PSI - Issue 13

Gustavo Henrique Bolognesi Donato et al. / Procedia Structural Integrity 13 (2018) 1879–1887 Leonardo G. F. Andrade and Gustavo H. B. Donato / Structural Integrity Procedia 00 (2018) 000–000

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the DNV-RP-F108 (2011). Each geometry presents different response in terms of loading modes, stress triaxiality and, thus, different M values are expected for varying specimens, materials and conditions. 3.1. FEM models for the specimens Model were developed considering ½ or ¼ symmetries whenever possible, including the appropriate boundary conditions as presented by Fig. 2. The FE code WARP3D (KOPPENHOEFER, 1994) was employed to provide the numerical solution of the elastic and elastic-plastic analyses; it incorporates J2 flow theory both for Small Geometry Change (SGC) or Large Geometry Change (LGC) settings. The considered mechanical properties represent a wide range of ferritic structural steels usually employed in structural components, pipelines and pressure vessels. The three classes of materials investigated are presented by Tab. 1.

Table 1. Mechanical properties of the considered materials for the Finite Element analyses. It is Worth mentioning that n is the inverse of the hardening exponent ( N ) of a material ( n = 1/N ). n ⁄ (MPa) 5 800 206000 0,3 10 500 20 300

All Finite Element models were pre-processed using MSC Patran software (2012). To guarantee a detailed description of the stress fields ahead of the crack tip, a very refined mesh was implemented in all models, as can be seen on Fig. 2a. Near the crack tip, a focused mesh was configured with a radius ρ = 0.0025 mm. First, plane strain models were developed, consisting of only one layer of 3D 8-node hexahedric elements of unitary thickness – here, transverse displacements were fixed to simulate plane strain conditions. After that, all 3D models were developed taking advantage of the aforementioned symmetries – in this cases, models employed between 15 and 22 layers of the same 3D elements, in accordance to the works of Nevalainen and Dodds (1995) and Cravero (2007). The plane strain models present approximately 3200 elements and 6800 nodes for the case of SE(T), 1300 elements and 2800 nodes for SE(B) and 4200 elements and 8800 nodes for C(T) specimens. The 3D models (including W = B , W = 2B and W = 4B ), in its turn, present around 92000 elements and 100000 nodes. Loading was implemented based on incremental displacements to favor numerical convergence.

Fig. 2. Mesh patterns and examples of boundary conditions and symmetries representative of an SE(B) specimen.