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Determining The Stress–Strain State of Elastic–Plastic Solids With A Lateral Crack-Like Defect with the Use of a Model with a Linear Size

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Abstract

A model of a physical section that describes stress–strain states in elastic–plastic solids weakened by cracks is proposed. The problem of plane deformation and the stress state of a solid of an infinite size of an arbitrary geometry, weakened by a physical section, is solved. It comes down to a system of two variational equations with respect to displacement fields in the parts of the solid bordering the interaction layer. For a material whose properties are close to those of a D16T alloy, the linear parameter introduced into the crack model is estimated, and the critical conditions of solids with lateral cracks in the case of a normal detachment are determined.

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References

  1. Engineering Fracture Mechanics, Vol. 70, No. 14 (Special Issue): Fundamentals and Applications of Cohesive Models (2003).

  2. D. S. Dugdale, “Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids 8 (2), 100–104 (1960).

    Article  ADS  Google Scholar 

  3. R. V. Goldshtein and N. M. Osipenko, “Fracture and Formation of Structures,” Dokl. Akad. Nauk SSSR 240 (4), 111–126 (1978).

    Google Scholar 

  4. Yu. V. Petrov, “Quantum Analogy in Fracture Mechanics,” Fiz. Tv. Tela 38 (11), 3385–3393 (1996).

    Google Scholar 

  5. V. D. Kurguzov, N. S. Astapov, and I. S. Astapov, “Fracture Model for Structured Quasibrittle Materials,” Prikl. Mekh. Tekh. Fiz. 55 (6), 173–185 (2014) [J. Appl. Mech. Tech. Phys. 55 (6), 1055–1065 (2014)].

    Google Scholar 

  6. V. M. Kornev and V. D. Kurguzov, “Multiparametric Sufficient Criterion of Quasi-Brittle Fracture for Complicated Stress State,” Eng. Fracture Mech. 75 (5), 1099–1113.

  7. H. Neuber, Kerbspannunglehre: Grunglagen für Genaue Spannungsrechnung (Springer-Verlag, 1937).

    Book  Google Scholar 

  8. V. V. Novozhilov, “On a Necessary and Sufficient Criterion for Brittle Strength,” Prikl. Mat. Mekh. 33 (2), 212–222 (1969) [J. Appl. Math. Mech., 33 (2), 201–210 (1969)].

    Google Scholar 

  9. G. N. Savin, Plane Problem of Moment Theory of Elasticity (Izd. Kiev. Gos. Univ., Kiev, 1965) [in Russian].

    Google Scholar 

  10. A. L. Aero, “Essentially Nonlinear Micromechanics of a Medium with a Variable Periodic Structure,” Usp. Mekh., No. 3, 130–176 (2002).

    Google Scholar 

  11. B. E. Pobedrya and S. E. Omarov, “Constitutive Relations in the Moment Theory of Elasticity,” Vestn. Mosk. Gos. Univ., Ser 1: Mat., Mekh. No. 3, 56–58 (2007).

    MATH  Google Scholar 

  12. V. V. Vasil’ev and S. A. Lur’e, “New Solution of the Plane Problem of an Equilibrium Crack,” Izv. Ross. Akad. Nauk, Mekh. Tv. Tela 51 (5), 61–67 (2016).

    Google Scholar 

  13. A. F. Revuzhenko, “Version of the Linear Elasticity Theory with a Structural Parameter,” Prikl. Mekh. Tekh. Fiz. 57 (5), 45–52 (2016) [J. Appl. Mech. Tech. Phys. 57 (5), 801–807 (2016)].

    MathSciNet  MATH  Google Scholar 

  14. S. E. Omarov, “Determining the Material Constant in the Problem of Equilibrium of an Infinite Elastic Plane Weakened by a Circular Hole,” Izv. Ross. Akad. Nauk, Mekh. Tv. Tela 44 (5), 144–149 (2009).

    Google Scholar 

  15. R. V. Goldshtein and N. M. Osipenko, “Estimating the Effective Strength of Solids under Compression,” Izv. Ross. Akad. Nauk, Mekh. Tv. Tela, No. 4, 80–93 (2017).

