Skip to main content

Stress Concentration Near Notches in Quasi-Orthotropic Body

  • Chapter
  • First Online:
Stress Concentration at Notches

Abstract

The twelfth chapter concerns with studying stress concentration near notches in quasi-orthotropic bodies, that is bodies with the special type of orthotropy when the characteristic equation has multiple roots. Basic relationships of plane elasticity theory for such media are presented and singular integral equations of first basic problem of theory of elasticity for a region containing curvilinear cracks are stated. Solutions for eigenvalues of a quasi-orthotropic wedge were obtained. Corresponding solutions for quasi-orthotropic plane with a rounded V-shaped notch were constructed. The interrelation between stress concentration factor and stress intensity factor in quasi-orthotropic plane with rounded or sharp V-shaped notches had been established. On this basis, the authors had derived stress intensity factors in V-shaped tip of two-sectional kinked crack using the superposition technique.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Benthem, J.P.: Stresses in the region of rounded corners. Int. J. Solids Struct. 23(2), 239–252 (1987)

    Article  Google Scholar 

  2. Blinowski, A., Rogaczewski, J.: On the order of singularity at V-shaped notches in anisotropic bodies. Arch. Mech. 52(6), 1001–1010 (2000)

    MATH  Google Scholar 

  3. Cho, S.B., Lee, K.R., Choy, Y.S.: A further study of two-dimensional boundary element crack analysis in anisotropic or orthotropic materials. Eng. Fract. Mech. 43(4), 589–601 (1992)

    Article  Google Scholar 

  4. Erdogan, F., Gupta, G.D., Cook, T.S.: The Numerical Solutions of Singular Integral Equations. In: Sih, G.C. (ed.) Methods of Analysis and Solutions of Crack Problems. Mechanics of Fracture, vol. 1, pp. 368–425. Springer, Netherlands (1973)

    Google Scholar 

  5. Erdogan, F., Ratwani, M., Yüceoglu, U.: On the effect of orthotropy in a cracked cylindrical shell. Int. J. Fract. 10(3), 369–374 (1974)

    Article  Google Scholar 

  6. Hasebe, N., Sato, M.: Stress analysis of quasi-orthotropic elastic plane. Int. J. Solids Struct. 50(1), 209–216 (2013)

    Article  Google Scholar 

  7. Hasebe, N., Sato, M.: Mixed boundary value problem for quasi-orthotropic elastic plane. Acta Mech. 226(2), 527–545 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kazberuk, A., Savruk, M.P., Chornenkyi, A.B.: Stress concentration around an elliptic hole or a parabolic notch in quasi-orthotropic plane. Mater. Sci. 52(3), 7–14 (2016)

    Google Scholar 

  9. Kazberuk, A., Savruk, M.P., Chornenkyi, A.B.: Stress distribution at sharp and rounded V-notches in quasi-orthotropic plane. Int. J. Solids Struct. 85–86, 134–143 (2016)

    Article  Google Scholar 

  10. Kostenko, I.S.: Elastic equilibrium of a closed orthotropic cylindrical shell with longitudinal notches. Mater. Sci. 16(5), 447–450 (1980)

    Article  Google Scholar 

  11. Krenk, S.: Influence of transverse shear on an axial crack in a cylindrical shell. Int. J. Fract. 14(2), 123–143 (1978)

    MathSciNet  Google Scholar 

  12. Lekhnitskii, S.G.: Theory of Elasticity of an Anisotropic Elastic Body. Mathematical Physics, 1st edn. Holden-Day, San Francisco (1963)

    Google Scholar 

  13. Lekhnitskii, S.G.: Anisotropic Plates. Gordon & Breach, New York (1968)

    Google Scholar 

  14. Linkov, A.M.: Boundary Integral Equations in Elasticity Theory. Kluwer Academic Pub, Dordrecht (2002)

    Book  MATH  Google Scholar 

  15. Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity, 2nd edn. Noordhoff International Publishing, Leyden (1977)

    Book  Google Scholar 

  16. Nowacki, W.: Teoria sprezystosci (Theory of Elasticity). PWN - Polish Scientific Publishers, Warsaw (1970)

    MATH  Google Scholar 

  17. Prusov, I., Lunskaya, L.: Elastic state of piecewise-homogeneous orthotropic plane with cutouts. Int. Appl. Mech. 5(8), 845–850 (1969)

    Google Scholar 

  18. Savin, G.N.: Raspredeleniye napryazheniy okolo otverstiy (Stress Distribution Around Holes). Naukova dumka, Kyiv (1968)

    Google Scholar 

  19. Savruk, M.P.: Dvumernyye zadachi uprugosti dla tel s treshchinami (Two-Dimensional Problems of Elasticity for Bodies with Cracks). Naukova dumka, Kyiv (1981)

