Skip to main content
SpringerLink
Log in

A Three-dimensional Numerical Study of Mixed Mode (I and II) Crack Tip Fields in Elastic–plastic Solids

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

Abstract

The stress fields near a crack front in a ductile solid are essentially three-dimensional (3D) in nature. The objective of this paper is to investigate the structure of these fields and to establish the validity of two-dimensional (2D) plane stress and plane strain approximations near the crack front under mixed mode (combined modes I and II) loading. To this end, detailed 3D and 2D small strain, elastic–plastic finite element simulations are carried out using a boundary layer (small scale yielding) formulation. The plastic zones and radial, angular and thickness variations of the stresses are studied corresponding to different levels of remote elastic mode mixity and applied load, as measured by the plastic zone size with respect to the plate thickness. The 3D results are compared with those obtained from 2D simulations and asymptotic solutions. It is found that, in general, plane stress conditions prevail at a distance from the crack front exceeding half the plate thickness, although it could be slightly smaller for mode II predominant loading. The implications of the 3D stress distribution on micro-void growth near the crack front are briefly discussed.

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

  • ABAQUS (2004). Users Manual, Version 6.4. Hibbitt, Karlsson and Sorensen Inc., Pawtucket, RI.

  • C. Betegon J.W. Hancock (1991) ArticleTitleTwo-parameter characterization of elastic-plastic crack tip fields Journal of Applied Mechanics 58 104–110

    Google Scholar 

  • J. Faleskog (1995) ArticleTitleEffects of local constraint along three-dimensional crack fronts – a numerical and experimental investigation Journal of the Mechanics and Physics of Solids 43 447–493 Occurrence Handle10.1016/0022-5096(94)00067-F

    Article  Google Scholar 

  • C.L. Hom M. McMeeking (1988) ArticleTitleCrack tip blunting in thin ductile sheets ASME-AMD 91 215–226

    Google Scholar 

  • J.W. Hutchinson (1968) ArticleTitleSingular behavior at the end of a tensile crack in a hardening material Journal of the Mechanics and Physics of Solids 16 13–31 Occurrence Handle0166.20704

    MATH  Google Scholar 

  • J.W. Hutchinson (1983) ArticleTitleFundamentals of the phenomenological theory of non-linear fracture mechanics ASME Journal of Applied Mechanics 50 1042–1051 Occurrence Handle1983nyap.book.....H

    ADS  Google Scholar 

  • Y. Kim X.K. Zhu Y.J. Chao (2001) ArticleTitleQuantification of constraint on elastic-plastic 3D crack front by the J-A2 three-term solution Engineering Fracture Mechanics 68 895–914

    Google Scholar 

  • J. Kim X. Gao T.S. Srivatsan (2003) ArticleTitleModeling of crack growth in ductile solids: a three-dimensional analysis International Journal of Solids and Structures 40 7357–7374

    Google Scholar 

  • J. Li X. Zhang N. Recho (2004) ArticleTitleJ-Mp based criteria for bifurcation assessment of a crack in elastic-plastic materials under mixed mode I-II loading Engineering Fracture Mechanics 71 329–343 Occurrence Handle10.1016/S0013-7944(03)00117-6

    Article  Google Scholar 

  • R.M. McMeeking D.M. Parks (1979) ArticleTitleOn criteria for J-dominance of crack tip fields in large scale yielding ASTM STP 668 175–194

    Google Scholar 

  • T. Nakamura D.M. Parks (1988a) Conditions for J-dominance in three-dimensional thin cracked plates. ASME-AMD 91 227–238

    Google Scholar 

  • T. Nakamura D.M. Parks (1988b) ArticleTitleThree-dimensional stress field near the crack front of a thin elastic plate Journal of Applied Mechanics 55 805–813

    Google Scholar 

  • T. Nakamura D.M. Parks (1989) ArticleTitleAntisymmetrical 3-D stress field near the crack front of a thin elastic plate International Journal of Solids and Structures 25 1411–1426 Occurrence Handle10.1016/0020-7683(89)90109-1

    Article  Google Scholar 

  • T. Nakamura D.M. Parks (1990) ArticleTitleThree-dimensional crack front fields in a thin ductile plate Journal of the Mechanics and Physics of Solids 38 787–812 Occurrence Handle10.1016/0022-5096(90)90040-B

