Skip to main content
SpringerLink
Log in

A theoretical resistance-curve based on nonproportional plastic strain

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Using an exact solution for an elliptical hole in a perfectly plastic material, an expression is derived for the resistance of a ductile material undergoing subcritical crack propagation in the plane. This resistance curve is based on an analogy to the J-integral where an energy dissipation rate is determined rather than an energy release rate. The Tresca yield condition under plane stress loading conditions is employed in this derivation as well as finite deformation theory. This resistance curve is applicable to the initial stage of subcritical crack growth for a ductile material subject to crack tip blunting.

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

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Abramowitz M, Stegun IA (1964) Handbook of mathematical functions with formulas, graphs and mathematical tables. National Bureau of Standards, Series 55. U.S. Printing Office, Washington

  • ASTM Committee E 1820-1 (2002) Standard test method for measurement of fracture toughness. Annual book of ASTM standards, vol 03.01. ASTM, West Conshohocken, pp 1031–1076

  • Byrd PF, Friedman MD (1971) Handbook of elliptic integrals for engineers and scientists, 2nd edn. Springer, New York

    Book  Google Scholar 

  • Gradshteyn IS, Ryzhik IM (1980) Table of integrals, series, and products. Integral entry 2.513–13 Academic Press, Orlando, p 132

  • Hertzberg RW (1996) Deformation and fracture mechanics of engineering materials, 4th edn. Wiley, Hoboken, p 366

    Google Scholar 

  • Rice JR (1968) A path independent integral and approximate analysis of strain concentrations by notches and cracks. J Appl Mech 35:379–386

    Article  Google Scholar 

  • Unger DJ (2005) Perfectly plastic caustics for the opening mode of fracture. Theor Appl Fract Mech 44:82–94

    Article  Google Scholar 

  • Unger DJ (2008) Path independent integral for an elliptical hole in a plate under tension for plane stress deformation theory. J Elast 92:217–226

    Article  Google Scholar 

  • Unger DJ (2010) Large plastic deformations accompanying the growth of an elliptical hole in a thin plate. J Elast 99:117–130

    Article  Google Scholar 

  • Unger DJ (2011) Analytical fracture mechanics. Dover Publications, Mineola

    Google Scholar 

  • Unger DJ (2016a) Path-dependent J-integral evaluations around an elliptical hole for large deformation theory. J Mech Behav Mater 25:77–81

    Google Scholar 

  • Unger DJ (2016b) Erratum to: clarification of terminology used in: path-dependent J-integral evaluations around an elliptical hole for large deformation theory. J Mech Behav Mater 25:189

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Civil Engineering, University of Evansville, Evansville, IN, 47722, USA

    David J. Unger

Authors
  1. David J. Unger
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to David J. Unger.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Unger, D.J. A theoretical resistance-curve based on nonproportional plastic strain. Int J Fract 210, 207–211 (2018). https://doi.org/10.1007/s10704-018-0272-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-018-0272-0

Keywords

Search

Navigation