Acta Mechanica

, Volume 229, Issue 4, pp 1759–1772 | Cite as

Impact of a torsional load on a penny-shaped crack sandwiched between two elastic layers embedded in an elastic medium

Original Paper
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Abstract

The paper is focused on the effect of a sudden impact of a torsional load on a penny-shaped crack sandwiched between two elastic layers embedded in an elastic medium. The axisymmetric mixed boundary value problem is reduced to the problem of solving a pair of dual integral equations by using Hankel and Laplace transforms. Further, the integral equations are then reduced to a Fredholm integral equation of second kind which is solved numerically. Expression for the stress intensity factor at the tip of the crack is obtained and plotted for different parameters and materials.

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References

  1. 1.
    Hadi Hafezi, M., Nik Abdullah, N., Correia, J.F., De Jesus, A.M.: An assessment of a strain-life approach for fatigue crack growth. Int. J. Struct. Integr. 3(4), 344–376 (2012)CrossRefGoogle Scholar
  2. 2.
    Kundu, T.: Fundamentals of Fracture Mechanics. CRC Press, Boca Raton (2008)Google Scholar
  3. 3.
    Shah, R.C., Kobayashi, A.S.: Stress intensity factor for an elliptical crack under arbitrary normal loading. Eng. Fract. Mech. 3(1), 71–96 (1971)CrossRefGoogle Scholar
  4. 4.
    Itou, S.: Transient dynamic stress intensity factors around a crack in a nonhomogeneous interfacial layer between two dissimilar elastic half-planes. Int. J. Solids Struct. 38, 3631–3645 (2001)CrossRefMATHGoogle Scholar
  5. 5.
    Ghosh, M.L.: Disturbance in an elastic half space due to an impulsive twisting moment applied to an attached rigid circular disc. Appl. Sci. Res. 14(1), 31–42 (1964)CrossRefGoogle Scholar
  6. 6.
    Eason, G.: The displacements produced in an elastic half-space by a suddenly applied surface force. J. Inst. Math. Appl. 2, 299–326 (1966)MathSciNetCrossRefMATHGoogle Scholar
  7. 7.
    Shail, R.: The impulsive Reissner–Sagocci problem. J. Math. Mech. 19, 709–716 (1970)MathSciNetMATHGoogle Scholar
  8. 8.
    Shibuya, T.: On the torsional impact of a thick elastic plate. Int. J. Solids Struct. 11, 803–811 (1975)CrossRefMATHGoogle Scholar
  9. 9.
    Sih, G.C., Chen, E.P.: Normal and shear impact of layered composite with a crack: dynamic stress intensification. J. Appl. Mech. 47, 351–358 (1980)CrossRefMATHGoogle Scholar
  10. 10.
    Keer, L.M., Jabali, H.H., Chantaramungkorn, K.: Torsional oscillation of a layer bonded to an elastic half-space. Int. J. Solids Struct. 10, 1–13 (1974)CrossRefMATHGoogle Scholar
  11. 11.
    Arin, K., Erdogan, F.: Penny-shaped crack in an elastic layer bonded to dissimilar half spaces. Int. J. Eng. Sci. 9(2), 213–232 (1971)CrossRefMATHGoogle Scholar
  12. 12.
    Erdogan, F., Arin, K.: Penny-shaped interface crack between an elastic layer and a half space. Int. J. Eng. Sci. 10(2), 115–125 (1972)CrossRefMATHGoogle Scholar
  13. 13.
    Kassir, M.K., Bregman, A.M.: The stress-intensity factor for a penny-shaped crack between two dissimilar materials. J. Appl. Mech. 39(1), 308–310 (1972)CrossRefGoogle Scholar
  14. 14.
    Chen, E.P.: Elastodynamic response of a penny-shaped crack in a cylinder of a finite radius. Int. J. Eng. Sci. 17(4), 379–385 (1979)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    He, M.Y., Hutchinson, J.W.: The penny shaped crack and the plane strain crack in an infinite body of power law material. J. Appl. Mech. 48, 830–840 (1981)CrossRefMATHGoogle Scholar
  16. 16.
