# When do you need fatigue Life calculation

If you perform a finite element analysis (FEA), the results include stresses and strains in the structure. The accuracy of the calculation is good and the deviations from reality are - if the FEA is handled properly - small. The FEA is therefore a very reliable tool and it helps the designer to understand how a component is loaded and where the critical points are.

In case of a purely static load, you can compare the maximum calculated stresses or strains with a reasonable limit value, e.g. the yield strength. Due to uncertainties in the load assumptions, geometric deviations between model and reality, manufacturing influences, you will use a safety factor and then you can dimension purely statically.

A completely different situation exists if the structure is stressed dynamically, i.e. by a time-varying load (can also be caused by temperature change). In such a case, it is no longer the absolute value of the acting stresses that is decisive, but in particular the oscillation amplitude of the stresses and their frequency.

The following picture should explain this: A railroad axle is stressed by a bending torque resulting from the axle loads. If the axle is stationary, there is a purely static stress as with a bending beam, which can be calculated very easily.

On the upper side there is pressure, the lower side is stressed by tensile stresses. In the case of the rolling axis, the particles now alternate from the pressure side to the tension side and the number of these alternations corresponds to the number of revolutions.

The stress amplitude a material can support over a large number of cycles is much smaller than the static yield stress. Furthermore, the stress amplitude is relevant for fatigue design and not the absolute value of the stress. This means that the location of failure resulting from fatigue effects must not be identical with the location of maximum static stress. Consequently a static analysis is not sufficient for a design of a dynamically loaded part.

The stresses resulting from fatigue cause a crack on the surface which then grows into the component and reduces the area of the cross section. Depending on the number of cycles the area of cross-section becomes smaller and smaller and finally the existing area is no longer sufficient to support the loading and the part will break suddenly.

This sudden damage can lead to bad accidents and technical history is full of examples. Planes, railway vehicles, oil-platforms failed because of exceeding fatigue limits and many people lost their lives in these accidents.

The inventor of the fatigue phenomena was August Wöhler, the creator of S-N-curves, also known as Wöhler-Curves. August Wöhler (1819 – 1914) worked in the field of fatigue of railway components.

Based on his work it was possible to create a theory which is most helpful when designing dynamically loaded structures.