Issue 48

M. K. Hussain et alii, Frattura ed Integrità Strutturale, 48 (2019) 599-610; DOI: 10.3221/IGF-ESIS.48.58 604 Example 1: Mode I Problems The first set of examples considered are single edge notched plate under uniform tension (SENT) and single edge notched plate under in-plane bending (SENB) as pure mode I examples (as shown in Fig. (3)). The geometrical parameters considered for the SENT and SENB are as follows:  1.0 w and  1.2 h as shown in Fig. (3). The uniform tensile loading  (=1.0) and a bending loading  3 .2 / h w (=7.2) are considered for the SENT and SENB specimens, respectively (Fig. (3a) and 3(b)). The notch angles   0°, 15°, 30°, 45°, 60°, 75°, 90, 105° and 120° are considered for validating the present method. Young’s modulus  1 E and Poisson’s ratio   0.25 are considered. One-half (shaded portion in Fig. (3a) and Fig. (3b)) of the geometries is modeled due to the symmetry with appropriate boundary conditions. The typical mesh with 211 number of elements (NE) and 702 number of nodes (NN) used for both the specimens is shown in Fig. (3c). The notch tip element to notch length ratio is considered as  0.025 N L a for both the specimens. The optimum points    opt op N r r L obtained using Eq. (14) are found to be centered around 0.79 for all the notch angles in the present examples (for a detailed description, one may refer to Ref. [29]). It has been observed that  FE v at the optimal points opt r obtained using Eqn. (14) are very accurate. The mode I NSIFs calculated at the respective optimal points and are listed in Tab. (1) and Tab. (2) for the SENT and SENB specimens, respectively. Figure 3: (a) Single edge notched plate under uniform tension (SENT), (b) single edge notched plate under in-plane bending (SENB) and (c) typical FE mesh used for both SENT and SENB specimens (NE=211, NN= 702 ).     I F Present Gross and Mendelson [10] Zhan and Hahn [33] Chen [12] 0 2.7856 2.8237 2.8301 – 15 2.8019 – – – 30 2.8279 2.8448 2.8408 2.8440 45 2.8775 – – – 60 2.9620 2.9716 2.9937 2.9700 75 3.1005 – – – 90 3.3191 3.3244 3.3716 3.3220 105 3.6532 – – – 120 4.1578 4.1458 4.0133 – Table 1: Normalized NSIF I F for the SENT specimen (  0.5 a w ).