Soderbergcurves

Soderberg curves refer to a fatigue design criterion used to assess components subjected to fluctuating or cyclic loading. The concept provides a simple, conservative boundary in a plot of alternating (sigma_a) versus mean (sigma_m) stress, indicating combinations that are expected to give long or infinite life.

The Soderberg criterion states that a combination of stresses is acceptable if sigma_a divided by the endurance limit S_e plus sigma_m divided by the yield strength S_y does not exceed one: sigma_a / S_e + sigma_m / S_y ≤ 1. Here S_e is the material’s fatigue limit at zero mean stress, and S_y is the yield strength. The boundary line, often called the Soderberg line, intersects the sigma_a axis at S_e and the sigma_m axis at S_y. Plotting various loading cases yields a region below the line that is deemed safe for high-cycle fatigue, with the region above representing overstress.

Compared with other mean-stress criteria, the Soderberg approach is more conservative than Goodman, since it relies on the yield strength and endurance limit rather than ultimate tensile strength. It is particularly applicable to materials with a clearly defined endurance limit and in designs where safety under fluctuating loads is paramount. Limitations include reduced applicability to materials lacking a well-defined fatigue limit or to nonuniaxial or highly variable loading states; it also assumes proportional loading and linear superposition of stresses.

In practice, engineers use Soderberg curves to inform dimensioning and safety factors in mechanical elements such as shafts, gears, and fasteners, balancing simplicity with a cautious assessment of fatigue life.