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Stressed State of a Plane with Periodic System of Closely Located Curvilinear Holes with Edge Cracks

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Materials Science Aims and scope

A plane periodic problem of the theory of elasticity for an isotropic plane with infinite row of closely located curvilinear holes with edge cracks is solved by the method of singular integral equations. The stress intensity factors (SIF) at the tips of edge cracks propagating from symmetric holes of various shapes (elliptic holes, rhombic holes with rounded vertices, and narrow slots) are computed for arbitrary distances between the holes under the conditions of tension of the plane at infinity (mode I). The SIF for the edge cracks at the rounded vertices of the corresponding bilateral notches in the elastic plane are found as a result of the limit transition as the distances between the holes approach zero.

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References

  1. A. Karlsson and J. Backlund, “Summary of SIF design graphs for cracks emanating from circular holes,” Int. J. Fract., 14, No. 6, 585–596 (1978).

    Article  Google Scholar 

  2. V. M. Mirsalimov, Fracture of Elastic and Elastoplastic Bodies with Cracks [in Russian], Èlm, Baku (1984).

  3. M. P. Savruk and A. Kazberuk, “Stresses in an elastic plane with periodic system of closely located holes,” Fiz.-Khim. Mekh. Mater., 45, No. 6, 70–81 (2009); English translation: Mater. Sci., 45, No. 6, 831–844 (2009).

  4. V. S. Kravets’, “Stress-strain state of a plane with periodic system of holes containing edge cracks or plasticity strips,” in: A. M. Samoilenko and R. M. Kushnir (editors), Contemporary Problems of Mechanics and Mathematics [in Ukrainian], Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine, Vol. 2, Lviv (2018), pp. 44–46; www.iapmm.lviv.ua/mpmm2018.

  5. V. S. Kravets’ and M. P. Savruk, “Two-dimensional periodic problem of the theory of elasticity for an isotropic plane with curvilinear holes and edge cracks,” Fiz.-Khim. Mekh. Mater., 54, No. 6, 102–109 (2018); English translation: Mater. Sci., 54, No. 6, 866–874 (2019).

  6. H. Neuber, “Die halbelliptische Kerbe mit Riss als Beispiel zur Korrelation von Mikro- und Makrospannungskonzentrationen,” Ing.-Arch., 46, No. 6, 389–399 (1977).

    Article  Google Scholar 

  7. D. H. Chen, H. Nisitani, and K. Mori, “Stress intensity factors of a semi-infinite plate having a semi-elliptical notch with a crack under tension,” Trans. Japan. Soc. Mech. Eng., A55, 948–953 (1989).

    Article  Google Scholar 

  8. Y. Murakami (editor), Handbook of Stress Intensity Factors for Researchers and Engineers, Pergamon Press, Oxford (1987).

    Google Scholar 

  9. M. P. Savruk and A. Kazberuk, Stress Concentration at Notches, Springer, Cham (2017).

    Book  Google Scholar 

  10. M. P. Savruk, Two-Dimensional Problems of Elasticity for Bodies with Cracks [in Russian], Naukova Dumka, Kiev (1981).

  11. V. V. Panasyuk (editor), Fracture Mechanics and Strength of Materials, Vol. 2, M. P. Savruk, Stress Intensity Factors for Bodies with Cracks [in Russian], Naukova Dumka, Kiev 1988.

  12. H. Tada, P. C. Paris, and G. R. Irwin, The Stress Analysis of Cracks, ASME, New York (2000).

    Google Scholar 

  13. Y. Yamamoto, Y. Sumi, and K. Ao, “Stress intensity factors of cracks emanating from semi-elliptical side notches in plates,” Int. J. Fract., 10, No. 4, 593–595 (1974).

    Article  Google Scholar 

  14. Y. Murakami, “A simple procedure for the accurate determination of stress intensity factors by finite element method,” Eng. Fract. Mech., 8, No. 4, 643–655 (1976).

    Article  Google Scholar 

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Correspondence to V. S. Kravets’.

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Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 55, No. 6, pp. 17–25, November–December, 2019.

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Kravets’, V.S. Stressed State of a Plane with Periodic System of Closely Located Curvilinear Holes with Edge Cracks. Mater Sci 55, 794–803 (2020). https://doi.org/10.1007/s11003-020-00372-7

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