Issue 42

M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 214-222; DOI: 10.3221/IGF-ESIS.42.23 218 Figure 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 . N UMERICAL INVESTIGATIONS Determination SED parameters he quasi ideally 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 presents at the notch tip in the moment that proceed the crack, tension calculated in a notched specimen under tensile load, specimen with a bland curvature radius. This σ t can be evaluated using U notched specimen with a curvature radius greater than 4 mm, a bland notch: is recommended to use a semi-circular notches, in this paper it has been choose to use a plate with symmetric U notch. 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 average maximum load 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 are under plane strain conditions. According with the procedure described above, it’s possible to define the tension at the notch tip. In Tab. 4 is exhibit the tension σ t and the parameters of SED method, calculated through Eq. 2 and 3. Density [Kg/m 3 ] σ t [MPa] R c [mm] W c [MJ/m 3 ] 100 3.19 0.20 0.169 145 4.39 0.24 0.143 300 6.06 1.0 0.065 708 26.7 0.62 0.285 Table 5 : Values of tension at the notch tip and respective SED parameters. Application SED method on specimens with different type of notch, mode I Through the SED parameters determined previously, is possible to apply the SED method on the notched specimens tested in the previous paragraphs. In the same way followed to determine the σ t tension, the SED method were applied through linear elastic finite element analysis, using plane elements (PLANE 184) and creating the control volume around the notch tip. The results are reported in Fig. 3.a. All the specimens are in mode I loads configuration. For the majority of the results, the scatter band is contained between + 10 % and – 22 %, a reasonable dispersion in engineering field. Application SED method on specimens with different type of notch, mode I ASCB specimens were tested under pure mode I, pure mode II and mixed mode I+II. The first approach is to use the SED parameters defined for mode I (Tab. 5) in the case of the mode II and mixed mode: for the higher densities, in mixed mode and in mode II the error is greater than 35 %, while for the lowest densities the error is contained between ± 10 %, Graph 1b. It has been noticed that the strain energy density increase from mode I to mode II. If it’s possible to T