PSI - Issue 16

22 Andrzej Kurek et al. / Procedia Structural Integrity 16 (2019) 19–26 4 Andrzej Kurek, Justyna Koziarska, Tadeusz Łagoda, Karolina Łago da / Structural Integrity Procedia 00 (2019) 000 – 000

3. Determination of fatigue characteristics

Fatigue characteristics are determined based on data from cyclic tests taken from literature presented by Sun and Shang (2010) and Boller and Seeger (1987) for 9 materials. The analysis comprised materials for which tests were carried out at high deformation amplitude, that is considerable plastic deformations. These characteristics were determined on the basis of deformations εa and tensions σ a resulting from the theory of small deformations and deformations ε aT and tensions σ aT determined based on the theory of finite deformations determined from the theory of small deformations. In many works, while analysing deformations, also those logarithmic deformations, one must start from presenting typical Wöhler’s curve. Y et , there are works in which this attempt is taken although the materials analysed were characteristic for strong non-elastic behaviours. Nevertheless, in this situation, the objective was not achieved as presented in the paper by Narybnek et al. (2017). This work focuses on materials with high ductility. In the literature, there are the analyses of deformations in various terms, also as dependence of fatigue life on hardness as Roessle and Fatemi (2000) showed. Inter alia, the lack of relationship between the fatigue limit coefficient and the real rupture strength was presented. Yet, significantly better correlations were discovered of fatigue limit coefficient with tension strength and hardness. In the literature, this topic is not new but it is not much popular. Taking into account the facts presented above, we can proceed to the analysis of fatigue characteristics. The total value of deformation amplitude in both theories may be recorded as the sum of elastic and plastic deformation amplitude, that is:

   



.

(7)

a

ae

ap

On the basis of tension amplitude σ a elastic deformation amplitude is determined = , where E – longitudinal elasticity module (Young’s Modulus). Then, plastic deformation amplitude is calculated from the following formula:

(8)

a ap   

ae  

(9)

The basic fatigue characteristic within the scope of low number of cycles is Manson (1965)-Coffine (1954)- Basquin (1910) characteristic, relating total deformation amplitude to the number of cycles. This characteristic is most popular and most frequently used. The original Manson-Coffine-Basquin characteristic was constructed for tension-compression, registering deformation amplitude ε a , tension amplitude σa and the number of cycles to be destroyed N f . It is common knowledge that on the basis of elastic deformation amplitude εa according to (7) and the number of cycles to be destroyed N f the following characteristic is obtained:   b f f ae N E 2 '    , (10) where: ′ - fatigue limit coefficient at tension-compression, b – fatigue limit exponent. In consequence, we obtain, based on (8) and the number of cycles to be destroyed N f   c f f ap N ' 2    , (11)