PSI - Issue 52

D. Amato et al. / Procedia Structural Integrity 52 (2024) 1–11 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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Fig. 1 (a) Hollow-Cylindrical specimen geometry; (b) cross-sectional view of initial elliptical notch [7].

The samples were tested in several loading conditions: cyclic tension, cyclic tension-torsion and pure cyclic torsion. The scope of this study is to analyse only the cyclic tension test as it showed a significant mismatch with the numerical simulation in terms of crack growth rates. In this test, the applied load was a cyclic axial force = 80 with a stress ratio =0.1 and a frequency of 10 . 3. Plasticity Models Two stress-strain models were adopted to characterize the effective response of the material in the transition from the linear-elastic behaviour to the elastic-plastic one. The material is assumed to behave as elastic-plastic with isotropic hardening. The first inelastic analysis was performed using a Bi-Linear model (B-L), whereas a second attempt was performed with a non-linear stress-strain curve: the Ramber-Osgood stress-strain model (R-O relationship). A comparison of the two material laws is provided in Fig. 2, where the difference between the two model is noticeable, especially in the transition area between the elastic and the plastic parts of the diagram.

3.1. Bi-Linear stress-strain model

The Bi-Linear stress strain model is a simple mathematical law used to approximate the complex elastic-plastic response of a metallic material undergoing a mechanical load. The idea behind this formulation is to assume a linear behaviour of the material across all its strength range. To discern between the elastic and the plastic region, two different material constants are defined: the Youngs or tangent modulus and the secant modulus, the latter defined as the slope of the line connecting the yield point with the ultimate tensile stress.