CAE Simulation & Solutions

Maschinenbau Ingenieurdienstleistungen GmbH

Technical Office for Engineering Services

# Finite Life Fatigue Strength

In the 19^{th} century the German engineer August Wöhler found out, that alternating loads were more dangerous for structures than constant loads of the same magnitude. The characteristic parameters hereby are the stress range or the stress amplitude (= half the stress range) and the number of load cycles. In general an increase of the stress amplitude results in a decrease of the number of load cycles leading to crack initiation. This effect can be illustrated in a logarithmic diagram as the so called S-N-curve or in German the Wöhler curve with the inclination k (see figure: S-N-curve). For a given stress amplitude, the according load cycle number for critical damage and a fatigue crack can be found. In this context damage describes the ratio between the service load cycle number n_{i} and the permissible value N_{i} (see figure). Damage increases proportional to the number of load cycles. When reaching the value of 1.0 a crack will appear with the same probability the S-N-curve is based on.

Finite life fatigue strength or maybe more precisely variable amplitude fatigue strength describes the resistance of a structure under consideration of realistic load histories. The shape of the stress spectrum plays an important role, defining stress ranges or stress amplitudes and their number of load cycles. From measured data or MBS simulations load histories can be defined. With the help of Finite Element simulations stress histories can subsequently be derived. Using procedures such as rainflow counting finally a stress spectrum can be defined. These spectra usually consist of a larger number of steps each defined as stress amplitude and number of cycles. In the figure below a stress spectrum with two steps is shown (s_{a1}, n_{1} und s_{a2}, n_{2}). With the help of a representative S-N-curve the partial damage of each step can be calculated.

Some codes also include a so called Cutoff threshold. Stress amplitudes below Cutoff don’t have to be taken into account with respect to damage. This value is comparable to the threshold stress value for crack growth under cyclic loading. Even an existing small crack will not continue to grow below this threshold. This cutoff value is generally lower than the fatigue strength of the material.

In many mechanical engineering applications the stress amplitude decreases with increasing number of load cycles. In some cases a constant amplitude stress spectrum is of interest.

*Figure: S-N-Curve*

Using an accumulation rule, in the simplest case Miner’s linear damage accumulation rule, the total damage can be calculated and predictions on the possible number of load cycles until failure can be made. These estimates are again based on the probability of survival of the S-N-curve.

Finite life fatigue strength has usually to be considered as soon as the number of load cycles exceeds approximately 10000. This value depends on the design code used. Up to this cycle number the strength assessment can mostly be performed as for static loading. Nevertheless cyclic yielding is not allowed, even at very low cycle numbers. If cyclic yielding is involved, low cycle fatigue is an issue and special strain based methods are needed to deal with this problem.

The software LIMIT includes various design codes and guidelines for different types of proof of strength. All previously mentioned assessment types are available:

- - Finite life fatigue strength / variable amplitude fatigue strength
- - Static strength
- - Infinite life fatigue strength