Skip to main content
Log in

Stress concentration around a spheroidal crack caused by a harmonic wave incident at an arbitrary angle

  • Published:
International Applied Mechanics Aims and scope

Abstract

A method is proposed to study the stress concentration around a shallow spheroidal crack in an infinite elastic body. The stress concentration is due to the diffraction of a low-frequency plane longitudinal wave by the crack. The direction of wave propagation is established in which the combined concentration of mode I and mode II stresses is maximum

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. N. M. Borodachev, “Weight function for an internal flat elliptic crack,” Probl. Prochn., No. 4, 59–66 (1997).

  2. N. D. Vaisfel'd and G. Ya. Popov, “Nonstationary dynamic problems of elastic stress concentration around a spherical defect,” Izv. RAN, Mekh. Tverd. Tela, No. 3, 90–102 (2002).

  3. E. V. Glushkov and N. V. Glushkov, “Diffraction of elastic waves by spatial cracks of arbitrary shape in plan,” Prikl. Mat. Mekh., 60, No. 2, 282–289 (1996).

    Google Scholar 

  4. V. T. Grinchenko and V. V. Meleshko, Harmonic Vibration and Waves in Elastic Bodies [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  5. A. N. Guz and V. V. Zozulya, Brittle Fracture of Materials under Dynamic Loads [in Russian], Naukova Dumka, Kiev (1993).

    Google Scholar 

  6. G. S. Kit and M. V. Khai, Method of Potentials in Three-Dimensional Problems of Thermoelasticity for Cracked Bodies [in Russian], Naukova Dumka, Kiev (1989).

    Google Scholar 

  7. M. A. Martynenko and A. F. Ulitko, “Stress state near the vertex of a spherical notch in an unbounded elastic medium,” Int. Appl. Mech., 14, No. 9, 911–918 (1978).

    MathSciNet  Google Scholar 

  8. V. V. Mykhas'kiv and I. O. Butrak, “Three-dimensional dynamic problems for an elastic body with a shallow crack,” Fiz.-Khim. Mekh. Mater., 39, No. 1, 63–70 (2003).

    Google Scholar 

  9. L. A. Fil'shtinskii, “Diffraction of elastic waves by cracks, holes, and inclusions in an elastic medium,” Izv. AN SSSR, Ser. Mekh. Tverd. Tela, No. 4, 119–127 (1991).

  10. M. V. Khai, Two-Dimensional Integral Equations such as the Newtonian Potential and Their Application [in Russian], Naukova Dumka, Kiev (1993).

    Google Scholar 

  11. A. Böstrom and P. Olsson, “Scattering of elastic waves by nonplanar cracks,” Wave Motion, 9, No. 1, 61–76 (1987).

    Article  Google Scholar 

  12. A. N. Guz, “Formulation of problems in dynamic fracture mechanics,” Int. Appl. Mech., 35, No. 6, 531–536 (1999).

    MATH  Google Scholar 

  13. A. N. Guz, “On some nonclassical problems of fracture mechanics taking into account the stresses along cracks,” Int. Appl. Mech., 40, No. 8, 937–941 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  14. A. N. Guz, V. V. Zozulya, and A. V. Men'shikov, “General spatial dynamic problem for an elliptic crack under the action of a normal shear wave, with consideration for the contact interaction of the crack faces,” Int. Appl. Mech., 40, No. 2, 156–159 (2004).

    Article  Google Scholar 

  15. H. S. Kit, M. V. Khaj, and V. V. Mykhas'kiv, “Analysis of dynamic stress concentration in an infinite body with parallel penny-shaped cracks by BIEM,” Eng. Fract. Mech., 55, No. 2, 191–207 (1996).

    Article  Google Scholar 

  16. O. A. Menshykov, M. V. Menshykova, and W. L. Wendland, “On use of the Galerkin method to solve the fracture mechanics problem for a linear crack under normal loading,” Int. Appl. Mech., 41, No. 11, 1324–1329 (2005).

    Article  Google Scholar 

  17. V. V. Mykhas'kiv, “Opening-function simulation of the three-dimensional nonstationary interaction of cracks in an elastic body,” Int. Appl. Mech., 37, No. 1, 75–84 (2001).

    Article  Google Scholar 

  18. V. V. Mykhas'kiv, “Boundary integral formulation of three-dimensional problems of steady vibrations of an infinite body with a crack located on an open Lyapunov surface,” J. Math. Sci., 90, No. 2, 1956–1960 (1998).

    MathSciNet  Google Scholar 

  19. V. V. Mikhas'kiv, J. Sladek, V. Sladek, and A. I. Stepanyuk, “Stress concentration near an elliptic crack in the interface between elastic bodies under steady-state vibrations,” Int. Appl. Mech., 40, No. 6, 664–671 (2004).

    Article  Google Scholar 

  20. Ch. Zhang and D. Gross, On Wave Propagation in Elastic Solids with Cracks, Computational Mechanics Publications, Southampton (1998).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

__________

Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 70–77, January 2006.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mikhas'kiv, V.V., Butrak, I.O. Stress concentration around a spheroidal crack caused by a harmonic wave incident at an arbitrary angle. Int Appl Mech 42, 61–66 (2006). https://doi.org/10.1007/s10778-006-0059-2

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10778-006-0059-2

Keywords

Navigation