PSI - Issue 16

Andrzej Kurek et al. / Procedia Structural Integrity 16 (2019) 19–26 23 Andrzej Kurek, Justyna Koziarska, Tadeusz Łagoda, Karolina Łago da / Structural Integrity Procedia 00 (2019) 000 – 000 5 where: , – plastic fatigue deformation coefficient, c – plastic fatigue deformation exponent. Finally, by substituting (9) and (10) to (6) we obtain original Manson-Coffine-Basquin characteristic which is applied most frequently     b f f a N E 2 '     c f f N ' 2  . (12)

Whereas, for the theories of large deformations, we present the above characteristic in the analogous way:

' '



   ' ' 2 b N

  '' ' ' 2 c f f N 





f

aT

f

E

, (13) where: ′′ – fatigue limit coefficient at tension-compression for finite deformations, ′′ – fatigue limit exponent for finite deformations, ′′ – fatigue plastic deformation coefficient for finite deformations, ′′ – fatigue plastic deformation exponent for finite deformations. Another characteristic (Ramberg-Osgood (1943)) relates deformation amplitude to tension amplitude in accordance with formula (7). The elastic part is defined by means of formula (8) and the plastic part by means of = ( ′ ) 1/ ′ , (14) where: ′ – deformation cyclic strengthening coefficient, ′ – cyclic strengthening exponent. The final form of Ramberg-Osgood formula after substituting formulas (8) and (14) to (7) is = + ( ′ ) 1/ ′ . (15) The presented model of determining Ramberg-Osgood fatigue characteristic for large deformations – finite deformations may be presented as = + ( ′′ ) 1/ ′′ , (16) where: ′′ – deformation cyclic strengthening coefficient for finite deformations, ′′ – cyclic strengthening exponent for finite deformations. Fig. 2 presents the schematic transformation from engineering system (small deformations theory) to the system connected with finite deformations. Therefore, in the event of finite deformations we obtain smaller deformations accompanied by larger tensions. Thus, it seems that when we have significant deformation, fatigue characteristics determined based on such deformations will differ considerably from the characteristics determined based on the small deformations theory, that is in a traditional way. Table 1 and Table 2 include the materials constants of the materials analyzed. The analysis of material constants shows that n” > n ’, that is cyclic strengthening exponent for finite deformations is higher than the cyclic strengthening exponent. What is more, deformation cyclic strengthening coefficient for finite deformations K” is also higher than deformation cyclic strengthening coefficient K’ . Whereas, the analysis of cyclic fatigue properties demonstrates that some parameters for finite deformations are higher and some are lower. This is a uniform tendency for all the materials. Fatigue limit exponent for finite deformations b” is higher in terms of the absolute value than the fatigue limit exponent b’ . The fatigue limit coefficient at tension-compression is also higher for finite deformations ′′ . Fatigue plastic deformation exponent