# When do you need Fatigue Life Calculation

When a finite element method (FEM) is performed, the results include the stresses and strains in the structure. The accuracy of the calculation is good and the deviations from reality are small when the FEM is used correctly. FEM is therefore a very reliable tool and helps the designer to understand how a component is loaded and where the critical points are.

For purely static stress, the calculated maximum stresses or strains can be compared with a reasonable limit, e.g. the yield strength. Due to the uncertainties in the load assumptions, the geometry deviations between model and reality and the manufacturing influences, a safety factor is applied and a purely static design can be performed.

The situation is completely different when the structure is subjected to dynamic stress, i.e. by a time-varying load (which can also be caused by a temperature changes). In this case, it is no longer the absolute value of the acting stresses that is decisive, but the amplitude of the stresses and their frequency.

The following figure illustrates this: A railway axle is stressed by a bending moment resulting from the axle loads. When the axle is stationary, the load is purely static, like a bending beam, and can be calculated very easily.

The upper side is stressed by compressive stresses, the lower side by tensile stresses. With the rolling axle, the particles now move from the compression side to the tension side and the number of these changes corresponds to the number of revolutions.

The stress amplitude that can be withstood by a material with a large number is much smaller than the yield strength. Furthermore, it is not the absolute value of the stress that is decisive, but the stress amplitude (or half the stress amplitude), which cannot be determined from a static calculation.

This also means that the location of the fatigue failure may no longer coincide with the location of a statically calculated maximum stress. A purely static design is therefore not suitable for physically correct recording of fatigue phenomena.

In the case of very small stresses, well below the fatigue strength, a so-called **fatigue strength verification**, which can be carried out with little effort, may be sufficient.

If the stresses exceed a critical level, they can cause a crack - usually on the surface - to propagate through the component, reducing the load-bearing area. Depending on the number of load cycles, the load-bearing cross-sectional area becomes smaller and smaller until finally, usually at a peak load, a sudden fracture occurs.

This sudden failure is characteristic of fatigue problems and can be devastating. There are many examples of this throughout the history of technology: oil platforms, railways, aircraft and automobiles are all affected.

The discoverer of these fatigue phenomena is August Wöhler (1819 - 1914), who was the first to recognise these relationships during his research work on railway axles.

The S-N curves named after him are still a useful basis for estimating fatigue life.