Conclusion
Formulas have been derived for the failure probability of a body containing internal (structural) disk-type cracks of random size and orientation on axisymmetric loading. The calculations are based on the assumption that the cracks do not interest, where Sack's criterion is used with radius and orientation-angle distributions. Trends in the failure probability are related to the load, state of strain, material strength and structural characteristics, and body size (number of cracks in the body).
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P. M. Vitvitskii and S. Yu. Popina, Strength and Brittle-Failure Criteria for Stochastically Defective Bodies [in Russian], Naukova Dumka, Kiev (1980).
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Translated from Fiziko-Khimicheskaya Mekhanika Materialov, No. 6, pp. 50–57, November–December, 1989.
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Vitvits'kii, P.M. Failure probability under axisymmetric loading in a body having internal diskoid cracks. Mater Sci 25, 599–606 (1990). https://doi.org/10.1007/BF00727087
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DOI: https://doi.org/10.1007/BF00727087