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Stress-strain state and stress intensity factors of an inclined elliptic defect in a plate under biaxial loading

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Abstract

We consider a mathematical model of the stress-strain state of a plate with an inclined elliptic defect. We obtain approximate formulas for the stress tensor, the displacements, and the principal stresses near the defect vertex. The obtained formulas are compared with the results obtained by the holographic photoelasticity method.

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References

  1. J. Eftis and N. Subramonian, “The Inclined Crack under Biaxial Load,” Engng Fract. Mech. 10(1), 43–67 (1978).

    Article  Google Scholar 

  2. G. C. Sih and B. C. Cha, “A Fracture Criterion for Three Dimensional Crack Problem,” Engng Fract. Mech. 6(4), 699–723 (1974).

    Article  Google Scholar 

  3. P. S. Theocaris and J. G. Michopoulos, “A Closed-Form Solution of a Slant Crack under Biaxial Loading,” Engng Fract. Mech. 17(2), 97–123 (1983).

    Article  Google Scholar 

  4. J. G. Williams and P. D. Ewing, “Fracture under Complex Stress — The Angles Crack Problem,” Int. J. Fract. Mech. 8(4), 441–446 (1972).

    Google Scholar 

  5. H. Liebowitz, J. Eftis, and D. Johns, “Several Recent Theoretical and Experimental Studies in Fracture Mechanics,” in Fracture Mechanics. Construction Fracture, Ed. by R. V. Goldstein (Mir, Moscow, 1980), pp. 168–202 [in Russian].

    Google Scholar 

  6. J. Eftis, N. Subramonian, and H. Liebowits, “Crack Border Stress and Displacement Equations Revisited,” Engng Fract. Mech. 9(1), 189–210 (1977).

    Article  Google Scholar 

  7. M. L. Williams, “On the Stress Distribution at the Base of a Stationary Crack,” J. Appl. Mech. 24(1), 109–114 (1957).

    MATH  MathSciNet  Google Scholar 

  8. G. C. Sih, “On theWestergaard Method of Crack Analysis,” Int. J. Fract. Mech. 2(4), 628–631 (1969).

    Google Scholar 

  9. N. I. Muskhelishvili, Some Fundamental Problems of Mathematical Elasticity Theory (Nauka, Moscow, 1966) [in Russian].

    Google Scholar 

  10. J. Eftis and H. Liebowits, “On the Modified Westergaard Equation for Certain Plane Crack Problem,” Int. J. Fract. Mech. 8(4), 383–392 (1972).

    Google Scholar 

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

    Google Scholar 

  12. V. V. Panasyuk, Mechanics of Material Quasibrittle Fracture (Naukova Dumka, Kiev, 1991) [in Russian].

    Google Scholar 

  13. A. Ya. Krasovskii,Material Brittleness at Low Temperatures (Naukova Dumka, Kiev, 1980) [in Russian].

    Google Scholar 

  14. N. A. Makhutov, Deformation Fracture Criteria and Strength Calculation of Construction Elements (Mashinostroenie, Moscow, 1981) [in Russian].

    Google Scholar 

  15. V. A. Vinokurov, “Use of Fracture Mechanics Aspects to Estimate the Properties of Welded Joints,” Svar. Proizv., No. 5, 2–4 (1977).

  16. P. Paris and G. C. Sih, “Analysis of Stressed State near Cracks,” in Applied Problems of Fracture Viscosity (Mir, Moscow, 1968), pp. 64–142 [in Russian].

    Google Scholar 

  17. A. A. Kaminskii, Brittle Fracture near Holes (Naukova Dumka, Kiev, 1982) [in Russian].

    Google Scholar 

  18. P. S. Theocaris and C. P. Spyropoulos, “Photoelastic Determination of Complex Stress Intensity Factors for Slant Crack under Biaxial Loading with Higher-Order Term Effects,” Acta Mech. 48(1–2), 57–70 (1983).

    Article  MATH  Google Scholar 

  19. R. J. Sanford and J. W. Dally, “A General Method for Determining Mixed-Mode Stress Intensity Factors from Isochromatic Fringe Patterns,” Engng Fract. Mech. 11(4), 621–633 (1979).

    Article  Google Scholar 

  20. A. A. Ostsemin, “Determining the Stressed State and Stress Intensity Factors in Constructions with Crack-Like Defects by the Holographic Interferometry Method,” Vestnik Mashinostr., No. 8, 21–28 (2009).

  21. A. A. Ostsemin, “Two-Parameter Determination of Stress Intensity Factors for an Inclined Crack by the Holographic Interferometry Method,” Zavodskaya Laboratoriya, No. 12, 45–48 (1991).

  22. A. Ya. Aleksandrov and M. Kh. Akhmetzyanov, Polarization-Optical Methods of Mechanics of Deformable Body (Nauka, Moscow, 1973) [in Russian].

    Google Scholar 

  23. A. A. Ostsemin, S. A. Deniskin, L. L. Sitnikov, et al., “Determination of the Stress State of Bodies with Flaws by the Method of Holographic Photoelasticity,” Probl. Prochn., No. 10, 77–81 (1982) [Strength of Materials (Engl. Transl.) 14 (10), 1375–1380 (1982)].

  24. L. L. Sitnikov, A. A. Ostsemin, S. A. Deniskin, and A. A. Zagrebalov, “Determining the Stress Intensity Factor K I by the Holographic Photoelasticity Method,” Zavodskaya Laboratoriya, No. 9, 81–83 (1982).

  25. A. A. Ostsemin, “Two-Parameter Determination of the Stress Intensity Factor K I by the Holographic Interferometry Method,” Zavodskaya Laboratoriya. Diagnostika Materialov, No. 3, 47–50 (2008).

  26. J. F. Doyle, S. Kamle, and J. Takezaki, “ErrorAnalysis of Photoelasticity in Fracture Mechanics,” Exp. Mech. 21(11), 429–435 (1981).

    Article  Google Scholar 

  27. G. P. Karzov, V. P. Leonov, and B. T. Timofeev, Welded Pressurized Vessels: Strength and Endurance (Mashinostroenie, Leningrad, 1982) [in Russian].

    Google Scholar 

  28. V. I. Trufyakov (Editor), Strength of Welded Joints under Variable Loads (Naukova Dumka, Kiev, 1990) [in Russian].

    Google Scholar 

  29. A. A. Ostsemin and P. B. Utkin, “Application of Criteria of Elastoplastic Fracture Mechanics in Estimating the Properties of Welded Joints,” Vopr. Materialov., No. 3, 151–160 (2007).

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Correspondence to A. A. Ostsemin.

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Original Russian Text © A.A. Ostsemin, P.B. Utkin, 2010, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2010, No. 2, pp. 73–88.

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Ostsemin, A.A., Utkin, P.B. Stress-strain state and stress intensity factors of an inclined elliptic defect in a plate under biaxial loading. Mech. Solids 45, 214–225 (2010). https://doi.org/10.3103/S002565441002007X

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