**Introduction**

In the past, the fatigue design was based on the attempt of engineers to find the endurance limit of the materials in order to determine the limiting stress below of which the fatigue failure will not take place. Therefore, the testing was only focused on high number of cycles (greater than 10^5 cycles). Although this approach was sensible for many industrial components it led to over-design of components which were subjected to less than 10^5 cycles of operation.

In general, industrial gas turbines usually suffer from low cycle fatigue (LCF). This occurs due to the high load (high stresses) that is applied under few cycles of operation. Some large industrial gas turbines may work for almost a year without stopping for maintenance. But, at every cycle of operation (start-up, operation and shutdown), they may lose almost 10% of their lifetime (due LCF). So, in general, it is not so important the number of times that the load is applied, but the damage that produces when it is applied. Since the damage is associated with the plastic deformation, LCF is frequently called “high strain fatigue”.

In LCF, due to the high stresses, there is a large energy concentration (greater than in high cycle fatigue – HCF) and the material spends only a small percentage of its lifetime in the crack initiation phase (about 10%), whilst most of its lifetime is spent in the crack propagation phase (about 90%).

The material of the component that is subjected to very high load it is possible to deform plastically and to redistribute the load. If this does not happened (no plastic deformation by the load), the load will just stretch the elastic line (up and down). In that case LCF will not take place and the fatigue life of the component could be estimated using the Goodman’s diagram (elastic type analysis). However, if the plastic strain εp is high enough, there will be some plastic deformation in the second part of the cycle. The material and the load condition will be responsible for the effects that will have the following cycles on the component.

Figure 2: Typical hysteresis loop in the stress-strain curve [1].

**Equations**

The cyclic stress-strain curve can be compared with the monotonic stress-strain curve in order to determine the effects of cyclic loading. The cyclic stress-strain curve, as the monotonic stress-strain curve, includes both elastic and plastic strains:

Figure 3: Typical strain-life curve [1].

- The cyclic strength coefficient, K’.
- The cyclic strain hardening exponent, n’.
- The fatigue ductility coefficient, ε’f.
- The fatigue ductility exponent, c.
- The fatigue strength coefficient, σ’f.
- The fatigue strength exponent, b.

**References**

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