Archive of Applied Mechanics

, Volume 61, Issue 6–7, pp 471–478 | Cite as

Notes on plastic reloading zone in the asymptotic analysis of elastic-plastic crack extension

  • H. Yuan
  • W. Brocks
Originals
  • 15 Downloads

Summary

The asymptotic structures of near-tip stress and deformation fields are studied for steady-state crack extension in elastic-plastic solids. The condition for the existence of a plastic reloading zone is formulated. If a plastic reloading zone is to exist in hardening materials, the effective stress must become unbounded as the crack flank is approached. It is shown explicitly in the case of mode III that solutions with logarithmic singularity produce negative plastic dissipation in the plastic reloading sector.

Keywords

Neural Network Complex System Information Theory Nonlinear Dynamics Effective Stress 

Über die rückplastizierte Zone bei asymptotischen Lösungen der elastisch-plastischen Rißausbreitung

Übersicht

Untersucht wird die asymptotische Form von rißspitzennahen Spannungs- und Verformungsfeldern bei der stationären Rißausbreitung in elastisch-plastischen Körpern. Die Bedingung für die Existenz einer rückplastizierten Zone wird formuliert. Wenn eine solche Zone bei verfestigendem Material vorhanden sein soll, muß die Vergleichsspannung bei Annäherung an die Rißflanke unendlich werden. Es wird gezeigt, daß bei Mode III die Lösungen mit logarithmischer Singularität negative Dissipation in der rückplastizierten Zone bedeuten würden.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Amazigo, J. C.; Hutchinson, J. W.: Crack tip fields in steady crack-growth with linear strain-hardening. J. Mech. Phys. Solids 25 (1977) 81–97Google Scholar
  2. 2.
    Brocks, W.; Yuan, H.: Numerical studies on stable crack growth. In: Blauel, J. D.; Schwalbe, K.-H. (eds.) Defect Assessment in components — Fundamentals and applications, pp. 19–33. (ESIS/EGF Publication 9), Bury St. Edmunds: Mech. Engineering Publ. 1991Google Scholar
  3. 3.
    Castañeda, P. P.: Asymptotic fields in steady crack growth with linear strain hardening. J. Mech. Phys. Solids 35 (1987) 227–268Google Scholar
  4. 4.
    Drugan, W. J.; Chen, X.-Y.: Plane strain elastic-ideally plastic crack fields for mode I quasi-static growth at large scale yielding. — I. A new family of analytical solutions. J. Mech. Phys. Solids 37 (1989) 1–26Google Scholar
  5. 5.
    Drugan, W. J.; Rice, J. R.; Sham, T.-L.: Asymptotic analysis of growing plane strain tensile cracks in elastic-ideally plastic solids. J. Mech. Phys. Solids 30 (1982) 447–473Google Scholar
  6. 6.
    Gao, Y.-C.: Elastic-plastic fields at the tip of a crack growing steadily in perfectly-plastic medium (in Chinese). Acta Mechanica Sinica 1 (1980) 48–56Google Scholar
  7. 7.
    Gao, Y.-C.; Hwang, K.-C.: Elastic-plastic fields in steady crack growth in a strain-hardening material. In: Franscois, D. (ed.) Proc. of Fifth Int. Conf. on fracture (ICF-5): Advances in fracture research, pp. 669–682, Oxford: Pergamon Press 1981Google Scholar
  8. 8.
    Gao, Y.-C.; Zhang, X.-T.; Hwang, K.-C.: The asymptotic near-tip solution for mode III crack in steady growth in power hardening media. Int. J. Fracture 21 (1983) 301–317Google Scholar
  9. 9.
    Hutchinson, J. W.: Singular behavior at the end of a tensile crack in a hardening material. J. Mech. Phys. Solids. 16 (1968) 13–31Google Scholar
  10. 10.
    Hutchinson, J. W.: Crack-tip singularity fields in nonlinear fracture mechanics: A survey of current status. In: Franscois, D. (ed.): Proc. Fifth Int. Conf. on Fracture (ICF-5): Advances in fracture research, pp. 2669–2684. Oxford: Pergamon Press 1981Google Scholar
  11. 11.
    Rice, J. R.; Drugan, W. J.; Sham, T. L.: Elastic-plastic crack growth. In: Paris, P. C. (ed.) Fracture Mechanics (ASTM STP 700), pp. 189–221. Philadelphia: American Society for Testing and Materials 1980Google Scholar
  12. 12.
    Rice, J. R.; Rosengren, G. F.: Plane strain deformation near a crack tip in a power-law hardening material. J. Mech. Phys. Solids 16 (1968) 1–12Google Scholar
  13. 13.
    Slepyan, L. I.: Growing crack during plane deformation of an elastic plastic body. Izv. Akad. Nauk. SSSR, Mekhanika Tverdogo Tela, 9 (1974) 57–67Google Scholar
  14. 14.
    Yuan, H.; Cornec, A.: On the significance of elastic-plastic crack propagation velocity in asymptotic solutions. In: Firrao, D. (ed.) Fracture behaviour and design of materials and structures (ECF 8), pp. 873–878. West Midlands Engineering Materials Advisory Service Ltd. 1990Google Scholar
  15. 15.
    Zhang, Z.-M.; Gao, Y.-C.: Plastic stress dynamic fields near a propagating crack-tip in a power-law material (in Chinese). Acta Mechanica Sinica 20 (1988) 19–30Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • H. Yuan
    • 1
  • W. Brocks
    • 2
  1. 1.Inst. für WerkstofforschungGKSS-Forschungszentrum Geesthacht GmbHGeesthachtFederal Rep. of Germany
  2. 2.Bundesanstalt für Materialforschung und-prüfungBerlin 45Federal Rep. of Germany

Personalised recommendations