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

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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. 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)

    Article  Google Scholar 

  2. Kundu, T.: Fundamentals of Fracture Mechanics. CRC Press, Boca Raton (2008)

    Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  7. Shail, R.: The impulsive Reissner–Sagocci problem. J. Math. Mech. 19, 709–716 (1970)

    MathSciNet  MATH  Google Scholar 

  8. Shibuya, T.: On the torsional impact of a thick elastic plate. Int. J. Solids Struct. 11, 803–811 (1975)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  28. Fox, L., Goodwin, E.T.: The numerical solution of non-singular linear integral equations. Philos. Trans. A.245, 501–534 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  29. Sih, G.C.: Mechanics of Fracture, vol. 4, p. 25. Noordhoff International Publishing, Leyden (1977)

    Google Scholar 

  30. Roylance, D.: Mechanics of Materials. Wiley, New York (1995)

    Google Scholar 

  31. Brown, J.W., Churchill, R.V.: Complex Variables and Applications, 8th edn, pp. 298–299. McGraw-Hill, New York (2009)

    Google Scholar 

  32. Rice, R.G., Do, D.D.: Applied Mathematics and Modeling for Chemical Engineers. Wiley, New York (1995)

    Google Scholar 

  33. Zakian, V.: Numerical inversions of Laplace transforms. Electron. Lett. 5, 120–121 (1969)

    Article  MathSciNet  Google Scholar 

  34. Zakian, V.: Optimization of numerical inversion of Laplace transforms. Electron. Lett. 6, 667–679 (1970)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Applied Sciences, Haldia Institute of Technology, Haldia, Purba Medinipur, 721657, India

    S. Karan & S. Basu

  2. Department of Mathematics, Jadavpur University, Kolkata, 700032, India

    S. C. Mandal

Authors
  1. S. Karan
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  2. S. Basu
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  3. S. C. Mandal
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Correspondence to S. Basu.

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Karan, S., Basu, S. & Mandal, S.C. Impact of a torsional load on a penny-shaped crack sandwiched between two elastic layers embedded in an elastic medium. Acta Mech 229, 1759–1772 (2018). https://doi.org/10.1007/s00707-017-2073-3

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  • DOI: https://doi.org/10.1007/s00707-017-2073-3

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