PSI - Issue 39

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

461

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well-known, the loading non-proportionality has a significant influence on fatigue process. As was experimentally observed by Fatemi (1985) and Socie (1987) in the past, the continuous rotation of the principal stress/strain axes under non-proportional cyclic loading results in the activation of multi-slip systems, which prevent the formation of stable dislocation substructures inside the material. Consequently, additional cyclic hardening occurs, resulting in a reduction of fatigue life in comparison with those under proportional uniaxial and multiaxial loading (Skibicki (2014)). The additional cyclic hardening should be taken into account for reasonable fatigue life evaluations. This aspect is even more important in presence of materials with high susceptibility to loading non-proportionality. As a matter of fact, for a loading with a high degree of non-proportionality and a material with high susceptibility, the fatigue life is up to ten times smaller than that obtained in the case of proportional loading. Therefore, the development of fatigue criteria, able to consider the main factors (that is, the stress/strain range and the cyclic path shape) affecting the lifetime under cyclic non-proportional loading, is becoming a high-priority issue for engineers engaged in fatigue design of structural components (Borodii (2001)). In particular, the criteria which consider the cyclic path shape in the fatigue damage calculation allow us to take into account the additional cyclic hardening experiencing in most metallic materials; as a result, the fatigue lifetime under complex loading can be estimated more accurately. Along the line of the criterion proposed by Borodii and Strizhalo (2000), Vantadori (2021) has recently formulated a strain-based fatigue criterion (named Refined Equivalent Deformation, RED, criterion) which implements a novel strain factor (function of material constants, strain path orientation and degree of non-proportionality) in the damage parameter relationship. The goal of the present paper is to discuss the accuracy of the RED criterion in estimating fatigue lifetime of metallic components. In particular, the theoretical results are compared with some experimental data available in the literature, related to solid and hollow specimens made of TC4 titanium alloy, subjected to both proportional and non-proportional biaxial loading (Wu et al. (2014)).

Nomenclature * f

novel strain factor exp N experimental fatigue life f N theoretical fatigue life w unit vector normal to the critical plane ASME ε ∆ standard definition of the strain range β

phase shift between tensile and torsional loading

equivalent normal strain amplitude

eq ,a ε

normal displacement vector related to the critical plane tangential displacement vector related to the critical plane

N η C η

elastic Poisson ratio

e ν

1 af , σ − 1 af , τ −

fatigue limit under fully reversed normal stress fatigue limit under fully reversed shear stress

i Φ angle of the i-th non-proportional strain path with respect to the material principal axis i ϕ coefficient of non-proportionality of the i-th non-proportional strain path

2. Examined experimental fatigue data The Low Cycle Fatigue (LCF) tests examined are related to an experimental campaign carried out by Wu et al. (2014) on plain specimens made of TC4 titanium alloy, whose chemical composition (in wt %, balance Ti) is: Al=6.4, V=4.1, Fe=0.2, C=0.01, N=0.01, H=0.002, O=0.16. As far as the static mechanical properties are concerned, the elastic modulus, E , and the elastic Poisson ratio, e ν , are equal to 108.4 GPa and 0.25, respectively. After a heat treatment, the material microstructure was homogeneous and consisted of fully equiaxed and columnar alpha grains with intergranular beta phase. The specimens were machined from full bars with a diameter of 35 mm.