# Basics of fatigue strength

The basics of fatigue strength has set out in detail, including the schema in the lower part of Figure HAIBACH. This will serve hereafter to illustrate the essential relationships in the fatigue strength.

Based on the stress-strain curve of the material (a) the tensile strength R_{m} and yield strength R_{e} are shown as the upper limit values of the stress. In line with the overall maximum stress proof the unique exceeding the tensile strength would mean a failure of the component.

The fatigue strength of S_{D} provides a stress value, up to which an oscillating stress (b) as often as is bearable without breaking. A oscilation stress above the fatigue limit (c) leads to a finite number of load cycles for fatigue fracture, wherein the fracture occurs the more likely, the higher the load. For a oscilation stress with constant amplitude, this dependence is represented by the fatigue limit line, the inclined part of the Woehler line. The complete stress-line extending from the tensile strength curve over time up to the endurance limit.

# Relationships in the fatigue strength

Important: If the oscilation stress on with constant amplitudes but with the same maximum value as in case (c) with a more or less random-like sequence of differently sized amplitudes (d), the tolerable number of cycles will exceed the fatigue limit line. A strain curve of this kind is for the operation of most components, including also be assessed for tower constructions of wind turbines, characteristic and the procedures of operating resistance. With the Gaßner life line it is one of the fatigue limit line corresponding dependence between the stress level and the finite lifetime, expressed in number of cycles.

# The life line

The **life line** can be determined by means of experiments or simulations of random-like strain sequence. However, it can also, starting from the coupled WOEHLER line with a damage accumulation hypothesis gain calculation. Thus, the starting point is prior to the previous studies within this report.

To what extent is the life line of the WÖHLER line settles to higher numbers of cycles, it follows from the properties of the considered load-time function. These are often given in the form of load collectives, where the individual load cycles by means of counting methods (e.g. **rainflow method**) are classified into corresponding stress classes (collectives).

Wie stark die Lebensdauer eines geschweißten Bauteils bei vorgegebenen Beanspruchungswert S_{a} von der Form des Amplitudenkollektivs abhängt, veranschaulicht die Abbildung rechts. Unter einer vorgegebenen Beanspruchung von S_{a}=250 MPa kann demnach die Lebensdauer je nach Kollektivform zwischen 10^{4} und 10^{8} Schwingspiele betragen. Die Lebensdauer fällt erwartungsgemäß umso kürzer aus, je völliger die Kollektivform ist, d.h. je mehr Schwingspiele mit einer relativ großen Amplitude im zeitlichen Beanspruchungsverlauf enthalten sind. Bei der Lebensdauerlinie für das rechteckige Beanspruchungskollektiv handelt es sich um die Zeitfestigkeitslinie aus WÖHLER-Versuchen. Insofern erweist sich die WÖHLER-Linie als unterer Grenzfall aller möglichen Lebensdauerlinien.

How much depends on the life of a welded component at given stress value S_{a} of the shape of the amplitude collective, illustrates the figure on the right. Under a given stress of S_{a} = 250 MPa can therefore be the life depending on the collective form 10^{4}-10^{8} load cycles. The lifetime falls as expected from the shorter, the more fully is the collective form i.e. are the more resonant cycles included with a relatively large amplitude in the time course of stress. In the life line for the rectangular stress collective is the fatigue limit line from WOEHLER attempts. In this respect the WOEHLER line proves to be lower limiting case of all possible life lines.