PSI- Issue 9

Riccardo Fincato et al. / Procedia Structural Integrity 9 (2018) 136–150 Author name / Structural Integrity Procedia 00 (2018) 000 – 000

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a)

b)

Figure 1 a) sketch of tangential and normal components of stress rate for a generic stress state on the plastic surface; b) schematic representation of a generic stress state in the principal stress space. where ˆ  I is the deviatoric tangential (or projection) tensor (Hashiguchi, 2009) and the variable A is computed accordingly to Momii et al. (2015). In detail, A is function of the similarity ratio R and two material parameters T 1 and T 2 that were set to 0.9 and 1.0 in this study, respectively. It is worth mentioning that the constant T 1 can assume values between 1 0 1 T   . In conclusion, if the tangential inelastic stretch is considered then the cumulative inelastic strain to fracture H i becomes a function of p D and t D as in the second of Eq. (8). The present section deal with the numerical analyses carried out implementing the previous constitutive equations via user subroutine for the commercial code Abaqus (ver. 6.14-5). The DSS model parameters were calibrated reproducing a uniaxial tensile load for the SS400 steel reported in Van Do et al. (2014) and subsequently adjusted to reproduce the behavior of a thin steel bridge pier analyzed by Nishikawa et al. (1998). The analyses reported in section 3.4 offer an additional investigation that aims to point out the effect on the damage evolution of three non-proportional bidirectional loading conditions. Nishikawa et al. (1998) conducted a series of experiments on thin steel piers in order to analyse the horizontal load carrying capacity of the structures subjected to an increasing unidirectional horizontal load. The schematic of the pier is reported in Figure 2a together with its FE modeling, the loading sequence is instead reported in Figure 2b. In order to save computational time just half of the column was considered, applying symmetric boundary conditions. Moreover, the experimental results showed that the plastic deformations, and the buckling, appear in a region close to the base of the pier. Therefore, the structure was modeled according to its real geometry until a height equal to two times the internal diameter from the bottom and the remaining part was modeled with a beam element. A similar strategy was adopted by Gao et al. (1998). The geometric specifications are reported in Table 1. The lower part of the pier was meshed with eight-node hexahedral elements with reduced integration (i.e. Abaqus C3D8R elements) and the nodes of the top cross section were connected to the beam with rigid links. A mesh refinement was considered close to the base of the pier, where the maximum accumulation of plastic deformation is expected. The minimum element size is 9.8 mm (circumference) x 2.25 mm (thickness) x 15 mm (axial), comparable with the minimum element size used by Van Do et al. (2014), who conducted a mesh size sensitivity analysis on the same study case. The total number of elements amount to 51841. 3. Numerical analyses 3.1. Description of the FE model