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Influence of Tension Along a Mode I Crack in an Elastic Body on the Formation of a Nonlinear Zone

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International Applied Mechanics Aims and scope

The state of the art in modeling the fracture process in various bodies with cracks is critically analyzed. Theoretical approaches to the adequate description of the fracture behavior of bodies due to crack propagation observed experimentally are considered. The potentials of various approaches to the improvement of modern models are evaluated. The problem of the equilibrium state of a nonlinear elastic body with a central mode I crack under biaxial tension is solved. The effect of tensile stresses acting along the crack on its opening displacement and shape of the nonlinear zone is examined

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References

  1. V. L. Bogdanov, A. N. Guz, and V. M. Nazarenko, “Stress–strain state of a material under forces acting along a periodic set of coaxial mode II penny-shaped cracks,” Int. Appl. Mech., 46, No. 12, 1339–1350 (2010).

    Article  MathSciNet  Google Scholar 

  2. P. W. Bridgman, “Recent work in the field of high pressures,” Rev. Modern Physics, 18, No. 1, 1–93 (1946).

    Article  MathSciNet  ADS  Google Scholar 

  3. P. M. Vitvitskii, V. V. Panasyuk, and S. Ya. Yarema, ”Plastic deformation in the vicinity of a crack and the criteria of fracture (a review),” Strength of Materials, 5, No. 2, 135–151 (1973).

    Article  Google Scholar 

  4. I. I. Goldenblatt, Some Problems of the Mechanics of Deformable Media, Noordhoff, Groningen (1962).

    Google Scholar 

  5. A. N. Guz, A. A. Kaminsky, and V. M. Nazarenko, Fracture Mechanics, Vol. 5 of the 12-volume series Mechanics of Composite Materials [in Russian], ASK, Kyiv (1996).

  6. A. A. Il’yushin, ”Some issues of plastic deformation theory,” Prikl. Mat. Mekh., 7, No. 4, 245–272 (1943).

    MathSciNet  Google Scholar 

  7. A. A. Kaminsky and D. A. Gavrilov, Delayed Fracture of Polymeric and Composite Materials with Cracks [in Russian], Naukova Dumka, Kyiv (1992).

    Google Scholar 

  8. A. A. Kaminsky, G. I. Usikova, E. E. Kurchakov, E. A. Dmitrieva, and S. P. Doroshenko, ”Experimental study of the plastic zone near a crack tip,” Probl. Mashinostr. Avtomatiz., No. 6, 79–85 (1991).

  9. A. A. Kaminsky, G. I. Usikova, and E. A. Dmitrieva, ”Experimental study of the distribution of plastic strains near a crack tip during static loading,” Int. Appl. Mech., 30, No. 11, 892–897 (1994).

    Article  ADS  Google Scholar 

  10. A. A. Kaminsky, L. A. Kipnis, and V.A. Kolmakova, ”On the Dugdale model for a crack at the interface of different media,” Int. Appl. Mech., 35, No. 1, 58–63 (1999).

    Article  ADS  Google Scholar 

  11. A. A. Kaminsky, M. V. Dudik, and L. A. Kipnis, ”Initial kinking of an interface crack between two elastic media under tension and shear,” Int. Appl. Mech., 45, No. 6, 635–642 (2009).

    Article  MathSciNet  ADS  Google Scholar 

  12. E. E. Kurchakov, ”Stress-strain relation for nonlinear anisotropic medium,” Int. Appl. Mech., 15, No. 9, 803–807 (1979).

    MATH  MathSciNet  ADS  Google Scholar 

  13. V. V. Panasyuk, Limiting Equilibrium of Brittle Bodies with Cracks [in Russian], Naukova Dumka, Kyiv (1968).

    Google Scholar 

  14. V. Z. Parton and E. M. Morozov, Mechanics of Elastic-Plastic Fracture, Hemisphere, Washington (1989).

    MATH  Google Scholar 

  15. M. M. Filonenko-Borodich, Theory of Elasticity, Dover, New York (1965).

    MATH  Google Scholar 

  16. L. P. Khoroshun, ”Discretization of the plane problem for a cracked body with nonlinear stress–strain diagram under tension,” Int. Appl. Mech., 46, No. 11, 1238–1252 (2010).

    Article  Google Scholar 

  17. R. Clausius, ”Ueber eine veranderte Form des zweiten Hauptsatzes der mechanischen Warmetheorie,” Annalen der Physic und Chemie, 93, No. 12, 481–506 (1854).

    Article  ADS  Google Scholar 

  18. G. P. Cherepanov, Mechanics of Brittle Fracture, McGrow-Hill, New York (1979).

    MATH  Google Scholar 

  19. P. P. Cortet, S. Santucci, L. Vanel, and S. Ciliberto, ”Slow crack growth in polycarbonate films,” Europhysics Letters, 71, No. 2, 242–248 (2005).

    Article  ADS  Google Scholar 

  20. C. K. Desai, A. S. Kumar, S. Basu, and V. Parameswaran, “Measurement of cohesive parameters of crazes in polystyrene films,” in: Conf. Proc. of the Society for experimental mechanics series (2011), pp. 519–526.

