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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campaign of experimental investigations carried out in the last decades (Algarni et al., 2015; Bai et al., 2009; Bao and Treitler, 2004; Bao and Wierzbicki, 2004; Brünig et al., 2013; Gao et al., 2011; Papasidero et al., 2015) pointed out that the stress triaxiality and the Lode angle are the main two factors that affect the ductility behavior in metals. In fact, monotonic loading tests, for different geometries and under different loading conditions (uniaxial extension, pure shear, plane strain, uniaxial compression), proved a different failure behavior for the same material. On the other hand, the literature still lacks a proper characterization of the damage evolution under non-proportional loading paths. In the recent years, Faleskog and Barsoum (2013), Papasidero et al. (2014), Cortese et al. (2016) and Algarni et al. (2017) conducted a series of experiments aimed to identify the effect of the loading path on ductility. In detail, the work of Faleskog and Barsoum (2013), Papasidero et al. (2014) and Corstese et al. (2016) consisted in the application of several non-proportional loading paths, as the result of the combination of tension-torsion or compression-torsion, on steel and aluminum tubular samples. On the other hand, Algarni et al. tried to describe the crack formation on notched Iconel 718 bars in low cycle fatigue investigations. A common aspect that emerged from those previous works is that the deformation at fracture is higher when the load is proportional, suggesting that the damage accelerates whenever non-proportional loading conditions are triggered. The present paper aims to investigate the influence of the loading path on the ductile damage evolution. In detail, the numerical analyses focus the attention of the structural response of a steel bridge column subjected to various loading condition. A modified Mohr-Coulomb criterion (Bai and Wierzbicki, 2010) is adopted for the description of the damage behavior of SS400 steel pier, with a modification of the damage evolution law, in order to take into account the effect of the non-proportionality of the load. Next, section 2, the theoretical Damage Subloading surface model (i.e. DSS) is presented, with particular emphasis on the ductile damage criterion. The subsequent section 3 is divided into two parts; the first one deals with the calibration of the material parameters, whereas the second offers an overview of the effect of three non-proportional loadings on the bridge pier. Nomenclature

, σ σ Cauchy stress, corotational stress rate , α α back stress, corotational back stress rate s similarity centre σ conjugate Cauchy stress α conjugate back stress E tensor of the elastic constants F isotropic-hardening function F 0 initial size of the normal-yield surface H isotropic hardening variable D H cumulative plastic variable (i.e. equivalent plastic strain) R similarity ratio λ plastic multiplier D ductile damage scalar variable σ m mean stress Mises  von Mises stress η stress triaxiality  Lode angle  Lode angle parameter (-1 <  < 1) f  equivalent strain at fracture a b  Heaviside step function: 0 if 0; 1 if a b a b a b    

a b    

0

2. Theoretical approach

The present section deals with the theoretical framework for the description of the elastoplastic and damage model named Damage Subloading Surface model (i.e. DSS). The DSS model was formulated from the unconventional plasticity model Extended Subloading Surface, presented by Hashiguchi in Hashiguchi (2009, 1989), and upgraded to