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Quasi-brittle fracture diagram of structured bodies in the presence of edge cracks

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Abstract

The Neuber-Novozhilov approach is used to obtain necessary and sufficient fracture criteria. Using a modified Leonov-Panasyuk-Dugdale model, simple relations for the critical fracture parameters are derived for opening mode edge cracks for the case where the diameter of the prefracture zone coincides with the diameter of the plasticity zone. These relations are suitable for studying fracture where the crack length is negligibly small. A fracture diagram using critical stresses under both criteria is proposed for a wide range of crack length. At a certain level of loading, three regions are identified, in the first of which the crack is stable, in the second, the crack extends but remains stable, and in the third, the crack is unstable. Experimental data on the fracture of specimens with edge cracks are obtained. It is established that the theoretical critical fracture curves are in good agreement with the obtained critical parameters for flat tensile specimens with two collinear edge cracks.

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References

  1. V. M. Kornev, “Estimation diagram of quasi-brittle fracture for bodies with a hierarchy of structures. Multiscale necessary and sufficient fracture criteria,” Fiz. Mezomekh., 13, No. 1, 47–59 (2010).

    Google Scholar 

  2. G. Neuber, Kerbspannunglehre: Grunglagen fur Genaue Spannungsrechnung, Springer-Verlag, Berlin (1937).

    Google Scholar 

  3. V. V. Novozhilov, “On the necessary and sufficient criteria of brittle strength,” Prikl. Mat. Mekh., 33, No. 2, 212–222 (1969).

    Google Scholar 

  4. V. M. Kornev, “Generalized sufficient strength criteriia. Description of the prefracture zone,” J. Appl. Mech. Tech. Phys., 43, No. 5, 763–769 (2002).

    Article  MathSciNet  Google Scholar 

  5. V. M. Kornev, “Stress distribution and crack opening in the prefracture region (Neuber-Novozhilov approach),” Fiz. Mezomekh., 7, No. 3, 53–62 (2004).

    MathSciNet  Google Scholar 

  6. M. Ya. Leonov and V. V. Panasyuk, “Development of fine cracks in a solid,” Prikl. Mekh., 5, No. 4, 391–401 (1959).

    MathSciNet  Google Scholar 

  7. D. S. Dugdale, “Yielding of steel sheets containing slits,” J. Mech. Phys. Solids, 8, 100–104 (1960).

    Article  ADS  Google Scholar 

  8. I. M. Kershtein, V. D. Klyushnikov, E. V. Lomakin, and S. A. Shesterikov, Fundamentals of Experimental Fracture Mechanics [in Russian], Izd. Mosk. Gos. Univ., Moscow (1989).

    Google Scholar 

  9. D. Broek, Elementary Engineering Fracture Mechanics, Martinus Nijhoff, Boston (1982).

    Google Scholar 

  10. A. Neimitz, “Jump-like crack growth models of theory of critical distances. Are they correct?” ESIS Newsletter, No. 44, 20–26 (2008).

  11. M. P. Savruk, “Stress intensity factors in bodies with cracks,” in: Fracture Mechanics and Strength of Materials [in Russian], Vol. 2, Naukova Dumka, Kiev (1988), p. 620.

    Google Scholar 

  12. Y. Murakami (ed.), Stress Intensity Factors Handbook, Vol. I, Pergamon Press, Oxford-New York (1987).

    Google Scholar 

  13. D. Taylor, “The theory of critical distances,” Eng. Fract. Mech., 75, 1696–1705 (2008).

    Article  Google Scholar 

  14. A. G. Demeshkin and V. M. Kornev, “Crack path kinking under generalized stress state,” J. Appl. Mech. Tech. Phys., 50, No. 3, 532–539 (2009).

    Article  ADS  Google Scholar 

  15. T. V. Krasnikova and E. B. Petrilenkova, Foams Based on Polymer Binders and Microspheres [in Russian], Leningr. Dom Nauch.-Tekh. Propagandy, Leningrad (1971).

    Google Scholar 

  16. P. G. Krzhechkovskii, “Fracture mechanics of spheroplasts,” Probl. Prochnosti, No. 11, 110–115 (1982).

  17. E. V. Karpov, “Fracture of spheroplast samples with different types of stress concentrators,” J. Appl. Mech. Tech. Phys., 43, No. 4, 630–637 (2002).

    Article  Google Scholar 

  18. B. D. Annin, A. G. Demeshkin, and E. V. Karpov, “Various mechanisms of fracture of spheroplasts,” in: Tr. Tsentr. Nauch.-Issled. Inst. Krylova, No. 52, 13–20 (2010).

  19. F. Berto and P. Lazzarin, “On higher order terms in the crack tip stress field,” Int. J. Fract., 161, 221–226 (2010).

    Article  Google Scholar 

  20. A. Cornec, I. Scheider, and K.-H. Schwalbe, “On the practical application of the cohesive model,” Eng. Fract. Mech., 70, 1963–1987 (2003).

    Article  Google Scholar 

  21. G. Lin, X.-G. Meng, A. Cornec, and K.-H. Schwalbe, “The effect of strength mis-match on mechanical performance of weld joints,” Int. J. Fract., 96, 37–54 (1999).

    Article  Google Scholar 

  22. V. M. Kornev and N. S. Astapov, “Model of fracture of a piecewise homogeneous medium during layering of elastoplastic structured materials,” Mekh. Komposits. Mater. Konstr., 16, No. 3, 347–360 (2010).

    Google Scholar 

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Correspondence to V. M. Kornev.

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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 52, No. 6, pp. 152–164, November–December, 2011.

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Kornev, V.M., Demeshkin, A.G. Quasi-brittle fracture diagram of structured bodies in the presence of edge cracks. J Appl Mech Tech Phy 52, 975–985 (2011). https://doi.org/10.1134/S0021894411060162

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  • DOI: https://doi.org/10.1134/S0021894411060162

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