Issue 32

N. Bisht et alii, Frattura ed Integrità Strutturale, 32 (2015) 1-12; DOI: 10.3221/IGF-ESIS.32.01 9 distribution of σ yy occurred on the upper and lower side of the crack, whereas σ xx and τ xy show asymmetrical distribution around the crack tip. Figure 10 : Von Mises stress distribution for two offset edge crack geometry for H=2 mm. Figure 11 : Von Mises stress distribution for two offset edge crack geometry for H=20. Figure 12 : Schematic representation of state of stress ahead of the crack tip, r and θ are the polar coordinates. The σ xx component is about 0.1 to 0.75 times of σ yy at the crack tip element. Fig. 13 and 14 also reveal that σ xx and σ yy are lower in magnitude compared to a single edge crack. The normal stress component σ xx increases with increasing offset distance, but its magnitude remains less than a single edge crack. It is also seen that σ xx is least when two cracks are very close to each other (H ≤ 2 mm). It is well established that mode I SIF mainly depends upon variation of σ yy at the crack tip. The present analysis shows that σ yy is higher for single edge crack as compared to multiple cracks with different offset distance H. Hence, in Fig. 9 K I for H = 0 mm is found to be higher as compared to other multiple crack configurations. It is also seen in Fig.13 that σ yy is minimum for H = 2 mm. Thus mode I SIF shown in Fig. 8 is found to attain minimum value at H = 2 mm, and thereafter it increases but remains less than a single edge crack. The variation of τ xy for different crack offset distance H = 0, 2, 10, 16 mm is shown in Fig.15. The figure shows that shearing stress is zero for single edge crack (H = 0 mm) and maximum for H = 2 mm. It is seen that as H increases, the shearing stress decreases. Thus, mode II SIF which is mainly due to shear component attains maximum value at H = 2 mm and thereafter it reduces as H increases. The results shown in fig. 8 also confirms that for single edge crack (H = 0 mm), mode II SIF is zero. This is also in conformity with the theoretical results for single edge crack.