  21. H. Liebowitz (ed.), Fracture. An Advanced Treatise, Vols. 1–7, Academic Press, New York (1968–1974).

  22. A. L. Gain, J. Carroll, G. H., Peulino, and J. Lambros, ”A hybrid experimental/numerical technique to extract cohesive fracture properties for mode-I fracture of quasi-brittle materials,” Int. J. Fract., 169, No. 2, 113–131 (2011).

    Article  MATH  Google Scholar 

  23. A. N. Guz, I. A. Guz, A. V. Men’shikov, and V. A. Men’shikov, ”Three-dimensional problems in the dynamic fracture mechanics of materials with interface cracks (review),” Int. Appl. Mech., 49, No. 1, 1–61 (2013).

    Article  MATH  ADS  Google Scholar 

  24. A. N. Guz, ”Establishing the foundations of the mechanics of fracture of materials compressed along cracks (review),” Int. Appl. Mech., 50, No. 1, 1–57 (2014).

    Article  MathSciNet  ADS  Google Scholar 

  25. H. Helmholtz, Ueber die Erhaltung der Kraft, Wissenschaftliche Abhandlungen, Reimer, Berlin (1847).

    Google Scholar 

  26. J. W. Hutchison, ”Singular behaviour at the end of a tensile crack in a hardening material,” J. Mech. Phys. Solids, 16, No. 1, 13–22 (1968).

    Article  ADS  Google Scholar 

  27. A. A. Kaminsky, ”Long-term fracture mechanics of viscoelastic bodies with cracks,” Int. Appl. Mech., 50, No. 5, 3–79 (2014).

    Article  MathSciNet  Google Scholar 

  28. A. A. Kaminsky, ”Subcritical crack growth in polymer composite materials,“ in: G. Cherepanov (ed.), Fracture: A Topical Encyclopedia of Current Knowledge, Krieger Publishing Company, Malabar (1998), pp. 758–763.

    Google Scholar 

  29. A. A. Kaminsky and E. E. Kurchakov, ”Modeling of fracture process zone near a crack tip in a nonlinear elastic body,” Int. Appl. Mech., 47, No. 6, 735–744 (2011).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  30. A. A. Kaminsky and E. E. Kurchakov, ”Modeling a crack with a fracture process zone in a nonlinear elastic body,” Int. Appl. Mech., 48, No. 5, 552–562 (2012).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  31. H. Kauderer, Nichtlineare Mechanic, Springer-Verlag, Berlin (1958).

    Book  Google Scholar 

  32. L. P. Choroshun and O. I. Levchuk, “Stress distribution around cracks in linear hardening materials subject to tension: Plane problem,” Int. Appl. Mech., 50, No. 2, 128–140 (2014).

    Article  Google Scholar 

  33. G. C. Sih, Handbook of Stress Intensity Factors, Lehigh Univ. Press, Bethlehem (1973).

    Google Scholar 

  34. L. V. Voitovich, M. P. Melezhik, and I. S. Chernyshenko, ”Photoelastic modeling of the fracture of viscoelastic orthotropic plates with a crack,” Int. Appl. Mech., 46, No. 6, 677–682 (2010).

    Article  ADS  Google Scholar 

  35. A. A. Wells, ”Critical tip opening displacement as fracture criterion,” in: Proc. Crack Propagation Symp., Vol. 1, Cranfield (1961), pp. 210–221.

  36. J. G. Williams, Fracture Mechanics of Polymers, Wiley, New York (1984).

    Google Scholar 

  37. M. P. Wnuk, “Subcritical growth of fracture (inelastic fatigue),” Int. J. Fract. Mech., 7, No. 4, 383–407 (1971).

    Google Scholar 

  38. M. P. Wnuk and W. G. Knauss, “Delayed fracture in viscoelastoplastic solids,” Int. J. Solids Struct., 6, No. 7, 995–1010 (1970).

    Article  Google Scholar 

  39. M. B. Yaffee and E. J. Kramer, ”Plasticization effects on environmental craze microstructure,” J. Mater. Sci., 16, No. 8, 2130–2136 (1981).

    Article  ADS  Google Scholar 

  40. T. Yokobori, The Strength, Fracture and Fatigue of Materials, P. Noordhoff, Groningen (1965).

    MATH  Google Scholar 

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Authors and Affiliations

  1. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, 3 Nesterova St., Kyiv, Ukraine, 03057

    A. A. Kaminsky & E. E. Kurchakov

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  1. A. A. Kaminsky
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  2. E. E. Kurchakov
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Correspondence to A. A. Kaminsky.

Additional information

Translated from Prikladnaya Mekhanika, Vol. 51, No. 2, pp. 13–33, March–April 2015.

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Kaminsky, A.A., Kurchakov, E.E. Influence of Tension Along a Mode I Crack in an Elastic Body on the Formation of a Nonlinear Zone. Int Appl Mech 51, 130–148 (2015). https://doi.org/10.1007/s10778-015-0679-5

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  • DOI: https://doi.org/10.1007/s10778-015-0679-5

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