**7.1 Basics and classification**

The models available for describing the complex phenomena of thermo-mechanical fatigue range from engineering approaches to physically based models, thereby characterising the combined loading in differing complexity.

Comparison of Energy-Based and Damage-Related

smallest standard deviation (Riedler et al., 2005).

dependent TMF fatigue life criteria.

a scatter band of 1.6.

 **Calculated lifetime N**

 **cal**

 **[-]** 

1,E+01

1,E+02

1,E+03

1,E+04

1,E+05

Fatigue Life Models for Aluminium Components Under TMF Loading 341

have to be known, i.e., the local load parameters in consideration of the cyclic deformation behaviour have to be determined in advance. Especially for aluminium alloys the combination of stress and strain variables yields an adequate parameter as the cyclic deformation behaviour is dominantly affected by the ageing effect. If the temperature

Whilst a single-parameter plastic energy approach is an adequate criterion for the highly ductile aluminium alloy AlCuBiPb, for ductile gravity die casting alloys (AlSi7MgCu0.5 and AlSi8Cu3) it is a total strain based energy criterion. For brittle materials such as AlSi6Cu4 lost foam, a fracture mechanics based energy criterion with a cyclic *J* integral provides the

The so-called *unified energy approach* is derived based on this knowledge of material-

,, , , ( )( ) *Wc W W c u u ue u <sup>p</sup> u o ae a a*

*<sup>p</sup>* Δ = ⋅Δ +Δ = ⋅ + ⋅

*Bu NAW Bu u*

The specific hysteresis energy for a representative cycle consists of an elastic and a plastic portion. Whereas the elastic portion is formed by the maximum stress and the elastic strain amplitude, the plastic portion is formed by the amplitude values of stress and plastic strain. The material parameter *cu* takes values near 1. The fatigue life is determined by a power law approach according to (2). The quality of computing OP-TMF fatigue life for the examined cylinder head alloy made of aluminium and cast iron by means of the *unified energy approach* can be seen in figure 9. It shows 95% of the data points of the six examined alloys influenced by maximum temperature, average and local strain, pre-ageing as well as ageing in operation lying in a fatigue life scatter band of 2.5, and two-thirds of the data points lying in

> **Investigated materials: 3 Al cast alloys 1 Al wrought alloy 2 Cast iron alloys**

σ

1,E+01 1,E+02 1,E+03 1,E+04 1,E+05 **Experimental lifetime Nexp [-]**

Fig. 9. Quality of the TMF fatigue life simulation by means of the *unified energy approach*

ε

 σε

<sup>−</sup> = ⋅Δ (2)

 **Investigated OP- TMF influences: Maximum temp. Dwell time Mean strain Local strain Mean temperature Pre-ageing Cyclic ageing**

±2.5

±2.0

(1)

dependent ageing reduces the stress, the plastic strain increases in a similar way.

Most models for TMF fatigue life calculation are based on linear damage accumulation according to Palmgren-Miner (Palmgren, 1924; Miner, 1945).

Nonlinear cumulative approaches mainly come from Chaboche and Lemaitre (Chaboche & Lesne, 1988; Lemaitre & Chaboche, 1985).

The methods of calculation are mostly based upon local loading parameters such as stress, strain and temperature, which are calculated in complex components by means of elaborate material models. Thus the classification of models describing the fatigue life behaviour under TMF and LCF loading shows the same subdivision as the models describing the cyclic deformation behaviour and shall be briefly explained in the following.
