About Mean Stress Corrections

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Very often, the fatigue limit is determined using rotating bending specimens, so for R=-1. If we have another stress ratio (i.e. a mean stress unequal to zero), we need to apply a mean stress correction. But why don’t we just consider the part of the cycle that is tension? If that option would work, the fatigue limit for R=0 would be half of the fatigue limit for R=-1. Even the conservative mean stress correction of Goodman is not that conservative. So apparently it is not all about the tensile part of the cycle.

It is not completely clear what the full mechanism is, but at least one aspect plays a role: slip movements in the very first stage of initiation. This occurs also during compression.

The figure below shows how the MSC looks like in a Haigh diagram. In the tension-compression region the fatigue limit decreases, but in the tension-tension region, the fatigue limit hardly decreases anymore with increasing mean stress.

In the 19^th century, Goodman and Gerber developed the first mean stress correction methods. Goodman came up with a linear correction, which was all right for brittle materials, and Gerber presented a parabolic correction, which worked rather well for ductile materials. Both corrections however had one restriction; they only worked in the tension-compression region, so with relatively small mean stress levels. In the 20^th century, Schütz presented a linear correction for -1 < R < 0, in which the gradient depends on the material. The less ductile the material, the larger gradient, which is determined by the mean stress sensitivity factor M. FKM extended the correction method to R<-1 and R>0. From the figure below it can be recognized that especially in the tension-tension region the FKM method agrees much better with reality than the Goodman and Gerber methods.

So in reality, the effect of mean stress on the fatigue limit is very small. That does explain why fatigue limits of welded and bolted joints are insensitive to changes in mean stress. In welded joints there are very large residual stresses in tension which act as high mean stress levels. The same applies to bolted joints because of the high pre-load.

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