Principal Stresses vs. Equivalent Stresses in Fatigue

For those not too familiar with the theory of fatigue it is easy to think that equivalent stresses like Von Mises should be used for a fatigue life analysis.

This should however be avoided as an equivalent stress has nothing to do with fatigue, it is merely a calculation number to estimate the onset of yielding on macro scale in a multi-axial stress situation. Often for loading in shear a factor of (1/3)√3 is applied on the fatigue strength for tensional fatigue. This factor gives a nice estimation, but that is pure coincidence.

Fatigue damage (cracks) propagate perpendicular to the largest principal stress range, therefore this principal stress range determines the fatigue behaviour. Principal stresses in tension in other directions have hardly any influence on the crack growth as these stresses do not affect the shear stress in the activated slip planes.

In the case of shear stresses (2-D stress state with bi-axiality ratio of, or close to, -1), fatigue data for shear should be used. 3-D stress states are hardly ever relevant for fatigue, cracks always start at a free surface. Even with sub-surface initiation it can be argued that the stress state is 2-D, cracks start at inclusions or voids.

If there is a 2-D or 3-D stress state in which the largest principal stress direction varies, it is sometimes thought that using equivalent stresses is then applicable. This is still not true, equivalent stresses have no direction and certainly not a varying one. The best approach would be the “Critical Plane Approach”, i.e. analysing different crack growth directions (planes) and using for each plane the stress components (determined using the Mohr circles) perpendicular to that plane. Note that such an approach must be performed twice; and also for shear stresses.

To broaden your understanding of the theory of fatigue refer to our learning paths "Essentials of Metal Fatigue" or "Comprehensive Guide to Fatigue".

This blog was curated by Johannes Homan from Fatec Engineering.