    Ueda, S., Shindo, Y., Atsumi, A.: Torsional impact response of a penny-shaped crack lying on a bimaterial interface. Eng. Fract. Mech. 18(5), 1059–1066 (1983)CrossRefGoogle Scholar
  17. 17.
    Ueda, S., Shindo, Y., Atsumi, A.: Torsional impact response of a penny-shaped interface crack in a layered composite. Eng. Fract. Mech. 19(6), 1095–1104 (1984)CrossRefGoogle Scholar
  18. 18.
    Saxena, H.S., Dhaliwala, R.S.: A penny-shaped crack at the interface of two bonded dissimilar transversely isotropic elastic half-spaces. Eng. Fract. Mech. 37(4), 891–899 (1990)CrossRefGoogle Scholar
  19. 19.
    Saxena, H.S., Dhaliwala, R.S., He, W., Rokne, J.G.: Penny-shaped interface crack between dissimilar nonhomogeneous elastic layers under axially symmetric torsion. Acta Mech. 99, 201–211 (1993)MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Das, S., Patra, B., Debnath, L.: Stress intensity factors for an interfacial crack between an orthotropic half-plane bonded to a dissimilar orthotropic layer with a punch. Comput. Math. Appl. 35(12), 27–40 (1998)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Li, C., Weng, G.J.: Dynamic fracture analysis for a penny-shaped crack in an FGM interlayer between dissimilar half spaces. Math. Mech. Solids 7(2), 149–163 (2002)CrossRefMATHGoogle Scholar
  22. 22.
    Menshykov, O.V., Menshykov, V.A., Guz, I.A.: The contact problem for an open penny-shaped crack under normally incident tension–compression wave. Eng. Fract. Mech. 75, 1114–1126 (2008)CrossRefGoogle Scholar
  23. 23.
    Mykhaskiv, V.V., Khay, O.M.: Interaction between rigid-disc inclusion and penny-shaped crack under elastic time-harmonic wave incidence. Int. J. Solids Struct. 46(3), 602–616 (2009)CrossRefMATHGoogle Scholar
  24. 24.
    Lee, H.K., Tran, X.H.: On stress analysis for a penny-shaped crack interacting with inclusions and voids. Int. J. Solids Struct. 47, 549–558 (2010)CrossRefMATHGoogle Scholar
  25. 25.
    Dovzhik, M.V.: Fracture of a half-space compressed along a penny-shaped crack located at a short distance from the surface. Int. Appl. Mech. 48(3), 294–304 (2012)MathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Lee, D.-S.: Penny-shaped crack in a plate of finite thickness subjected to a uniform shearing stress. Z. Angew. Math. Phys. 64, 361–369 (2013)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Basu, S., Mandal, S.C.: Impact of torsional load on a penny-shaped crack in an elastic layer sandwiched between two elastic half-spaces. Int. J. Appl. Comput. Math. 2, 533–543 (2016)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Fox, L., Goodwin, E.T.: The numerical solution of non-singular linear integral equations. Philos. Trans. A.245, 501–534 (1953)MathSciNetCrossRefMATHGoogle Scholar
  29. 29.
    Sih, G.C.: Mechanics of Fracture, vol. 4, p. 25. Noordhoff International Publishing, Leyden (1977)Google Scholar
  30. 30.
    Roylance, D.: Mechanics of Materials. Wiley, New York (1995)Google Scholar
  31. 31.
    Brown, J.W., Churchill, R.V.: Complex Variables and Applications, 8th edn, pp. 298–299. McGraw-Hill, New York (2009)Google Scholar
  32. 32.
    Rice, R.G., Do, D.D.: Applied Mathematics and Modeling for Chemical Engineers. Wiley, New York (1995)Google Scholar
  33. 33.
    Zakian, V.: Numerical inversions of Laplace transforms. Electron. Lett. 5, 120–121 (1969)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Zakian, V.: Optimization of numerical inversion of Laplace transforms. Electron. Lett. 6, 667–679 (1970)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of Applied SciencesHaldia Institute of TechnologyHaldia, Purba MedinipurIndia
  2. 2.Department of MathematicsJadavpur UniversityKolkataIndia

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