Skip to main content
Log in

Maximum-energy-release-rate criterion applied to a tension-compression specimen with crack

  • Published:
Journal of Elasticity Aims and scope Submit manuscript

Abstract

The title problem is studied by using the explicit asymptetic analysis presented in the accompanying paper. The asymptotic analysis indicates that the very basic problem is a semi-infinite L-shaped crack governed by a single integral equation. This equation is discretized to a system of complex algebraic equations and solved by a standard HARWELL subroutine. It is found that the maximum-energy-release-rate criterion has two branches, one for tensile loads and one for compressive loads. Our numerical results indicate that the maximum energy-release rate is always associated with maximum K 1 and K 2=0, where K 1 and K 2 are the stress-intensity factors at the fractured tip. Thus, the well-known K-G relation valid for crack-parallel propagation also holds for non-crack-parallel propagations. This conclusion is, however, purely numerical.

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

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Erdogan, F. and Sih, G. C., “On the Crack Extension in Plates Under Plane Loading and Transverse Shear”, J. Basic Engrg., Trans., ASME, 85 (1963), 519–527.

    Google Scholar 

  2. McClintock, F. A., Discussion of [1].

  3. Cotterell, B., “The Paradox between the Theories for Tensile and Compressive Fracture”, Int. J. Fracture Mech. 5 (1969), 251–252.

    Google Scholar 

  4. Williams, J. G. and Ewing, P. D., “Fracture Under Complex Stress—The Angled Crack Problem”, Int. J. Fracture Mech. 8 (1972) 441–446.

    Google Scholar 

  5. Finnie, I. and Saith, A., “A Note on the Angled Crack Problem and the Directional Stability of Cracks”, Int. J. Fracture Mech. 9 (1973) 484–486.

    Google Scholar 

  6. Ewing, P. D. and Williams, J. G., “Further Observations on the Angled Crack Problem”, Int. J. Fracture Mech. 10 (1974) 135.

    Google Scholar 

  7. Sih, G. C., “Introductory Chapter: A Special Theory of Crack Propagation”, Mechanics of Fracture 1, Noordhoff, Leyden 1972.

    Google Scholar 

  8. Griffith, A. A., “The Phenomena of Rupture and Flow in Solids”, Phil. Trans. R. Soc. A221 (1921) 163–198.

    Google Scholar 

  9. Griffith, A. A., “The Theory of Rupture”, Proc. 1st Int. Congr. Appl. Mech., Delft (1924) 55–63.

  10. Hussain, M. A., Pu, S. L., and Underwood, J., “Strain-Energy-Release Rate for a Crack Under Combined Mode I and Mode II”, ASTM-STP-560, 2–28 (1974).

  11. Palaniswamy, K. and Knauss, W. G., “On the Problem of Crack Extension in Brittle Solids Under General Loading”, Calif. Inst. Tech. Report SM 74-8 (1974).

  12. Chatterjee, S. N., “The Stress Field in the Neighborhood of a Branched Crack in an Infinite Elastic Sheet”, Int. J. Solids Struct. 11 (1975) 521–538.

    Google Scholar 

  13. Wu, C. H., “Elasticity Problems of a Slender Z-Crack”, Journal of Elasticity 8 (1978) 183–205.

    Google Scholar 

  14. Coughlan, J. and Barr, B. I. G., “Fracture Path prediction”, Report, Dept. Civil Engrg. and Building, Glamorgan Polytechnic, U.K. (1974).

  15. McClintock, F. A. and Walsh, J. B., “Friction on Griffith Cracks in Rocks Under Pressure”, Proc. 4th U.S. Congr. Appl. Mech., Berkeley, 1015–1021 (1962).

  16. Williams, M. L., “Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension”, J. Appl. Mech. 74 (1952) 526–528.

    Google Scholar 

  17. Westmann, R. A., “Geometrical Effects in Adhesive Joints”, Int. J. Engrg. Sci. 13 (1975) 369–391.

    Google Scholar 

  18. Keller, H. B., Numerical Methods for Two-Point Boundary-Value Problems, Blaisdell Publishing Company (1968).

  19. Anderson, H., “Stress-Intensity Factors for a Slit with an Infinitesimal Branch at One Tip”, Int. J. Fract. Mech. 5 (1969) 371–372.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported by U.S. Army Research Office-Durham under Grant DAAG-29-76-G-0272.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wu, C.H. Maximum-energy-release-rate criterion applied to a tension-compression specimen with crack. J Elasticity 8, 235–257 (1978). https://doi.org/10.1007/BF00130464

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00130464

Keywords

Navigation