Issue 48

M. K. Hussain et alii, Frattura ed Integrità Strutturale, 48 (2019) 599-610; DOI: 10.3221/IGF-ESIS.48.58 607 The mode I and mode II NSIFs are also calculated in a similar way to that of the ASENT specimen. Tab. (4) lists the results of mode I and mode II NSIFs obtained using the PSDT. For comparison, the numerical and experimental results of Ayatollahi and Nejati [34] are also presented in Tab. (4) and it has been noticed that the present results are in good agreement with the published results. Thus, the results in all the examples indicate that the PSDT is simple and robust. The FE displacements at the optimal points are more accurate than the other points on the notch tip element. The PSDT can provide very good results with coarse mesh even with convention elements at the notch tip.         I F II F Present Ayatollahi and Nejati [34] (FEM) Ayatollahi and Nejati [34] (Experimental) Present Ayatollahi and Nejati [34] (FEM) Ayatollahi and Nejati [34] (Experimental) 0 30 0.7213 0.7100 0.7400 0.0027 0.0000 0.0200 60 1.1530 1.1300 1.1700 0.0000 0.0000 0.0500 90 2.3108 2.2900 2.2900 0.0000 0.0000 0.0600 10 30 0.5727 0.5600 0.6000 0.7470 0.7200 0.7200 60 0.9599 0.9400 0.9900 1.2619 1.1700 1.1100 90 2.0187 2.0000 1.9500 2.1169 2.0200 2.1300 20 30 0.2148 0.2000 0.2200 1.2006 1.1800 1.1800 60 0.4940 0.4800 0.4800 1.9260 1.8600 1.8900 90 1.3013 1.2900 1.2700 3.0792 3.1200 3.0300 30 30 0.1980 – – 1.3447 – – 60 0.0555 -0.0100 0.0900 2.0788 2.0200 1.9200 90 0.4395 – – 3.2716 – – Table 4: Comparison of the normalized NSIFs I F and II F for the SV-BD specimen (  a w 0.5). C ONCLUSIONS n this paper, the efficacy of an FE based NSIF extraction technique: the point substitution displacement technique (PSDT) has been demonstrated by determining the NSIFs of various configurations under mode I and mixed mode (I/II) loading conditions. The NSIFs are determined from the FE notch flank displacements at the optimum point(s) in the notch tip elements. The efficacy of the present method is examined with two mode I and two mixed mode (I/II) problems. The results obtained using the present method is validated with the available results. The results show that the PSDT is simple, robust and easy to be implemented in the available FE code. Further, accurate values of mode I and II NSIFs can be obtained using coarse meshes. R EFERENCES [1] Williams, M.L. (1952). Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mechs., 19, pp. 526–528. [2] Dunn, M.L. and Suwito, W. (1997). Fracture initiation at sharp notches: Correlation using critical stress intensities, Int. J. Solids Struct., 34(29), pp. 3873–3883. DOI: 10.1016/S0020-7683(96)00236-3 [3] Seweryn, A. (1994). Brittle fracture criterion for structures with sharp notches, Eng. Fract. Mech., 47, pp. 673–81. DOI: 10.1016/0013-7944(94)90158-9 I