The Discovery of Fatigue
In the 1840s, railway axles began failing catastrophically after years of service — at stress levels well below the material's static strength. August Wohler systematically investigated this phenomenon, subjecting specimens to millions of loading cycles and recording when they broke. His resulting S-N curves revealed that cyclic loading at stresses far below yield could cause failure, and that below a certain stress level (the endurance limit), steel specimens survived indefinitely. This discovery founded the field of fatigue analysis.
The S-N Curve Anatomy
A typical S-N curve for steel shows three distinct regions. The low-cycle fatigue region (N < 10³) involves plastic deformation and high stresses near yield. The finite-life region (10³ < N < 10⁶) follows the Basquin power law on log-log axes — a straight line whose slope (exponent b) characterizes the material's fatigue resistance. The endurance limit region (N > 10⁶) shows a horizontal asymptote where the curve flattens, indicating stresses below which fatigue failure theoretically cannot occur.
Modifying Factors
The laboratory S-N curve must be modified for real components. Surface finish, size, reliability, temperature, and loading type all reduce the effective endurance limit. A component with rough machining (kₛ = 0.5), large diameter (k_size = 0.7), and elevated temperature might have an effective endurance limit only 20-30% of the laboratory value. These modification factors, tabulated in design handbooks, are essential for conservative engineering design.
Beyond the Wohler Curve
While the S-N approach remains the standard for high-cycle fatigue design, modern fatigue analysis has expanded significantly. Strain-life methods (Coffin-Manson) handle low-cycle fatigue with plastic deformation. Fracture mechanics (Paris law) tracks crack growth from initial defects. Probabilistic approaches account for the large scatter inherent in fatigue data. Statistical analysis of S-N data using Weibull or log-normal distributions provides reliability-based design criteria for critical applications.