PSI - Issue 42

Abdulla Abakarov et al. / Procedia Structural Integrity 42 (2022) 1046–1053

1052

A. Abakarov and Y. Pronina / Structural Integrity Procedia 00 (2019) 000–000

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are shielded by large cracks on both sides — this is observed for cracks lying inside the relaxation zone of one of the big cracks (the circles bounding the relaxation zone lie near the values l ( t ∗ ) / l 0 = 1). However, for the configuration SBS — when the small cracks are shielded by large cracks on one side — the length of small cracks initially lying inside the relaxation zone, can double. However, this phenomenon may be a ff ected by the change in the threshold value K SCC I . The question also arises: how could some small cracks in configurations BSB and BSBSB grow if their mode I SIFs at t ∗ did not exceed the threshold value K SCC I (as was observed in numerical experiments)? This may be explained by the fact that at t = 0 their SIFs k I were greater than the threshold value K SCC I and they had time to grow up, but in the process of growth of the neighboring big cracks, they fell into the relaxation zone and their final mode I SIFs decreased. When a small crack lies between the bigger ones, its SIF I may become even negative despite the fact that the plane is under the tension. This e ff ect was also observed in Section 4.2. We also considered the edge e ff ect for large stacks of cracks. Figure 7 shows the mode I SIFs (at t ∗ ) of the big cracks in the central cell of stacks containing 23 and 44 big and small alternating cracks, calculated by the use of the “procedure of periodization” and the same SIFs in stack containing 23 big and small alternating cracks, calculated without using this procedure. The SIFs are normalized to the initial mode I SIF of a single small crack. As one can see, the stress state in the central part of the finite arrays stabilizes rather slowly with the increase in the number of cracks, especially for relatively small distances between the cracks. Using 23 cracks gives a relatively large error for modeling the behavior of an infinite periodic array of cracks (that agrees with the results of Abakarov and Pronina (2022)) even with the use of the “procedure of periodization”. Thus, we examined the e ff ect of interaction of cracks of di ff erent lengths grouped into stack arrays, on their stress assisted growth. It was established that introducing the relaxation zone of the same size for the cracks of the same length is not always reasonable. The size of this zone should depend on the threshold value K SCC I as well as on the relative configuration of a considered group of cracks. First, the amplifying and shielding e ff ects of neighboring parallel cracks on a given crack may compete: the overall e ff ect in such cases depends on the relative distances from the considered crack tip to the amplifying and shielding neighbors (see Kachanov (1993); Abakarov and Pronina (2022)). Second, as it was observed in some cases, even when the mode I SIFs almost do not increase, the mode II SIFs increase significantly; mixed mode conditions may alter the crack growth direction and thus its rate (see Wang et al. (1996); Abakarov et al. (2022)). Moreover, not only the nearest neighbors can a ff ect the growth of a certain crack, but also the father away neighbors; and these “neighbors of neighbors” can even change the qualitative pattern of the considered crack behavior. 4.5. The edge e ff ect for large stacks 5. Concluding remarks

Acknowledgements

This study was supported by the Russian Science Foundation, grant No 21-19-00100.

References

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