Issue 42

M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 196-204; DOI: 10.3221/IGF-ESIS.42.21 200 R ESULTS he methods described above have been applied to five different geometries of notched plates subjected to mixed mode I+II loading. For each geometry K 1 and K 2 have been first calculated according to Gross and Mendelson (Eqs. 1 and 2), by means of FE analyses adopting very refined meshes in the close neighbourhood of the notch tip (size of the smallest element of the order of 10 -5 mm). Afterwards the approximate methods have been applied, taking into consideration three different values of the control radius R 0 (0.1, 0.01 and 0.001 mm) and by using coarse and refined FE meshes. The mesh has been performed by means of 8-nodes elements (PLANE 183), using the FE code ANSYS® 14.5. In the FE analyses a Poisson’s ratio ν equal to 0.3 and a Young’s modulus E equal to 206 GPa have been adopted. In the summary tables the normalized NSIFs are reported, according to the definition: , 1 i i i normalized K K a      (13) Case studies: geometries and results The geometries taken into consideration (Fig. 4) consist in notched finite or infinite plates subjected to mixed mode I+II loading. The geometry of the finite plates is characterized by equal width and height, 2 W = H = 10 mm, while plates of infinite extension are characterized by 2 W = H = 10 mm. Diamond shape notches (Fig. 4a) are characterized by a projected notch depth 2 a = 2 mm and a notch inclination angle φ = 45 o . Two different notch opening angle 2 ߙ have been analysed: 45° and 30°. The obtained results and the comparison between the different approaches are reported in Table 1 and Table 2. The square hole (Fig. 4b) is characterized by a projected notch depth 2 a = 2 mm and a notch opening angle 2α = 90 o . The obtained results and the comparison between the different approaches are reported in Table 3. Figure 4 : Case studied for the application of the method: diamond shape notch (a) , square hole (b) , central tilted crack in a finite plate (c) and central tilted crack in a plate of infinite extension (d) . D ISCUSSION abs. 1-5 show the results obtained from different geometries of notched plates subjected to mixed mode I+II loading, by adopting coarse and refined meshes for the application of the approximate methods. All the considered approaches allow to obtain very good approximations when refined meshes are adopted in the FE analyses, being the deviations, with respect to the values calculated according to Gross and Mendelson [10], lower than 1% in most of the cases. The obtained results become more interesting when coarse meshes, which require shorter calculation time, are adopted in the FE analyses. It can be observed that the approach of Lazzarin et al. [28] enables to obtain very good approximations, being the deviations lower than 1% in most of the cases analyzed in the present contribution. It should be noted that this method has not been applied to cracks subjected to mixed mode loading (Tables 4, 5), since an indeterminate system of equations would be obtained. The percentage error increases to about 3-6% in the case of Treifi et al. approach [29], which reaches a maximum percentage deviation of 12-18% in the case of tilted cracks (Table 5). T T