Acta Mechanica Sinica

, Volume 8, Issue 2, pp 156–164 | Cite as

High-order asymptotic analysis for the crack in nonlinear material

  • Xia Lin
  • Wang Tzuchiang


Accurate high-order asymptotic analyses were carried out for Mode II plane strain crack in power hardening materials. The second-order crack tip fields have been obtained. It is found that the amplitude coefficientk 2 of the second term of the asymptotic field is correlated to the first order field as the hardening exponentn<n * (n *≈5), but asn≥n *,k 2 turns to become an independent parameter. Our results also indicated that, the second term of the asymptotic field has little influence on the near-crack-tip field and can be neglected whenn<n *. In fact,k 2 directly reflects the effects of triaxiality near the crack tip, the crack geometry and the loading mode, so that besidesJ-integral it can be used as another characteristic parameter in the two-parameter criterion.

Key Words

asymptotic analysis near-crack-tip field triaxiality 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech, 1968, 35: 377–386Google Scholar
  2. 2.
    Rice JR and Rosengren GF. Plane strain defformation near a crack tip in a power law hardening material. J Mech Phys Solids, 1968, 16: 1–12.zbMATHCrossRefGoogle Scholar
  3. 3.
    Hutchinson JW. Singular behaviour at the end of a tensile crack in a hardening material. J Appl Mech Phys Solids, 1968, 16: 13–31zbMATHCrossRefGoogle Scholar
  4. 4.
    Hutchinson JW. Plastic stress and strain fields at a crack tip. J Appl Mech Phys Solids, 1968, 16: 337–347CrossRefGoogle Scholar
  5. 5.
    Shih CF and German MD. Requirements for a one parameter characterization of crack tip fields by The HRR singularity. Int J Fracture Mech, 1981, 17: 27–43Google Scholar
  6. 6.
    McMeeking RM and Parks DM. Elastic-Plastic Fracture Mechanics ASME STP, 1979, 668: 175–194Google Scholar
  7. 7.
    Needleman A and Tvergaard V. Elastic-Plastic Fracture: Second Symposium, Volume I Inelastic Crack Analysis. ASME STP. 1983, 803: 80–115Google Scholar
  8. 8.
    Wang TC. Proceedings of ICF International Symposium on Fracture Mechanics (Beijing). 1983: 243–248Google Scholar
  9. 9.
    Li YC and Wang TC. High-order asymptotic field of tensile plane-strain nonlinear crack problems. Scientia Sinica (Series A), 1986, 29: 941–955zbMATHGoogle Scholar
  10. 10.
    O'Dowd NP and Shih CF. Family of crack-tip fields characterized by a triaxiality parameter: Part I—Structure of fields. J Mech Phys Solids, 1991, 39: 989–1015.CrossRefGoogle Scholar
  11. 11.
    O'Dowd NP and Shih CF, Family of Crack-Tip Fields Characterized by a Triaxiality Parameter: Part II—Fracture applications. to appear in J Mech Phys SolidsGoogle Scholar
  12. 12.
    Betegon C and Hancock JW. J Appl Mech, 1991, 58: 104–110Google Scholar
  13. 13.
    Bradford R. Persistence of the HRR fields for general yielding in Mode II. Int J Fracture, 26 (1984): 85–98CrossRefGoogle Scholar
  14. 14.
    Symington M, Shih CF, and Ortiz M. Brown University Report, MRG/DMR 8714665/1 1988Google Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 1992

Authors and Affiliations

  • Xia Lin
    • 1
  • Wang Tzuchiang
    • 1
  1. 1.Institute of MechanicsChinese Academy of SciencesBeijingChina

Personalised recommendations