loading. A component can fail at nominal stresses below monotonic yield strength, so a static stress check alone is insufficient. Use stress histories and material/component fatigue data consistent with the intended service.

Stress description

For a uniaxial cycle, sigma_a = (sigma_max - sigma_min)/2 and sigma_m = (sigma_max + sigma_min)/2. An S–N curve describes stress amplitude versus cycles to failure for stated test conditions. An endurance limit is an idealized long-life threshold for some materials and conditions, not a universal guarantee of infinite service life. Other materials are specified by fatigue strength at a chosen life.

Worked mean-stress check

A component cycles between 100 and 400 MPa. Its corrected endurance strength S_e = 250 MPa, ultimate strength S_ut = 600 MPa and yield strength S_y = 500 MPa are given for this example.

sigma_a = 150 MPa; sigma_m = 250 MPa.

Using the modified Goodman approximation for tensile mean stress, utilization = sigma_a/S_e + sigma_m/S_ut = 150/250 + 250/600 = 1.0167. The proportional-load factor is n = 1/1.0167 = 0.9836, so it does not pass even the n = 1 Goodman long-life check. Its peak-stress yielding factor is 500/400 = 1.25. These different results illustrate why fatigue and static checks are separate.

No numerical life in cycles follows from these strengths alone. Predicting finite life requires an applicable S–N relation and a mean-stress model; an arbitrary stress-ratio power cannot supply that missing information.

Variable-amplitude loading

The Palmgren–Miner approximation sums D = sum(n_i/N_i), where n_i is the applied number of cycles in block i and N_i is the corresponding constant-amplitude life from suitable fatigue data. Nominal failure is estimated at D = 1. The rule neglects sequence effects and is approximate.

For example, 20000 cycles at a level with N_1 = 100000 plus 30000 cycles at a level with N_2 = 200000 gives D = 0.2 + 0.15 = 0.35. With subsequent cycles only at the second level, the model estimates (1-0.35)200000 = 130000 additional cycles to D = 1. This is a model prediction, not a guaranteed remaining life.

Practical checks

Account for surface condition, size, temperature, environment, reliability and notches. A fatigue stress-concentration factor K_f can differ from the elastic factor K_t. Avoid counting a correction twice. For large cyclic plastic strains use a suitable strain-life method; for an existing crack use fracture-mechanics data. Multiaxial nonproportional histories need more than a simple uniaxial Goodman calculation.

Quick check

A fully reversed cycle has sigma_m = 0 and R = -1. Miner damage is dimensionless. A stress amplitude below yield strength does not by itself establish fatigue safety.