SNcurve

An S-N curve, also known as a Wöhler curve, is a graphical representation of a material’s fatigue behavior under uniaxial cyclic loading. It plots the relationship between the cyclic stress amplitude (S) and the number of cycles to failure (N). The curve is obtained from fatigue tests that impose controlled stress amplitudes until failure, and it is used to predict life under repetitive loading.

In many metals, the curve shows that higher stress amplitudes lead to fewer cycles to failure, while lower amplitudes permit more cycles. In the high-cycle fatigue region, the data are often described by Basquin’s law, S_a = S_f' (2N)^b, or equivalently log S_a = log S_f' + b log(2N). Some ferrous alloys exhibit an endurance limit, a stress below which fatigue failure does not occur regardless of N; many nonferrous alloys do not have a true endurance limit, so the curve continues to decline with N.

Test conditions influence the SN curve. Key factors include loading mode (fully reversed or with a mean stress), specimen size, surface finish, temperature, and environment. To account for nonzero mean stress, mean-stress corrections such as Goodman, Gerber, or Soderberg are used to adjust allowable stress for a given N.

Applications and limitations: engineers use S-N curves to estimate life under cyclic loading and to guide safety factors in design. The curves are empirical and exhibit scatter due to material variability, surface flaws, manufacturing, and loading complexity. They are most reliable for the same material, heat treatment, geometry, and environment as the tested specimens and are often complemented by other fatigue models for complex or multiaxial loading.