    Google Scholar 

  16. A. Needleman and E. van der Giessen, “Micromechanics of Fracture: Connecting Physics to Engineering,” MRS Bull. 26 (3), 211–214 (2001).

    Article  Google Scholar 

  17. V. E. Panin, Yu. V. Grinyaev, V. I. Danilov, et al., Structural Levels of Plastic Strain and Fracture (Nauka, Novosibirsk, 1990) [in Russian].

    Google Scholar 

  18. L. I. Domozhirov and N. A. Makhutov, “Hierarchy of Cracks in Cyclic Fracture Mechanics,” Izv. Ross. Akad. Nauk, Mekh. Tv. Tela, No. 5, 17–26 (1999).

    Google Scholar 

  19. G. I. Barenblatt and G. S. Golitsyn, “Similarity Criteria and Scales for Crystals,” Fiz. Mezomekh. 20 (1), 116–119 (2017) [Phys. Mesomech. 20 (1), 111–114 (2017)].

    Google Scholar 

  20. J. D. Carrol, W. Z. Abuzaid, J. Lambros, and H. Sehitoglu, “On the Interactions between Strain Accumulation, Microstructure, and Fatigue Crack Behavior,” Int. J. Fracture 180, 223–241 (2013).

    Article  Google Scholar 

  21. P. S. Volegov, D. S. Gribov, and P. V. Trusov, “Damage and Fracture: Classical Continuum Theories,” Fiz. Mezomekh. 18 (3), 11–24 (2015) [Phys. Mesomech. 20 (2), 157–173 (2017)].

    Google Scholar 

  22. V. V. Glagolev and A. A. Markin, “Finding the Elastic Strain Limit at the Tip Region of a Physical Cut with Arbitrarily Loaded Faces,” Prikl. Mekh. Tekh. Fiz. 53 (5), 174–183 (2012) [J. Appl. Mech. Tech. Phys. 53 (5), 784–792 (2012)].

    MATH  Google Scholar 

  23. V. V. Glagolev, L. V. Glagolev, and A. A. Markin, “Stress–Strain State of Elastoplastic Bodies with Crack,” Acta Mech. Solida Sinica 28 (4), 375–383 (2015).

    Article  Google Scholar 

  24. A. A. Ilyushin, Plasticity, Vol. 1: Elastic–Plastic Deformations (Gostekhteoretizdat, Moscow–Leningrad, 1948) [in Russian].

    Google Scholar 

  25. I. I. Vorovich and Yu. P. Krasovskii, “Method of Plastic Solutions,” Dokl. Akad. Nauk SSSR 126 (4), 740–743 (1959).

    Google Scholar 

  26. H. G. Hahn, Elastizit¨atstheorie: Grundiagen der linearen Theorie und Anwendungen auf eindimensionale, ebene und r¨aumliche Probleme (Teubner, Stuttgart, 1985).

    Book  Google Scholar 

  27. G. P. Cherepanov, Mechanics of Brittle Fracture (Nauka, Moscow, 1974; McGraw-Hill, New York, 1979).

    MATH  Google Scholar 

  28. V. Z. Parton and E. M. Morozov, Mechanics of Elastic–Plastic Fracture (Nauka, Moscow, 1985; Hemisphere, Washington, 1989).

    MATH  Google Scholar 

  29. G. V. Klevtsov and L. R. Botvina, “Microscopic and Macroscopic Plastic Deformation As a Criterion of the Limiting State of a Material during Fracture,” Probl. Prochn., No. 4, 24–28 (1984).[Strength Mater. 16 (4), 473–479 (1984)].

    Google Scholar 

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Correspondence to V. V. Glagolev.

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Original Russian Text © V.V. Glagolev, L.V. Glagolev, A.A. Markin.

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 6, pp. 143–154, November–December, 2018.

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Glagolev, V.V., Glagolev, L.V. & Markin, A.A. Determining The Stress–Strain State of Elastic–Plastic Solids With A Lateral Crack-Like Defect with the Use of a Model with a Linear Size. J Appl Mech Tech Phy 59, 1085–1094 (2018). https://doi.org/10.1134/S0021894418060147

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  • DOI: https://doi.org/10.1134/S0021894418060147

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