PSI - Issue 2_A

M Perl et al. / Procedia Structural Integrity 2 (2016) 3625–3646 M. Perl, and M. Steiner/ Structural Integrity Procedia 00 (2016) 000–000

3642 18

The effect of crack density in a thick vessel is similar to that in thinner ones. Fig. 19 represents the same crack configuration as Fig. 18, but in a thicker vessel of R 0 /R i =1.7. In this case, the increase in K IAmax is ~22%, similar to the ~24%, for the thinner vessel R 0 /R i =1.2 (Fig. 18).

Fig. 19. K IA /K 0 vs . ψ along the fronts of lunular coplanar crack arrays of ellipticity a/c=1.0, and densities of δ=0, 0.6, 0.8, and 0.89 (a/t=0.1, R 0 /R i =1.7, ε =100%).

4.2.3 Coplanar crack arrays - concluding remarks Two general conclusions can be drawn from the above analysis regarding coplanar crack arrays emanating from the inner surface of an autofrettaged spherical vessel: 1. As crack density in the array increases, the absolute value of the SIF due to autofrettage increases along the entire crack front as a result of crack interaction. This increase is larger for deeper cracks and more accentuated in the vicinity of the vessel's inner surface. However, the relative thickness of the vessel hardly has any influence on this increase. 2. As a/c decreases, crack interaction becomes weaker. 4.3 Ring cracks Spherical pressure vessel which are made of two hemispheres joined together by a girth weld on the equatorial plane are susceptible to multiple coplanar cracking on the weld plane. In certain cases the coplanar cracks coalesce to become an axisymmetric inner ring crack on the equatorial plane. Fig. 20 depicts the normalized SIFs, K IA Ring /K 0 8 , for various relative crack depths, a/t=0.025, 0.05, 0.1, 0.2, 0.4, and 0.6, prevailing in three spherical vessels of relative thickness R 0 /R i =1.1, 1.2, and 1.7. The magnitude of the residual stress field increases with vessel thickness, 8 In the case of a ring crack a/c→0, and thus in equation (2) Q=1 and the normalizing SIF becomes � � � �� � √�� .