Issue 42

M. Peron et alii, Frattura ed Integrità Strutturale, 42 (2017) 196-204; DOI: 10.3221/IGF-ESIS.42.21 202 Coarse mesh (48 finite elements) Refined mesh (2206 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 0.618 1.209 0.1 and 0.075 Lazzarin et al. 0.613 1.229 -0.81 1.65 0.613 1.229 -0.81 1.65 0.1 Treifi et al. 0.604 1.249 -2.27 3.31 0.632 1.184 2.27 -2.07 0.1 New method 0.635 1.175 2.75 -2.81 0.625 1.200 1.13 -0.74 0.1 New modified method 0.629 1.196 1.78 -1.08 0.01 and 0.0075 Lazzarin et al. 0.617 1.205 -0.16 -0.33 0.617 1.210 -0.16 0.08 0.01 Treifi et al. 0.617 1.211 -0.16 0.17 0.618 1.200 0.00 -0.74 0.01 New method 0.601 1.394 -2.75 15.30 0.617 1.212 -0.16 0.25 0.01 New modified method 0.618 1.192 0.00 -1.41 0.001 and 0.00075 Lazzarin et al. 0.618 1.166 0.00 -3.56 0.618 1.182 0.00 -2.23 0.001 Treifi et al. 0.618 1.213 0.00 0.33 0.617 1.202 -0.16 -0.58 0.001 New method 0.627 1.167 1.46 -3.54 0.618 1.178 0.00 -2.56 0.001 New modified method 0.619 1.130 0.16 -6.53 Table 3 : Comparison between approximate methods for NSIFs evaluation of diamond-shaped notch (2 α = 90°). Coarse mesh (64 finite elements) Refined mesh (3395 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 0.655 0.638 0.1 Treifi et al. 0.636 0.642 -2.90 0.63 0.660 0.637 0.76 -0.16 0.1 New method 0.697 0.620 6.41 -2.82 0.639 0.645 -2.44 1.10 0.1 New modified method 0.639 0.645 -2.44 1.10 0.01 Treifi et al. 0.613 0.654 -6.41 2.51 0.635 0.647 -3.05 1.41 0.01 New method 0.708 0.616 8.09 -3.45 0.653 0.640 -0.31 0.31 0.01 New modified method 0.653 0.640 -0.31 0.31 0.001 Treifi et al. 0.624 0.651 -4.73 2.04 0.644 0.644 -1.68 0.94 0.001 New method 0.712 0.615 8.70 -3.61 0.662 0.636 1.07 -0.31 0.001 New modified method 0.657 0.639 0.31 0.16 Table 4 : Comparison between approximate methods for NSIFs evaluation of central tilted crack (2 α = 0°) in a plate of finite extension. C ONCLUSIONS n the present contribution three methods for the rapid calculation of the NSIFs, based on the averaged strain energy density, are compared. The first method, proposed by Lazzarin et al., is based on the calculation of the SED averaged in two different control volumes centred at the notch tip. This approach cannot be applied to notch with zero opening angle (cracks) subjected to mixed mode loading. The second method, presented by Treifi et al., overcomes this problem taking advantage of the strain energy density averaged within two control volumes (semi-circular sector) centred at the notch tip. Then a new method based on the evaluation of the total and deviatoric strain energy density has been proposed. I