Journal of Applied Mechanics and Technical Physics

, Volume 59, Issue 7, pp 1227–1234 | Cite as

Stress Analysis for Perforated Cylinders with Combined Use of the Boundary Element Method and Nonlocal Fracture Criteria

  • M. A. LeganEmail author
  • V. A. Blinov


When using local fracture criteria, it is usually assumed that a fracture begins when the maximum equivalent stress reaches the limit value at least at one point of the body. However, under conditions of an inhomogeneous stress state, it is suitable to use nonlocal failure criteria which take into account the nonuniformity of the stress distribution and yield limit load estimates that are closer to the experimental data. An algorithm of the joint use of the boundary element method (in the version of the fictitious stress method) and gradient fracture criterion for calculations of the strength of plane construction elements is composed. The computations are carried out using a program written in FORTRAN. Results on the limit loading obtained numerically and analytically based on the local criterion of maximum stress and nonlocal fracture criteria (gradient criterion and Nuismer criterion) are compared both among themselves and with the experimental data on the failure of ebonite specimens. A brittle fracture of ebonite cylinders with a hole under diametric compression is studied experimentally. It is shown that nonlocal criteria lead to limit loading values which are closer to the experimental ones than the local criterion. The estimates obtained by the local maximum stress criterion are significantly less than the experimental ones. The estimates found for limit loads by the Nuismer criterion are greater than similar ones determined by the local criterion; nevertheless, they are less than the experimental ones, while the limit load values according to the gradient criterion are closest to the experimental values. Using the nonlocal fracture criteria in designing constructions with stress concentrators will allow us to increase the design values of the limit loads.


brittle fracture stress concentration nonlocal fracture criteria experimental data 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Mellor, M. and Hawkes, I., Measurement of tensile strength by diametral compression of discs and annuli, Eng. Geol., 1971, vol. 5, no. 3, pp. 173–225. CrossRefGoogle Scholar
  2. 2.
    Efimov, V.P., Gradient approach to determination of tensile strength of rocks, J. Min. Sci., 2002, vol. 38, no. 5, pp. 455–459. CrossRefGoogle Scholar
  3. 3.
    Legan, M.A., Brittle fracture of structures elements with stress concentrators, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2013, vol. 13, no. 3, pp. 70–76.Google Scholar
  4. 4.
    Efimov, V.P., Rock tests in nonuniform fields of tensile stresses, J. Appl. Mech. Tech. Phys., 2013, vol. 54, no. 5, pp. 857–865. ADSCrossRefGoogle Scholar
  5. 5.
    Efimov V.P. Tensile strength of rocks by test data on disc-shaped specimens with a hole drilled through the disc center, J. Min. Sci., 2016, vol. 52, no. 5, pp. 878–884. Google Scholar
  6. 6.
    Frocht, M.M., Photoelasticity, New York: Wiley, 1948, vol. 2.Google Scholar
  7. 7.
    Chen, C.S., Pan, E., and Amadei, B., Fracture mechanics analysis of cracked discs of anisotropic rock using the boundary element method, Int. J. Rock Mech. Min., 1998, vol. 35, no. 2, pp. 195–218. CrossRefGoogle Scholar
  8. 8.
    Ke, C.-C., Chen, C.-S., and Tu, C.-H., Determination of fracture toughness of anisotropic rocks by boundary element method, Rock Mech. Rock Eng., 2008, vol. 41, no. 4, pp. 509–538. ADSCrossRefGoogle Scholar
  9. 9.
    Crouch, S.L. and Starfield, A.M., Boundary Element Methods in Solid Mechanics, London: Jeorge Allen and Unwin, 1983.CrossRefzbMATHGoogle Scholar
  10. 10.
    Legan M.A., Correlation of local strength gradient criteria in a stress concentration zone with linear fracture mechanics, J. Appl. Mech. Tech. Phys., 1993, vol. 34, no. 4, pp. 585–592. ADSCrossRefzbMATHGoogle Scholar
  11. 11.
    Legan M.A., Determination of the breaking load and the position and direction of a fracture using the gradient approach, J. Appl. Mech. Tech. Phys., 1994, vol. 35, no. 5, pp. 750–756. ADSCrossRefzbMATHGoogle Scholar
  12. 12.
    Banerjee, P.K. and Butterfield, R., Boundary Element Methods in Engineering Science, New York: McGraw-Hill, 1981.zbMATHGoogle Scholar
  13. 13.
    Whitney, J.M. and Nuismer, R.J., Stress fracture criteria for laminated composites containing stress concentrations, J. Compos. Mater., 1974, vol. 8, no. 3, pp. 253–265. ADSCrossRefGoogle Scholar
  14. 14.
    Novozhilov, V.V., Theory of Elasticity, Amsterdam: Elsevier, 1961.zbMATHGoogle Scholar
  15. 15.
    Sheremet, A.S. and Legan, M.A., Application of the gradient strength criterion and the boundary element method to a plane stress-concentration problem, J. Appl. Mech. Tech. Phys., 1999, vol. 40, no. 4, pp. 744–750. ADSCrossRefGoogle Scholar
  16. 16.
    Novikov, N.V. and Maistrenko, A.L., Crack resistance of crystalline and composite superhard materials, Mater. Sci., 1984, vol. 19, no. 4, pp. 298–304. CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Inc. 2018

Authors and Affiliations

  1. 1.Lavrent’ev Institute of Hydrodynamics, Siberian BranchRussian Academy of SciencesNovosibirskRussia
  2. 2.Novosibirsk State Technical UniversityNovosibirskRussia

Personalised recommendations