PSI - Issue 42

Abdulla Abakarov et al. / Procedia Structural Integrity 42 (2022) 1046–1053 A. Abakarov and Y. Pronina / Structural Integrity Procedia 00 (2019) 000–000

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Fig. 1. BSB (a) and BB (b) configurations.

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Fig. 3. BSBSB (a) and BBB (b) configurations.

Fig. 2. SBS (a) and B (b) configurations.

also estimated. Large arrays of cracks were analyzed, e.g., in the papers of Kamaya and Haruna (2007), Tohgo et al. (2009), Fujii et al. (2015) and Bolivar et al. (2017). As mentioned above, interaction of cracks includes amplification and shielding e ff ects. The stress enhancement zone (where cracks growth is accelerated) expands from the vicinity of the pre-existing crack tip. A shielding e ff ect is due to the relaxation zone around the flanks of the pre-existing crack. This zone (which is also called inactive) is usually presented as a circle around the crack as its diameter. According to Kamaya and Haruna (2007), Tohgo et al. (2009), Bolivar et al. (2017), in the stress relaxation zone, the initiation of new cracks is suppressed. It is also assumed that in such regions, cracks may not be able propagate and coalesce with others (see, e.g. Wang et al. (1996) and Tohgo et al. (2009)). Parallel surface cracks of equal length were considered by Kamaya and Haruna (2007). In Kachanov (1993), it is noted that the local SIFs for parallel multicrack arrays are mainly influenced by the nearest neighbors, and their expressions are very close to that of the two-crack case. In this paper we examine whether the circular relaxation zone around the pre-existing crack may suppress the growth of other cracks inside this zone and investigate the e ff ect of the father away neighbors. We restrict our study by considering the shielding e ff ect caused by interaction of parallel cracks of unequal lengths with various relative distances between them and their centers located on the same line.

2. Description of the problem

The 2-D problem of an infinite plane weakened by parallel cracks under the action of uniaxial tension in the direc tion perpendicular to the crack lines is considered. Here, we neglect the change in the direction of crack propagation, considering their rectilinear growth. Several stacked configurations of cracks of various sizes are considered: three cracks with the bigger one in the center (Fig. 1a), three cracks with the smaller one in the center (Fig. 2a), and finite numbers of parallel cracks or an approximate model of infinite stack (Fig. 3a).The same configurations are considered with zero length of the small cracks (i.e. without small cracks — Figs. 1b, 2b, 3b). In the text to follow, we will denote these configurations by the use of B and S for the Bigger and Smaller cracks (see the captions for these figures).