PSI - Issue 3

F. Berto et al. / Procedia Structural Integrity 3 (2017) 126–134 F. Berto et al. / Structural Integrity Procedia 00 (2017) 000–000

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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.

Fig. 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).

Central tilted cracks in a plate of finite (Fig. 4c) or infinite (Fig. 4d) extension are characterized by a projected crack length 2 a = 2 mm and a crack inclination angle φ = 45 o . The obtained results and the comparison between the different approaches are reported in Tables 4, 5. It is worth noting that the case of the infinite plate has been modelled as a finite plate characterized by width and height two orders of magnitude greater than the crack length.

Table 1. Comparison between approximate methods for NSIFs evaluation of diamond-shaped notch (2 α = 45°). Coarse mesh (64 finite elements)

Refined mesh (3128 finite elements) K 2 Δ K 1 (%) Δ K 2 (%) K 1 K 2 Δ K 1 (%) Δ K 2 (%) 0.911

R 0 [mm]

Method

K 1

Gross and Mendelson

0.656 0.650 0.694 0.681 0.664 0.657 0.665 0.671 0.656 0.659 0.658 0.671 0.658 0.654 0.648 0.670 0.686 0.660 0.657 0.621 0.677 0.656 0.660 0.673 0.675 0.658 K 1

0.1 and 0.075

Lazzarin et al. Treifi et al. New method Lazzarin et al. Treifi et al. New method Lazzarin et al. Treifi et al. New method

0.919 0.878 0.891 0.908 0.909 0.895 0.883 0.911 0.901 0.907 0.856 0.905

-0.91 5.79 3.81 1.22 0.15 1.37 2.29 0.00 0.46 0.31 2.29 0.30

0.88 -3.62 -2.20 -0.33 -0.22 -1.76 -3.07 0.00 -1.10 -0.44 -6.04 -0.66

0.650 0.693 0.666 0.655 0.663 0.657 0.656 0.657 0.658

0.919 0.878 0.905 0.912 0.897 0.909 0.909 0.908 0.901

-0.91 5.64 1.52 -0.15 1.07 0.15

0.88 -3.62 -0.66 0.11 -1.54 -0.22 -0.22 -0.33 -1.10

0.1 0.1 0.1

New modified method

0.01 and 0.0075

0.01 0.01 0.01

New modified method

0.001 and 0.00075

0.00 0.15 0.30

0.001 0.001 0.001

New modified method

Table 2. Comparison between approximate methods for NSIFs evaluation of diamond-shaped notch (2 α = 30°). Coarse mesh (64 finite elements)

Refined mesh (3063 finite elements) K 2 Δ K 1 (%) Δ K 2 (%) K 1 K 2 Δ K 1 (%) Δ K 2 (%) 0.813

R 0 [mm]

Method

Gross and Mendelson

0.1 and 0.075

Lazzarin et al. Treifi et al. New method Lazzarin et al. Treifi et al. New method Lazzarin et al. Treifi et al. New method

0.818 0.803 0.792 0.810 0.811 0.847 0.789 0.812 0.807 0.784 0.779 0.809

-0.92 2.45 4.89 0.92 0.46 -5.05 3.52 0.31 0.92 2.91 3.21 0.31

0.62 -1.23 -2.58 -0.37 -0.25 4.18 -2.95 -0.12 -0.74 -3.57 -4.18 -0.49

0.650 0.681 0.663 0.655 0.638 0.657 0.656 0.660 0.659

0.817 0.796 0.808 0.813 0.829 0.811 0.811 0.805 0.807

-0.61 4.13 1.38 0.15 -2.45 0.46

0.49 -2.09 -0.62 0.00 1.97 -0.25 -0.25 -0.98 -0.74

0.1 0.1 0.1

New modified method

0.01 and 0.0075

0.01 0.01 0.01

New modified method

0.001 and 0.00075

0.31 0.92 0.76

0.001 0.001 0.001

New modified method