PSI - Issue 42

Lucas Mangas Araújo et al. / Procedia Structural Integrity 42 (2022) 1591–1599 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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the influence of stress invariants I1 and J3 on the mechanical behavior of metallic materials. More precisely, the effects provoked by these parameters on Ductile Fracture and ULCF responses will be discussed. Moreover, the coupling of these invariants with kinematic and isotropic hardening will be analyzed. For this purpose, one uses a Gao-based formulation [3] with kinematic and isotropic hardenings to describe SAE 1045 steel behavior and compares the results with the experimental data of Bai [1]. As far as the authors are aware, there is a lack of works that demonstrate the role of the stress invariants in different situations and to what extent one needs to consider them in practical situations. Within the context of this contribution, the only recent study found and worth mentioning is the one from Pereira et al. [5]. Figure 1 provides a schematic overview of this contribution.

Fig. 1. Schematic overview of the present study.

2. Mathematical and numerical modeling 2.1. Gao’s equivalent stress

The hydrostatic stress and third invariant 3 have a strong influence on the behavior of metallic materials. In this regard, the present work considers the model proposed by Gao et al. [3], who formulated a new equivalent stress incorporating 1 and 3 : (1) with , and denoting material parameters. is constrained by and by the relation: (2) which can be demonstrated by considering uniaxial loading conditions. Two remarks should be noted: i) Gao’s equivalent stress reduces to von Mises’s when = = 0 , ii) under uniaxial loading conditions, the Gao’s and Mises yield surfaces coincide.