PSI - Issue 39

Camilla Ronchei et al. / Procedia Structural Integrity 39 (2022) 460–465 Author name / Structural Integrity Procedia 00 (2021) 000–000

462

3

In particular, two types of specimens were produced according to the ASTM standards: solid specimens for tensile fatigue tests, and hollow specimens for torsional and biaxial tests. LCF tests were carried out under strain-controlled mode, and an axial-torsional extensometer was employed to measure both axial and shear strains. The experimental loading conditions (characterised by a fatigue ratio equal to - 1 and sinusoidal waveforms) consisted in: tensile, torsional, and combined tensile/torsional loading. Under biaxial loading, both proportional and non-proportional signals (with a phase shift, β , equal to 45° or 90°) were investigated. The details of the examined fatigue data are reported in Wu et al. (2014). From uniaxial LCF data, the parameters of the tensile and torsional Manson-Coffin curves were computed, as is reported in the original paper (Wu et al. (2014)). In order to check the material sensitivity to non-proportional loading, the fatigue limits under fully reversed normal stress, 1 af , σ − , and shear stress, 1 af , τ − , are derived from the elastic parameters of both tensile and torsional Mason-Coffin curves. As a matter of fact, according to the Papadopoulos’ statement (Skibicki (2014)), the present titanium alloy can be regarded as sensitive to non-proportional loading being the ratio between 1 af , τ − and 1 af , σ − lower than 1 3 . 3. Theoretical framework of the RED criterion The biaxial fatigue tests outlined in Section 2 are hereafter simulated through the Refined Equivalent Deformation (RED) criterion, recently proposed by Vantadori (2021) in order to take into account the additional cyclic hardening in the fatigue life estimation. According to such a criterion, the fatigue life assessment is carried out at a verification point (point P ) located on the specimen surface, and the orientation of the critical plane (function of mechanical/fatigue properties of the material) is linked to the averaged directions of the principal strain axes ( 1ˆ , 2ˆ and 3ˆ ), as reported in detail in Carpinteri et al. (2015). Under cyclic proportional loading, an equivalent strain amplitude (also named fatigue damage parameter), eq ,a ε , is computed by means of a quadratic combination of the amplitudes of both the normal, N ,a η , and the tangential, C ,a η , displacement vectors acting on the critical plane: ( ) ( ) ( ) 2 2 2 eq ,a N , a a a C , a ε η ε γ η = + (1) where a ε and a γ are defined by the well-known tensile and torsional Manson-Coffin equations, respectively. Finally, by equating such a damage parameter with the tensile Manson-Coffin equation, the number of loading cycles to failure, f N , is determined through an iterative procedure. Note that the additional cyclic hardening, experimentally observed in materials sensitive to non-proportionality, is not taken into account by means of Eq. (1) and, consequently, the fatigue lifetime estimation is not accurate enough for non-proportional loading. Therefore, in presence of materials with high susceptibility to loading non proportionality, a novel strain factor, * f , is implemented in the fatigue damage relationship by following the same philosophy of Borodii criterion (Borodii and Strizhalo (2000); Borodii (2001)):

* eq ,a f ε

ε

=

(2)

RED,a

where RED,a ε is defined as the refined equivalent deformation amplitude, and strain path orientation and degree of non-proportionality) is given by:

* f (function of material constants,

1 =  +

45

* ϕ α ° −  + Φ (1

)

f

* k sen

(3)

*





i

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