**6. Simulation of the cyclic deformation behaviour**

### **6.1 Basics and classification**

The description of the elastoplastic deformation behaviour of the construction material forms the basis for assessing the fatigue life of complex components. By means of the finite element method and proper material models it is possible to calculate the local loads (e.g. stress, strain, etc.) under the assumption of adequate boundary conditions.

The most basic material model describes an isotropic plastic hardening independent from the direction of loading. The expansion of the yield surface, which is determined by the *drag stress K* (defined size of the yield surface delimiting the elastic region), can be defined, e.g., in tabular form as a function of the plastic strain. Under cyclic loading each cycle in an isotropic material model leads to further hardening until the maximum strength is obtained and the model shows only elastic, ideal-plastic behaviour. Therefore the isotropic hardening model is adequate only for unidirectional loading. Many materials display the so-called Bauschinger effect under reversed loading (Bauschinger, 1881). The said effect means that plastic deformation occurs already at a significantly lower stress when the load is reversed. The cause of this effect is the formation of dislocation structures, which facilitate plastification in the opposite direction. The Bauschinger effect and the cyclic deformation behaviour, respectively, can only be described by consideration of kinematic hardening, thus using the *back stress* α (which defines the shift of the yield surface in the threedimensional stress space). In addition high temperatures cause a dependency of stress on the loading rate, which is due to time-dependent processes such as creep. The partitioning

seen, that the minimum creep strain rate of the single step test at 150 MPa is more than 300 times lower compared to the minimum creep strain rate in multiple step test and single step test with pre-aged specimen at the same stress level. Furthermore the test data of the multiple step test and test with pre-aged specimens show a very similar behaviour. Therefore the time at test temperature determines the minimum strain rate independent of

The description of the elastoplastic deformation behaviour of the construction material forms the basis for assessing the fatigue life of complex components. By means of the finite element method and proper material models it is possible to calculate the local loads (e.g.

The most basic material model describes an isotropic plastic hardening independent from the direction of loading. The expansion of the yield surface, which is determined by the *drag stress K* (defined size of the yield surface delimiting the elastic region), can be defined, e.g., in tabular form as a function of the plastic strain. Under cyclic loading each cycle in an isotropic material model leads to further hardening until the maximum strength is obtained and the model shows only elastic, ideal-plastic behaviour. Therefore the isotropic hardening model is adequate only for unidirectional loading. Many materials display the so-called Bauschinger effect under reversed loading (Bauschinger, 1881). The said effect means that plastic deformation occurs already at a significantly lower stress when the load is reversed. The cause of this effect is the formation of dislocation structures, which facilitate plastification in the opposite direction. The Bauschinger effect and the cyclic deformation behaviour, respectively, can only be described by consideration of kinematic hardening,

dimensional stress space). In addition high temperatures cause a dependency of stress on the loading rate, which is due to time-dependent processes such as creep. The partitioning

(which defines the shift of the yield surface in the three-

stress, strain, etc.) under the assumption of adequate boundary conditions.

strain (Minichmayr et al., 2005).

**6.1 Basics and classification** 

thus using the *back stress* 

Fig. 7. Influence of HCF interaction on the OP-TMF lifetime

**6. Simulation of the cyclic deformation behaviour** 

α

of time-independent plastic deformation and time-dependent creep effects for the deformation behaviour at elevated temperatures is already known from Manson (Manson et al., 1971). At the same time this forms the basis of the *strain range partitioning* concept.

A literature review yields a great number of material models which are able to describe the material behaviour for certain kinds of loading. According to (Christ, 1991) they may be classified according to the underlying approach as follows: empirical models, continuummechanical models, physically based models and multi-component models.
