PSI - Issue 16

Andrzej Kurek et al. / Procedia Structural Integrity 16 (2019) 19–26

20

2 Andrzej Kurek, Justyna Koziarska, Tadeusz Łagoda, Karolina Łago da / Structural Integrity Procedia 00 (2019) 000 – 000

Nomenclature b

fatigue limit exponent

b”

fatigue limit exponent for finite deformations fatigue plastic deformation exponent

c

c” K’ K” n’ n”

fatigue plastic deformation exponent for finite deformations

deformation cyclic strengthening coefficient

deformation cyclic strengthening coefficient for finite deformations

cyclic strengthening exponent

cyclic strengthening exponent for finite deformations longitudinal elasticity module (Young’s Modulus)

E l o l 1

original length

final length or relative deformation number of cycles to be destroyed

N f

ε a

deformation amplitude

ε’ f ε” f σ a σ’ f σ” f

fatigue plastic deformation coefficient

fatigue plastic deformation coefficient for finite deformations,

tension amplitude

fatigue limit coefficient at tension-compression

fatigue limit coefficient at tension-compression for finite deformations

Nevertheless, a material yield part is analysed most carefully because this part is a serious problem when rupture is initiated, as Choung and Cho (2008) studied. Deformation describes a degree of material alteration. Generally, it is measured by means of strain gauge sensors or extensometers during uniaxial loading state. In order to determine deformation, it is also possible to use elongation described with the following equation ∆ = 1 − , (1) where: l o – original length, l 1 – final length. The deformation is = ∆ . (2) The problem of considering high deformations in fatigue of materials is very rarely considered in the fatigue analysis. The authors of the present paper have recently presented this problem initially in papers by Kurek et al. (2016) and Łagoda et al . (2016). It is possible to present a determined logarithm uniaxial deformation curve for rods with round sections and rectangular sections – this fact is presented in numerous works e.g. by Choung and Cho (2008) and Zhang et al. (1999) – Fig. 1. This work presents various types of linear deformations; nevertheless, it is focused more comprehensively on the already-mentioned logarithmic deformation or relative logarithmic deformation in the general form as = ∫ 1 1 . (3) Most analyses in statistics refer to so called small deformations. It is also possible to use the theory of large deformations, that is finite deformations. This theory is useful for considerable plastic deformations. However, there are no counter-indications for applying this theory also for materials fatigue at extremely low number of cycles, where we have to do with considerable plastic deformations. Hitherto, in the fatigue analysis, the theory of small deformations has been applied as a rule. An exception to this rule is the work by Sun and Shang (2010), where it is