Skip to main content
Log in

Anisotropic plastic stress fields at a slowly propagating crack tip

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Under the condition that any perfectly plastic stress components at a crack tip are nothing but the functions of 0 only making use of equilibrium equations. Hill anisotropic yield condition and unloading stress-strain relations, in this paper, we derive the general analytical expressions of anisotropic plastic stress fields at the slowly steady propagating tips of plane and anti-plane strain. Applying these general analytical expressions to the concrete cracks, the analytical expressions of anisotropic plastic stress fields at the-slowly steady propagating tips of Mode I and Mode III cracks are obtained. For the isotropic plastic material, the anisotropic plastic stress fields at a slowly propagating crack tip become the perfectly plastic stress fields.

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

Access this article

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. Chitalcy, A.P. and F.A. McClintock, Elastic-Plastic mechanics of steady crack growth under anti-plane strain,J. Mech. Phys. Solids,19, 3 (1971), 147–163.

    Google Scholar 

  2. Slepyan, L.I., Growing crack in an elastic-plastic body under plane strain,Izv. AN SSSR Mekhanika Tverdogo Tela,9, 1 (1974), 57–67. (in Russian)

    Google Scholar 

  3. Rice, J.R., W.T. Drugan und T.L. Sham, Elastic-plastic analysis of growing crack, ASTM STP700 (1980), 189–221.

    Google Scholar 

  4. Gao, Yu-chen, Elastic-plastic field at the tip of a crack growing steadily in pefectly plastic medium,Acta Mechanica Sinica,1 (1980), 48–56. (in Chinese)

    Google Scholar 

  5. Hill, R.,The Mathematical Theory of Plasticity, Oxford (1950).

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicatcd by Chien Wei-zang

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bai-song, L. Anisotropic plastic stress fields at a slowly propagating crack tip. Appl Math Mech 10, 759–765 (1989). https://doi.org/10.1007/BF02019301

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02019301

Keywords

Navigation