PSI - Issue 16

Andrzej Kurek et al. / Procedia Structural Integrity 16 (2019) 19–26 21 Andrzej Kurek, Justyna Koziarska, Tadeusz Łagoda, Karolina Łago da / Structural Integrity Procedia 00 (2019) 000 – 000 3

mentioned that it is possible to use this theory for fatigue but with no need of applying it in this work because plastic deformations were not high enough to use them obligatorily.

Fig. 1. Diagram of a curve course during tension-compression test (Choung and Cho 2008).

The objective of this work is to prove that in the event of large deformations, it is possible to apply the theory of finite deformations for the analysis of fatigue within the scope of extremely low number of cycles instead of deformations characteristic for small deformations.

2. The determination of deformations amplitudes and finite tensions

It has been proven that for some materials in the event of extremely low number of cycles in the fatigue analysis for uniaxial tension-compression, it is required to consider a possibility of using relative logarithmic deformation instead of traditionally understood normal deformation determined based on the theory of small deformations known as “engineering deformation”. It is possible to use here the theory known from statistics for finite deformations, that is large deformations known internationally as “true strain” in the form   a aT     ln 1 . (4) In this case, it is also necessary to define real tension differently. In the event of assuming the constant material volume, i.e.: = 1 1 , (5) for large deformations, it is obtained after conversions ) (1 a a aT      . (6)