PSI - Issue 2_A

Liviu Marsavina et al. / Procedia Structural Integrity 2 (2016) 1861–1869 Author name / Structural Integrity Procedia 00 (2016) 000–000 �� � � � � � � �� � �� � �� � ����� � ��� � �� � � ��� When 2α= 0, K 1C equals the fracture toughness K IC . For rounded V-notches, a crescent-shaped control volume bounded by two radii differently centered was introduced: a circular notch edge with radius  as the inner boundary and a circle arc with radius r 0 + R c as the outer boundary, (Fig. 2.c). The length r 0 represents the distance between the origin of the polar coordinates (used to express the stress field) and the notch tip. The parameters r 0 depends on q which is a function only on the notch geometry (the opening angle 2α); r 0 is defined as � � � �� �� � �� ⁄ where � � ��� � ���⁄� . 1865

Fig. 2. Control volume for sharp V notch (a), crack case (b)and rounded V notch under mode I loading.

The radius of the control volume and the critical strain energy density depend only from the mechanical properties of the material as the Young’s Modulus, the fracture toughness, the Poisson’s ratio and the ultimate tensile strength σ u or σ t . 5. Numerical Investigations 5.1 Determination of SED parameters The quasi brittle behavior, for these foams, is exhibited for notched components, Fig. 1e, so the ultimate tensile strength σ u should be substituted with σ t , the maximum normal tension existing at the notch tip in the moment that proceed the fracture. This value was obtained experimentally using specimens similar with those from Fig 1.b but with a symmetric semicircular notches of radius 4 mm. A linear-elastic finite element analysis was carried out in ANSYS 14.5 software for all specimen geometries. Based on symmetry of loading and boundary conditions quarter of geometry was considered. The experimental average maximum load (Tables 2 and 4) was applied to the models for each notch geometry as uniaxial loads. The PLANE184 plane 8-node bi-quadratic elements with a suitably high mesh density in the area of the notch tip were employed, the analysis were performed under plane strain conditions. According with this procedure, it’s possible to define the tension at the notch tip. In Table 5 are presented the tension σ t and the parameters of SED method, calculated through Eqs. (2) and (3).

Table 5. Values of tension at the notch tip and respective SED parameters. Density [kg/m 3 ] σ t [MPa] R c [mm]

W c [MJ/m

3 ]

100 145 300 708

3.19 4.39 6.06 26.7

0.20 0.24

0.169 0.143 0.065 0.285

1.0

0.62