# Mechanical fatigue

Mechanical fatigue occurs when a component is subjected to a cyclic mechanical load at a largely constant temperature. The mechanical fatigue is essentially dependent on the magnitude and number of load changes as well as the ratio of upper- and lower stress level. The fatigue strength is the maximum bearable load at which no component failure occurs for a given number of load cycles. It is determined in the Woehler test or fatigue test. Since the fatigue strength or fatigue limit is subject to statistical scattering, several test bodies per load level and stress ratios are necessary to determine it. The vibration resistance for different load amplitudes is shown in the Woehler curve, which can be divided into the following three ranges.

- LCF: low cycle fatigue
- HCF: high cycle fatigue
- VHCF: very high cycle fatigue / endurance limit

If the Woehler test is carried out to determine the fatigue strength of the real component, it is called a component based Woehler curve. If, on the other hand, the test is performed with standardized specimens, it is referred to as a material based Woehler curve. Both approaches are used in practice as a basis for the evaluation, whereby the latter corresponds to the normal case due to its more universal applicability. Since the material base Woehler curve does not take into account all aspects, such as the manufacturing influences, of the real component, this is corrected for the evaluation by corresponding influencing factors.

## LCF: low cycle fatigue

Low cycle fatigue is used when the number of oscillation cycles that can be tolerated is below 10^{4} to 10^{5}. In this range, the stress amplitudes are usually above the yield point. In addition to the corresponding material data, a non-linear structural analysis to determine the local plastic strain is required to predict the tolerable number of load cycles on the basis of numerical simulation. For this it is necessary that the sequence of load application comes as close as possible to the real conditions. In the case of complex load-time curves, it is common practice to replace the transient processes with quasistatic equivalent loads to limit the calculation times, whereby the result quality can suffer somewhat.

## HCF: high cycle fatigue

Between low cycle fatigue and fatigue strength is the range of high cycle fatigue. With double logarithmic application, the Woehler curve in this section results in a falling line.

This is the typical load range when it comes to life time prediction by means of damage calculation. Different algorithms are used to convert the load history into a representative load collective. The sequence of events is lost. For each pair of values from upper to lower stress, the associated damage is then determined and added up. Since the stresses and strains are in the elastic range, this is permissible according to the superposition principle. Depending on the complexity of the load time history and the number of load channels, the collective determination and damage calculation can mean a bigger numerical effort. There are various linear and non-linear models for damage accumulation. The most common of these, because they are easy to apply, is the "Elementary Miner Rule" or the "Modified Miner Rule".

## VHCF: very high cycle fatigue / endurance limit

Below a certain load threshold, many materials have an unlimited service life from a technical point of view. Loads below this threshold define the fatigue strength range in the Woehler diagram. The transition from high cycle fatigue to the endurance limit is between 2-10^{6} and 5-10^{6} load cycles, depending on the material.

For the evaluation of a construction with regard to fatigue strength, the procedure is basically similar to that used for the high cycle fatigue analysis. The damage accumulation only deviates from the comparison of the value pairs of upper and lower stresses with the endurance limit values of the material. However, the determination of the load spectrum remains the same. The result of this assessment is not the maximum number of load cycles that can be yielded, but a safety value in relation to fatigue strength. The pair of values that provides the smallest security is decisive. The numerical effort also depends heavily on the amount of data in the load history.