Skip to main content
SpringerLink
Log in

Influence of load biaxiality on the fracture characteristics of two collinear cracks

  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

A theoretical investigation has been performed to determine the influence of load biaxiality on quantities pertinent to the brittle (elastic) fracture of an infinite sheet containing a pair of collinear cracks. It is shown how the biaxiality of the applied load affects the stress, the displacements and the maximum shear near the ends of the cracks, as well as the angle of initial crack extension and the displacement of the crack borders. The influence of load biaxiality on the rate at which the elastic strain energy of the entire body is altered with change in the length of the cracks is also demonstrated, and is used in conjunction with Griffith's crack instability hypothesis to show the effect of load biaxiality on the fracture load. The analysis indicates that loads applied parallel to the cracks influence the value of the critical (fracture) tensile load applied perpendicular to them, and that the Poisson ratio of the material determines the characteristics of this influence.

Résumé

On a procédé à une étude théorique en vue de déterminer l'influence de la biaxialité de la mise en charge sur les paramètres qui déterminent la rupture fragile (élastique) dans une feuille infinie comportant une paire de fissures colinéaires. On montre comment la biaxialité de charge appliquée affecte la contrainte, les déplacements et le cisaillement maximum au voisinage des extrémités des fissures, de même que l'angle de l'extension de fissure initiale et que le déplacement des bords de la fissure. L'influence de la biaxialité des charges sur la vitesse à laquelle l'énergie de déformation élastique de l'ensemble du corps se trouve altéré par le changement de longueur des fissures, est également démontrée. En combinaison avec l'hypothèse d'instabilité de fissure de Griffith, on fait usage de cette influence pour montrer l'effet de la biaxialité de contrainte sur la charge de ruine. L'analyse indique que les contraintes appliquées parallèlement aux fissures influencent la valeur de la charge critique de traction conduisant à rupture appliquée perpendiculairement à celles-ci, et que le module de Poisson du matériau détermine les caractéristiques de cette influence.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Eftis, N. Subramonian and H. Liebowitz,Engineering Fracture Mechanics 9 (1977) 189–210.

    Google Scholar 

  2. J. Eftis, N. Subramonian and H. Liebowitz,Engineering Fracture Mechanics 9 (1977) 753–764.

    Google Scholar 

  3. J. Eftis and N. Subramonian,Engineering Fracture Mechanics 10 (1978) 43–67.

    Google Scholar 

  4. J. Eftis and N. Subramonian,AIAA Journal 18, No. 3 (1980) 324–332.

    Google Scholar 

  5. J. Eftis and D.L. Jones,International Journal of Fracture 20 (1982) 267–289.

    Google Scholar 

  6. D.L. Jones and J. Eftis, “Fracture and Fatigue Characteristics of Aircraft Structural Materials Under Biaxial Loading,” Final Scientific Report to AFSOR, April 1981.

  7. T.J. Willmore,Quarterly Journal of Mechanics and Applied Mathematics II (1949) 53–63.

    Google Scholar 

  8. F. Erdogan, inProceedings 4th U.S. National Congress Applied Mechanics I, ASME (1962) 547–553.

  9. M. Maiti, S.K. De and S.S. Palit,International Journal of Fracture 15, No. 1 (1979) 41–46.

    Google Scholar 

  10. N.I. Muskhelishvili,Some Basic Problems of the Mathematical Theory of Elasticity, Nordhoff, Groningen (1963).

    Google Scholar 

  11. A.A. Griffith,Philosophical Transactions, Royal Society London 221 (1921) 163–198.

    Google Scholar 

  12. A.A. Griffith, inProceedings 1 st International Congress of Applied Mechanics, Delft (1924) 55–63.

  13. I.S. Sokolnikoff,Mathematical Theory of Elasticity, McGraw Hill, New York (1956).

    Google Scholar 

  14. W. Kaplan,Advanced Calculus, Addison-Wesley, Reading, Mass. (1959).

    Google Scholar 

  15. G.C. Sih,International Journal of Fracture Mechanics 2 (1966) 628–631.

    Google Scholar 

  16. J. Eftis and H. Liebowitz,International Journal of Fracture Mechanics 8 (1972) 383–391.

    Google Scholar 

  17. R.G. Bartle,The Elements of Real Analysis, J. Wiley, New York (1964).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Civil, Mechanical and Environmental Engineering, The George Washington University, 20052, Washington, D.C., USA

    John Eftis

Authors
  1. John Eftis
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eftis, J. Influence of load biaxiality on the fracture characteristics of two collinear cracks. Int J Fract 24, 59–80 (1984). https://doi.org/10.1007/BF00020268

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00020268

Keywords

Search

Navigation