Fatigue Life Calculator

Fatigue failure occurs when a material fractures under cyclic (repeated) loading at stress levels well below the static ultimate tensile strength. The material develops microscopic cracks that grow with each stress cycle until sudden fracture occurs. Fatigue is responsible for the majority of mechanical and structural failures in service. It is characterized by the number of cycles to failure (N) at a given stress amplitude (S) on an S-N curve.

The Basquin power-law equation relates stress amplitude (Sa) to cycles to failure (N): Sa = sigma_f x (2N)^b, where sigma_f is the fatigue strength coefficient and b is the fatigue strength exponent (Basquin exponent). Alternatively in the form N = (Sa / C)^(1/m), where C and m are material constants. For steel: typical b = -0.085 to -0.12; for aluminum: b = -0.10 to -0.15.

The endurance limit (Se) is the stress amplitude below which a material can theoretically withstand infinite cyclic loading without fatigue failure. Ferrous metals (steel) typically have a well-defined endurance limit at approximately 0.5 x Ultimate Tensile Strength (UTS), with maximum of 100 ksi for steels and 30 ksi for cast iron. Nonferrous metals (aluminum, copper) do not have a true endurance limit; their strength continues to decrease with increasing cycles.

The Goodman diagram (modified Goodman criterion) accounts for the effect of mean stress on fatigue life. When both alternating stress (Sa) and mean stress (Sm) are present: Sa/Se + Sm/Su = 1, where Se is the endurance limit and Su is the ultimate tensile strength. Points below the Goodman line are predicted to have infinite life; points above predict finite fatigue life. Tensile mean stress reduces fatigue life; compressive mean stress increases it.

Safety factors for fatigue design are typically higher than for static design due to the sensitivity of fatigue to stress concentrations, surface finish, environment, and scatter in test data. ASME Boiler and Pressure Vessel Code uses safety factors of 2 on stress amplitude and 20 on cycles. Structural engineering generally uses safety factors of 2-4 on stress for fatigue-critical details. Detail categories (AISC Table A-3) provide allowable stress ranges for bridge and building steel structures.