Advertisement

International Journal of Fracture

, Volume 106, Issue 1, pp 65–80 | Cite as

A general expression for an area integral of a point-wise J for a curved crack front

  • K. Eriksson
Article

Abstract

The expression for the J-integral at a point on a three-dimensional crack front, obtained from a surface independent integral, is in general a sum of a contour integral and an area integral. In this work a general expression of an area integral for a crack with a curved front is derived in curvilinear coordinates. In certain situations the area integral vanishes and previously known cases are a straight crack front in plane stress or plane strain. The general conditions for a vanishing area integral are studied. It is shown that the area integral is non-zero for cracks with a curved front in the direction of crack extension. Some examples of curved cracks are given, for which the area integral vanishes and that are of interest in practice.

J-integral point-wise curved crack area integral. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Amestoy, M., Bui, H.D. and Labbens, R. (1981). On the definition of local path independent integrals in threedimensional crack problems. Mechanical Research Communications 8, 231–236.Google Scholar
  2. Bergkvist, H. and Lan Huong, G.L. (1977). J-integral related quantities in axisymmetric cases. International Journal of Fracture 13, 556–558.Google Scholar
  3. Budiansky, B. and Rice, J.R. (1973). Conservation laws and energy-release rates. Journal of Applied Mechanics 40, 201–203.Google Scholar
  4. Carpenter, W.C., Read, D.T. and Dodds, R.H. (1986). Comparison of several path independent integrals including plasticity effects. International Journal of Fracture 31, 303–323.Google Scholar
  5. deLorentzi, H.G. (1982). On the energy release rate and the J-integral for 3-D crack configurations. International Journal of Fracture 19, 183–193.Google Scholar
  6. deLorenzi, H.G. (1985). Energy release rate calculations by the finite element method. Engineering Fracture Mechanics 21, 129–143.Google Scholar
  7. Eriksson, K. (1998). On the point-wise J-value of axisymmetric plane cracks. International Journal of Fracture 91, L31–L36.Google Scholar
  8. Eshelby, J.D. (1970). Energy relations and the energy-momentum tensor in continuum mechanics. Inelastic Behaviour of Solids, Kanninen, M.F., Adler, W.F., Rosenfield, A.R. and Jaffe, R.I. (eds.), McGraw-Hill, New York, 77–115.Google Scholar
  9. Fung, Y.C. (1965). Foundations of Solid Mechanics, Prentice Hall, New Jersey.Google Scholar
  10. Hellen, T.K. (1975). On the method of virtual crack extensions. International Journal for Numerical Methods in Engineering 9, 187–207.Google Scholar
  11. Hutchinson, J.W. (1968). Singular behavior at the end of a tensile crack tip in a hardening material. Journal of the Mechanics and Physics of Solids, 16, 13–31.Google Scholar
  12. Nikishkov, G.P. and Atluri, S.N. (1987). Calculation of fracture mechanics parameters for an arbitrary threedimensional crack, by the ‘Equivalent Domain Integral’ method. International Journal for Numerical Methods in Engineering 24, 1801–1821.Google Scholar
  13. Parks, D.M. (1974). A stiffness derivative finite element technique for determination of crack tip stress intensity factors. International Journal of Fracture 10, 487–502.Google Scholar
  14. Rice, J.R. (1968). A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 35, 379–386.Google Scholar
  15. Rice, J.R. and Rosengren, G.F. (1968). Plane strain deformation near a crack tip in a power-law hardening material. Journal of the Mechanics and Physics of Solids, 16, 1–12.Google Scholar
  16. Shih, C.F., Moran, B., and Nakamura, T. (1986). Energy release rate along a three-dimensional crack front in a thermally stressed body. International Journal of Fracture 30, 79–102.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • K. Eriksson
    • 1
  1. 1.Department of Solid MechanicsUniversity of LuleåSweden

Personalised recommendations