    MATH  Google Scholar 

  20. Savruk, M.P., Chornenkyi, A.: Periodic system of curvilinear cracks in quasi-orthotropic plane. In: Matematychni problemy mekhaniky neodnoridnykh struktur (Mathematical Problems of Mechanics of Nonhomogeneous Structures), pp. 303–305. Lviv (2014)

    Google Scholar 

  21. Savruk, M.P., Chornenkyi, A.: Stress-strain state quasi-orthotropic plane with curvilinear cracks. In: Panasyuk, V.V. (ed.) Mekhanika ruinuvannya materialiv i mitsnist’ konstruktsii (Fracture Mechanics of Materials and Strength of Structures), pp. 409–414. Lviv (2014)

    Google Scholar 

  22. Savruk, M.P., Chornenkyi, A.: Plane problem of the theory of elasticity for a quasi-orthotropic body with cracks. Mater. Sci. 51(3), 311–321 (2015)

    Article  Google Scholar 

  23. Savruk, M.P., Kazberuk, A.: Relationship between the stress intensity and stress concentration factors for sharp and rounded notches. Mater. Sci. 42(6), 725–738 (2006)

    Article  Google Scholar 

  24. Savruk, M.P., Kazberuk, A.: A unified approach to problems of stress concentration near V-shaped notches with sharp and rounded tip. Int. Appl. Mech. 43(2), 182–197 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Savruk, M.P., Kazberuk, A.: Two-dimensional fracture mechanics problems for solids with sharp and rounded V-notches. Int. J. Fract. 161, 79–95 (2010)

    Article  MATH  Google Scholar 

  26. Savruk, M.P., Kazberuk, A.: Curvilinear cracks in the anisotropic plane and the limit transition to the degenerate material. Mater. Sci. 50(2), 189–200 (2014)

    Article  Google Scholar 

  27. Savruk, M.P., Kazberuk, A.: Plane eigenvalue problems of the elasticity theory for orthotropic and quasi-orthotropic wedges. Mater. Sci. 50(6), 771–781 (2014)

    Article  Google Scholar 

  28. Savruk, M.P., Kazberuk, A.: Solution of the eigenvalue problems of the plane elasticity theory for orthotropic and quasi-orthotropic wedges. In: Mathematical Problems of Mechanics of Nonhomogeneous Structures, pp. 107–109. Lviv (2014)

    Google Scholar 

  29. Savruk, M.P., Kazberuk, A.: Stress concentration near sharp and rounded V-notches in orthotropic and quasi-orthotropic bodies. Theor. Appl. Fract. Mech. 84, 166–176 (2016)

    Google Scholar 

  30. Savruk, M.P., Osiv, P.M., Prokopchuk, I.V.: Chislennyy analiz v ploskikh zadachakh teorii treshchin (Numerical Analysis in Plane Problems of Theory of Cracks). Naukova dumka, Kyiv (1989)

    Google Scholar 

  31. Shevchenko, V.P., Dovbnya, K.M., Tsvang, V.A.: Orthotropic shells with cracks (cuts). In: Kontsentratsiya napryazhenij: Mekhanika kompozitov v 12 t. (Stress Concentration: Mechanics of Composites in 12 Volumes), vol. 7, pp. 212–249. Kyiv (1998)

    Google Scholar 

  32. Suo, Z.: Singularities, interfaces and cracks in dissimilar anisotropic media. Proc. Roy. Soc. Lond. Math. Phys. Sci. 427(1873), 331–358 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  33. Theocaris, P.S., Ioakimidis, N.I.: Mode I stress intensity factors at corner points in plane elastic media. Eng. Fract. Mech. 13(4), 699–708 (1980)

    Article  Google Scholar 

  34. Williams, M.L.: Stress singularities resulting from various boundary conditions in angular corners of plates in extension. J. Appl. Mech. 19(4), 526–530 (1952)

    Google Scholar 

  35. Wu, K.C., Chang, F.T.: Near-tip fields in a notched body with dislocations and body forces. J. Appl. Mech. 60(4), 936–941 (1993)

    Article  MATH  Google Scholar 

  36. Zhang, W., Deng, X.: Asymptotic stress field in a degenerate orthotropic material containing a cohesive zone ahead of a crack tip. J. Elast. 90(3), 271–282 (2008)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mykhaylo P. Savruk .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Savruk, M.P., Kazberuk, A. (2017). Stress Concentration Near Notches in Quasi-Orthotropic Body. In: Stress Concentration at Notches. Springer, Cham. https://doi.org/10.1007/978-3-319-44555-7_12

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-44555-7_12

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-44554-0

  • Online ISBN: 978-3-319-44555-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics