Skip to main content
SpringerLink
Log in

Analytic study on angular fields of HRR solution

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

By using the constructing function method, a systematic and strict analysis is carried out on the angular distribution field near a crack tip in a power-law hardening material and the analytic solution is provided for HRR problem. In addition, the equivalence of H equation and RR equation is proved. The present analytic solutions for HRR problem can reduce to (he well-known Williams solution in the limit case ofN→1 (orn→1) and Prandtl solution in the limit case ofN→0 (orn→∞). It is particularly interesting that from the deformation theory of plasticity one obtains the Prandtl solution based on the increatment theory of plasticity.

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

Access this article

Log in via an institution

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. Hutchinson, J. W., Singular behaviour at the end of a tensile crack in a hardening material,J.Mech. Phys. Solids, 1968, 16: 13.

    Article  MATH  Google Scholar 

  2. Hutchinson, J. W., Plastic stress and strain fields at a crack tip,J.Mech. Phys. Solids, 1968, 16: 337.

    Article  Google Scholar 

  3. Rice, J., Rosengren, G. F., Plane strain deformation near a crack in a power-law hardening material,J.Mech. Phys. Solids, 1968, 16: 1.

    Article  MATH  Google Scholar 

  4. Wang, W. X., Fan, T. Y., Analytic solution of mode I crack in materials with nonlinear behaviour,Phil. Mag. Lett., 1994, 59: 217.

    Google Scholar 

  5. Zhang, Z. F.,The Qualitative Theory of Ordinary Differential Equations (in Chinese), Beijing: Academic Press, 1985.

    Google Scholar 

  6. Fikhtensol’s, G. M.,Course of Differential and Integral Calculations (in Russian), 3rd ed., Moscow: Gosthchizdat, 1951, 599.

    Google Scholar 

  7. Fan, T. Y.,Foundation of Fracture Mechanics (in Chinese), Nanjing: Jiangsu Science and Technology Press, 1978.

    Google Scholar 

  8. Fan, T. Y., Sutton, M. A., Zhang, L. X., Plane stress steady crack growth in a powerlaw hardening material,Int. J. Fracture, 1997, Vol.84, in press.

Download references

Author information

Authors and Affiliations

  1. Institute of Naval Service, 300450, Tianjin, China

    Wenxin Wang

  2. Beijing Institute of Technology, 100081, Beijing, China

    Tianyou Fan & Liangxin Zhang

Authors
  1. Wenxin Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tianyou Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Liangxin Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Project supported by the National Natural Science Foundation of China (Grant No. 19132022).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, W., Fan, T. & Zhang, L. Analytic study on angular fields of HRR solution. Sci. China Ser. A-Math. 41, 313–323 (1998). https://doi.org/10.1007/BF02879051

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02879051

Keywords

Search

Navigation