Issue 42

M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 196-204; DOI: 10.3221/IGF-ESIS.42.21 201 The new proposed method, based on the evaluation of the total and deviatoric SED, allows to obtain a percentage error close to that observed in the case of Treifi et al. [29]. The deviation still remains greater than that observed in the case of Lazzarin et al. [28], because of the dependence of the deviatoric SED on the mesh size. This problem is overcome by the modified version of the new method that, through a control volume consisting of a circular ring, enables to exclude the region characterized by the highest stress gradient making the method less sensitive to the refinement level of the adopted mesh. The new method, particularly the modified version, provides very good approximations and a greater applicability than the approach of Lazzarin et al. [28] and [30], so it could be useful for rapid calculation of the NSIFs. Coarse mesh (64 finite elements) Refined mesh (3128 finite elements) R 0 [mm] Method K 1 K 2 Δ K 1 (%) Δ K 2 (%) K 1 K 2 Δ K 1 (%) Δ K 2 (%) Gross and Mendelson 0.656 0.911 0.1 and 0.075 Lazzarin et al. 0.650 0.919 -0.91 0.88 0.650 0.919 -0.91 0.88 0.1 Treifi et al. 0.694 0.878 5.79 -3.62 0.693 0.878 5.64 -3.62 0.1 New method 0.681 0.891 3.81 -2.20 0.666 0.905 1.52 -0.66 0.1 New modified method 0.664 0.908 1.22 -0.33 0.01 and 0.0075 Lazzarin et al. 0.657 0.909 0.15 -0.22 0.655 0.912 -0.15 0.11 0.01 Treifi et al. 0.665 0.895 1.37 -1.76 0.663 0.897 1.07 -1.54 0.01 New method 0.671 0.883 2.29 -3.07 0.657 0.909 0.15 -0.22 0.01 New modified method 0.656 0.911 0.00 0.00 0.001 and 0.00075 Lazzarin et al. 0.659 0.901 0.46 -1.10 0.656 0.909 0.00 -0.22 0.001 Treifi et al. 0.658 0.907 0.31 -0.44 0.657 0.908 0.15 -0.33 0.001 New method 0.671 0.856 2.29 -6.04 0.658 0.901 0.30 -1.10 0.001 New modified method 0.658 0.905 0.30 -0.66 Table 1 : Comparison between approximate methods for NSIFs evaluation of diamond-shaped notch (2 α = 45°). Coarse mesh (64 finite elements) Refined mesh (3063 finite elements) R 0 [mm] Method K 1 K 2 Δ K 1 (%) Δ K 2 (%) K 1 K 2 Δ K 1 (%) Δ K 2 (%) Gross and Mendelson 0.654 0.813 0.1 and 0.075 Lazzarin et al. 0.648 0.818 -0.92 0.62 0.650 0.817 -0.61 0.49 0.1 Treifi et al. 0.670 0.803 2.45 -1.23 0.681 0.796 4.13 -2.09 0.1 New method 0.686 0.792 4.89 -2.58 0.663 0.808 1.38 -0.62 0.1 New modified method 0.660 0.810 0.92 -0.37 0.01 and 0.0075 Lazzarin et al. 0.657 0.811 0.46 -0.25 0.655 0.813 0.15 0.00 0.01 Treifi et al. 0.621 0.847 -5.05 4.18 0.638 0.829 -2.45 1.97 0.01 New method 0.677 0.789 3.52 -2.95 0.657 0.811 0.46 -0.25 0.01 New modified method 0.656 0.812 0.31 -0.12 0.001 and 0.00075 Lazzarin et al. 0.660 0.807 0.92 -0.74 0.656 0.811 0.31 -0.25 0.001 Treifi et al. 0.673 0.784 2.91 -3.57 0.660 0.805 0.92 -0.98 0.001 New method 0.675 0.779 3.21 -4.18 0.659 0.807 0.76 -0.74 0.001 New modified method 0.658 0.809 0.31 -0.49 Table 2 : Comparison between approximate methods for NSIFs evaluation of diamond-shaped notch (2 α = 30°).