PSI - Issue 51

Victor Rizov et al. / Procedia Structural Integrity 51 (2023) 44–50 V. Rizov / Structural Integrity Procedia 00 (2022) 000–000

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Cracks 2 and 3 are also analyzed by the J -integral. The integration is performed along contours R and Q (Fig. 1). The J -integrals match the SERR. This fact verifies the SERR analysis. 3. Numerical results Numerical results which illustrate the influence of various factors on the SERR are presented here.

20  F N, curve 2 – at

40  F N and curve 3 – at

60  F N).

Fig. 2. The normalized SERR plotted against h h / 1 ratio (curve 1 - at

  G G D b N 0 /  . The locations of the cracks 1, 2 and 3 along the height of

The normalized SERR are presented as the beam are characterized by h h / 1 , 

 h h h / 2 1  and 

 h h h h / 3 2 1   ratios, respectively. Ratio,

0 1 / D D ,

characterizes the inhomogeneity. The following data are used: 0.5  m . The influence of the location of crack 1 in the height direction is illustrated in Fig. 2. The curves in Fig. 2 indicate that the SERR increases when h h / 1 increases. The results shown in Fig. 3 are obtained by using solution for crack 2. The SERR increases when   h h h / 2 1  increases (Fig. 3). Fig. 3 indicates also that the SERR decreases when h h / 1 increases (this can be explained by the decrease of the difference between the stiffness of parts, 2 3 S S and 3 4 S S , of the beam which are located behind 0.020  b m, 0.2  L , 1.4  n and

and ahead of the tip of crack 2, respectively). The normalized SERR is plotted against 

 h h h h / 3 2 1   ratio in Fig. 4 at three 

 h h h / 2 1  ratios by  h h h h / 3 2 1   ratio.

applying solution for crack 3. It can be observed that the SERR increases with increasing of 

The SERR decreases with increase of 

 h h h / 2 1  (Fig. 4).