    Article  Google Scholar 

  • R. Narasimhan A.J. Rosakis (1990) ArticleTitleThree-dimensional effects near a crack tip in a ductile 3PB specimen: Part 1- A numerical investigation Journal of Applied Mechanics 57 607–617

    Google Scholar 

  • N.P. O’Dowd C.F. Shih (1991) ArticleTitleFamily of crack tip fields characterized by a triaxiality parameter-I, Structure of fields Journal of the Mechanics and Physics of Solids 39 989–1015

    Google Scholar 

  • J.R. Rice G.F. Rosengren (1968) ArticleTitlePlane-strain deformation near a crack tip in a power-law hardening material Journal of the Mechanics and Physics of Solids 16 1–12 Occurrence Handle10.1016/0022-5096(68)90013-6

    Article  Google Scholar 

  • J.R. Rice (1968) ArticleTitleA path-independent integral and the approximate analysis of stress concentration by notches and cracks Journal of Applied Mechanics 35 379–386

    Google Scholar 

  • S. Roychowdhury R.H. Dodds SuffixJr. (2004) ArticleTitleEffect of T-stress on fatigue crack closure in 3-D small-scale yielding International Journal of Solids and Structures 41 2581–2606 Occurrence Handle10.1016/j.ijsolstr.2003.11.004

    Article  Google Scholar 

  • A.Y. Roy R. Narasimhan (1997) ArticleTitleJ dominance in mixed mode ductile fracture specimens International Journal of Fracture 88 259–279

    Google Scholar 

  • A.Y. Roy R. Narasimhan (1999) ArticleTitleConstraint effects on ductile fracture processes near a notch tip under mixed-mode Loading Engineering Fracture Mechanics 62 511–534

    Google Scholar 

  • A.Y. Roy R. Narasimhan P.R. Arora (1999) ArticleTitleAn experimental investigation of constraint effects on mixed-mode fracture initiation in a ductile aluminium alloy Acta Materiala 47 1587–1596

    Google Scholar 

  • C.F. Shih (1973) Elastic–plastic analysis of combined mode crack problems Harvard University Cambridge, Massachusetts, USA

    Google Scholar 

  • C.F. Shih M.D. German (1981) ArticleTitleRequirements for a one parameter characterization of crack tip fields by the HRR singularity International Journal of Fracture 17 27–43

    Google Scholar 

  • M. Symmington C.F. Shih M. Ortiz (1990) ArticleTitleA finite element method for determining the angular variation of asymptotic crack tip fields International Journal of Fracture 45 51–64

    Google Scholar 

  • Tohgo K., Otsuka A. and Gao H.W. (1988). The behavior of ductile crack initiation from a notch under mixed-mode loading. In: Proceedings of Far East Fracture Group Workshop (edited by Sakata, M.), Tokyo Institute of Technology, Japan, pp. 101–108.

  • H. Yuan W. Brocks (1998) ArticleTitleQuantification of constraint effects in elastic-plastic crack front fields Journal of the Mechanics and Physics of Solids 46 219–241 Occurrence Handle10.1016/S0022-5096(97)00068-9

    Article  Google Scholar 

  • Yusof F. and Hancock J.W. (2005). In-plane and out-of-plane constraint effects in three-dimensional elastic perfectly-plastic crack tip fields. Proceedings of 11th International Conference on Fracture – Turin (Italy), pp. 5354–5359.

  • A.T. Zehnder A.J. Rosakis (1988) ArticleTitleThree dimensional effects near a crack tip in a ductile three point bend specimen: Part II – An experimental investigation using Interferometry and Caustics ASME Journal of Applied Mechanics 57 618–626

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Structures Division, National Aerospace Laboratories, Bangalore, 560017, India

    H. Y. Subramanya & S. Viswanath

  2. Department of Mechanical Engineering, Indian Institute of Science, Bangalore, 560 012, India

    R. Narasimhan

Authors
  1. H. Y. Subramanya
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Viswanath
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Narasimhan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. Narasimhan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Subramanya, H.Y., Viswanath, S. & Narasimhan, R. A Three-dimensional Numerical Study of Mixed Mode (I and II) Crack Tip Fields in Elastic–plastic Solids. Int J Fract 136, 167–185 (2005). https://doi.org/10.1007/s10704-005-5422-5

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-005-5422-5

Keywords

Search

Navigation