Wöhlercurve

Wöhler curve, named after German engineer August Wöhler, is a graphical representation of a material's fatigue behavior under cyclic loading. It plots the stress amplitude S against the number of cycles to failure N on a log-log scale. The curve is obtained from fatigue tests in which specimens are subjected to repeated loading at a constant amplitude until they fail, with measurements of the stress range and the corresponding N. Common test methods include axial tension-compression, torsion, and rotating bending.

Interpreting the curve, higher stress amplitudes lead to fewer cycles to failure; as S decreases, N increases. For many steels, the curve reaches a horizontal asymptote at high N, called the endurance or fatigue limit, indicating a stress below which the material can endure an unlimited number of cycles. For many other materials, no sharp endurance limit exists, and the S-N curve continues to decline with N. The relationship is often described by Basquin's law: S_a = S'_f (N)^b, a power-law fitted to the high-cycle portion.

Applications: the Wöhler curve is used in fatigue design to estimate safe stress ranges for a required life, compare materials, and assess surface finish, temperature, and environmental effects, which can shift the curve. It is sensitive to mean-stress effects; corrections such as Goodman or Gerber may be applied to account for nonzero mean stress.

History: August Wöhler conducted early experiments in the 1840s–1850s, establishing that repeated loading can cause failure at stresses below a material's static strength, foundational to fatigue theory.