PSI - Issue 18

Matus Margetin et al. / Procedia Structural Integrity 18 (2019) 663–670

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Matus Margetin at al./ Structural Integrity Procedia 00 (2019) 000–000

3. Nonproportional loading There are several ways how to define proportionality (or nonproportionality) of loading histories. Socie and Marquis (2000) mentioned that definition of proportionality should be related with cyclic damage mechanism associated with a change in the dislocation structure. He stated that “a strain history that results in a fixed orientation of the principal axes associated with the alternating components of strain is proportional. The strain history is nonproportional if the principal axes rotate in time.” When using this criterion to definition of proportionality, only the alternating or cyclic strains and stresses should be taken into consideration. Base on this definition, two specific loading histories have been chosen for simulation described in this article. In our case nonproportional loading histories are composed from series of proportional loading cycles. While the stress (strain) principal axes does not rotate within one loading cycle, the orientation of principal axes changes during whole loading segment. The first loading signal is composed from two segments: fully reversed pure axial and pure torsion loading cycle. The second one is composed from fully reversed axial cycle, followed by fully reversed torsion cycle and then followed by fully reversed proportional axial/torsion combination with ratio between normal and shear stress amplitude equal to 1. 4. Modeled fatigue lifetime estimation All three multiaxial criterions have been used for fatigue lifetime calculations based on modeled signal described in previous section. The signal segments amplitudes have been calculated for each simulation in the way, that they have same value of equivalent von Mises stress amplitude corresponding to lifetime of 5x10 5 cycles to failure. The linear Palmren-Miner damage accumulation rule has been used for damage accumulation in each plane. Material parameters used in the calculation are summarized in table 1. Simulation in this section was carried off for material S355.

Table 1. Material parameters used in calculations. Material constant

S355

C55 179 176 670 340 287

σ c-1 [MPa] τ c-1 [MPa] σ u [MPa] σ y [MPa] τ f ` [MPa]

284 180 680 665 550

b τ [-]

-0.0736

-0.03196

Figure 4.a) shows the accumulated damage as a function of plane orientation φ in a case of loading signal composed from tension amplitude followed by torsion amplitude. Damage for loading sequence composed from tension, torsion and proportional combination is shown on Fig 4.b).

Fig. 4. Total accumulated damage as a function of plane orientation for all three criteria (a) S355; (b) C55.