PSI - Issue 13

Letícia dos Santos Pereira et al. / Procedia Structural Integrity 13 (2018) 1985–1992 Author name / Structural Integrity Procedia 00 (2018) 000–000

1988

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2.2. Extended finite element model The XFEM (Extended Finite Element Method) was presented in 1999 (Campilho et al., 2011). This model is simpler than GTN model, since it is not based on the ductile fracture phenomenology, but also allows the simulation of crack extension. This model has only two parameters to be calibrated; the first parameter (the maximum cohesive stress � ) describes the onset of damage, that is, when the damage will initiate - this parameter can be related to the strength of the material. The second parameter (the damage evolution D ) describes the evolution of the damage, respectively decreasing the stiffness of the affected elements. The most phenomenological quantity in this model is the cohesive energy � , which is the energy spent for the separation (Parmar et al., 2015). The energy can be related with the toughness of the material. The separation, in its turn, is simulated employing phantom-nodes created when the first parameter is reached, based on which separation at failure can be configured (SIMULIA, 2013). Depending on the simulated material and the adopted methodology, the decay model can change - the most suitable model to describe ductile steels is the exponential. It means that, as damage evolves until fracture, the stress decrease as a function of the displacement is exponential. All details regarding XFEM and its application for ductile fracture simulations can be found in Fries and Belytschko (2010) and Campilho et al. (2001). 3. Methodology 3.1. Materials, geometries and loading modes The material considered for the simulations is the API-5L X80 steel, widely employed in gas pipelines. The analyses employed an elastic-plastic constitutive model with J 2 flow theory and conventional Mises plasticity in Large Geometry Change ( LGC ) setting and including dynamic effects (considered density was 7,85 g/cm 3 ). The elastic behavior followed Hooke’s law with E = 206 GPa and υ = 0.3, while the elastic-plastic response was informed to the codes based on the true stress-strain curve available for this material and presented by Fig. 1(b) . The strain-rate sensitivity was implemented based on Johnson-Cook’s model (Pereira, 2017). Figure 2 presents the considered geometries for V-notched Charpy (based on ASTM E23, 2013 and EN ISO 148 1, 2010) and DWTT (based on ASTM E436, 2014) specimens submitted to 3-point bending loading schemes. The thickness for the DWTT specimen is not enforced by the aforementioned standard and was adopted 27.7 mm based on some gas pipelines of interest for the research group.

(a) (b) Fig. 2. (a) Charpy V-notch geometry in accordance with ASTM E23 (2013) and EN ISO 148-1 (2010); (b) DWTT geometry in accordance with ASTM E-436 (2014) and dimensions in mm 3.2. Numerical procedures The developed 3D finite element models were based on previous refined modeling conducted and validated in the research group. For GTN, only one quarter of the specimens were modeled with appropriate boundary conditions to ensure symmetry, saving computational resources (illustrated by Fig. 3(a) ) . For XFEM, it was not appropriate to use X-symmetry, consequently, half specimen was modeled. The mass of the hammers were considered, respectively,