PSI - Issue 18

Riccardo Fincato et al. / Procedia Structural Integrity 18 (2019) 75–85 Author name / Structural Integrity Procedia 00 (2019) 000–000

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4.2. Quasi-static loading conditions In case of a quasi-static loading condition, the overstress model exhibits the same response of a rate-independent elastoplastic model. However, conventional rate-dependent and rate-independent theories are characterized by the sudden development of plastic deformation whenever the stress state crosses the plastic surface. On the other hand, the subloading surface and the overstress subloading surface model are capable of generating a smooth development of irreversible deformation even for a stress state lower than the macroscopic yield stress. This aspect is fundamental for a more realistic description of the material behavior and, for example, can explain the fatigue phenomenon in metals components subjected to repeated solicitations in the conventional elastic range (Tsutsumi and Fincato, 2018). Fig. 4a shows the stress-strain curves obtained in the quasi-static loading simulation. The red solid line indicates the DOSS model response that allows a smooth generation of irreversible deformation during the loading, unloading and reverse loading conditions. On the contrary, the solid blue line obtained with a conventional rate-dependent model shows an abrupt change in inclination whenever the stress crosses the plastic potential. For a sub-yield stress state, no viscoplastic/plastic deformation can be generated. Moreover, the graphs of Fig. 4 display the rate-independent solution obtained with the damage subloading surface model formulated in Fincato and Tsutsumi (2017c). The almost perfect overlap between the DOSS model and the DSS model proves the correct implementation of the rate-dependent algorithm. Fig. 4b and c report the viscoplastic accumulation and the damage as a function of the nominal strain. In case of quasi-static loading condition, no accumulation is generated during the initial part of the elastic unloading since the overstress lies on the plastic surface, satisfying the condition R = R d .

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Fig. 4 Cyclic loading analyses for a quasi-static loading condition: (a) stress-strain curves, (b) cumulative plastic strain evolution, (c) damage evolution.