Finite vs. Infinite Life

Let us start to have a look to the fatigue limit (also known as fatigue strength). For constant amplitude loading this is the stress amplitude that indicates the transition from infinite life to finite life. If the stress amplitude is smaller than the fatigue limit, the fatigue life will be infinite. At least, for constant amplitude loading it will be. So if you want to design for infinite life, just keep all stress amplitudes below the fatigue limit. That looks pretty straightforward, but there are some issues:

• Is there really such a thing as the fatigue limit?
• How to obtain the fatigue limit?
• How to handle variable amplitude loading?

Does the Fatigue Limit exist?

Some materials, like titanium and most steels, have a clear fatigue limit. So below that limit, the fatigue life is indeed infinite. Unfortunately, a lot of other materials (aluminium, magnesium, copper, austenitic steel) do not show a very clear fatigue limit. There is still a knick in the S-N curve at a large number of cycles (10⁶ or more), but beyond that number of cycles, the S-N is not fully flat. The curve still has a very shallow gradient. In general it is not known how far this shallow gradient continues. For aluminium, the fatigue limit is often given for 5⋅10⁸ cycles. Although steel show a very distinct fatigue limit, there are still reports of fatigue failures at very high number of cycles (10⁸-10¹⁰). This phenomenon  (VHCF: very high cycle fatigue) however seems only to occur under very specific conditions. Despite of the fact that the knick in the S-N curve of lies around 10⁶ cycles, fatigue failure may occur at larger number of cycles. Some possible causes are mentioned above. Apart from that, the size of the component may play a role as well. S-N curves are often determined using small specimens, whereas structures are often much larger. Small specimens will fail soon after initiation, but the size of large structures allow cracks to grow to a much larger length before you get final failure.

Obtaining the Fatigue Limit

To get a reasonable accurate value of the fatigue limit, tests should be done. A very common type of testing to determine the fatigue limit is staircase testing.
But often, required data can be found in literature. That data is either obtained by testing or by estimating. Testing is OK, but estimating …… Look at the graph below. It suggests that there is a relation between the fatigue strength and ultimate strength of a material. But that relation is not linear. And the relation shows an awful lot of scatter. Morevover, static strength is determined by bulk material properties whereas fatigue is largely determined by surface conditions. Estimating the fatigue limit by applying some factor on the tensile strength is just too much of a simplification. Nevertheless, it is often done, e.g. in the FKM Guidelines. If you need to do so, e.g. in case of lack of data, be very careful!

Variable Amplitude Loading

As mentioned earlier, if you want to design for infinite life, just keep all stress amplitudes below the fatigue limit. As long as even the largest stress amplitude is below the fatigue limit, life will be infinite. But was happens if some amplitudes are above and some are below the fatigue limit. It is obvious that the amplitudes above the fatigue limit will lead to a finite life. The amplitudes below the fatigue limit will not contribute to the earliest phase of initiation. But once the crack is initiated (though still very small), those small amplitudes start contributing to damage accumulation. So in case of variable amplitude loading, also cycles with amplitudes below the fatigue limit have to be taken into account.