**Empirical models**

Empirical models represent the major group of this classification. With these models, usually the fatigue life and the parameters of the load cycles are linked. These models are simple, however the partly lacking physical interpretability is a disadvantage.

Furthermore they are effective only for a quite narrow load spectrum as there is no distinction between the individual effects. The empirical models can be set up for various levels of complexity and are divided into approaches based on strain life curves and damage parameters, methods describing creep damage, energy-based approaches, and approaches for partial damage accumulation.

## **Damage mechanics models**

Damage mechanics models usually describe the development of damage by means of methods from continuum mechanics. The origin of these models is found with Kachanov (Kachanov, 1986) and Rabotnov (Rabotnov, 1969) who were concerned with creep damage. Damage mechanics approaches see damage being caused by creep and plastification. As the damage rates are linked to the current damage value, damage accumulation is nonlinear and requires the damage variable to be integrated cycle by cycle.

### **Physically based models**

In general the physically based models play a minor role for practical application, which is due to their complexity and the difficulties in determining their input parameters experimentally. They attempt to characterise the damage development on the basis of atom, vacancy and dislocation movement. At the current state of knowledge and application, physically based models for fatigue life computations are primarily relevant for depicting the physical background of empirical and damage mechanics methods, respectively.

### **Fracture mechanics models**

Fracture mechanics models are linked to the local plastic strains at the crack tip, which can be described, for example, by a Δ*J* integral or a modified Δ*J* integral, respectively. A link to the physically based models exists with models for micro-crack propagation.
