Skip to main content
SpringerLink
Log in

The asymptotic structure of small-scale yielding interfacial free-edge joint and crack-tip fields

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Summary

The problem of the small-scale yielding (SSY) plane-strain asymptotic fields for the interfacial free-edge joint singularity is examined in detail, and comparisons are made with the interfacial crack tip. The geometries are idealized as isotropic elasto-plastic materials with Ramberg-Osgood power-law hardening properties bonded to a rigid elastic substrate. The resulting fields are shown to be singular and are presented in terms of radial and angular distributions of stress and displacement, and as idealized plastic slip-line sectors. A fourth-order Runge-Kutta numerical method provides solutions to fundamental equations of equilibrium and compatibility that are verified with those of a highly focused finite element (FE) analysis. It is shown that, as in the case of the crack, the asymptotic singular fields are only dependent on the hardening parameter and only a small range of interfacial mode-mix ratios are permitted. The order for the stress singularity may be formulated in terms of the hardening parameter and the elastic solution for incompressible material. The rigid-slip-line field for the interfacial free-edge joint is presented, and it is shown that there is some significant similarity between the asymptotic fields of the deviatoric polar stresses for the joint and the crack-tip having an elastic wedge sector.

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

  • M. L. Williams (1959) ArticleTitleThe stresses around a fault or crack in dissimilar media Bull. Seismol. Soc. America 49 199–204 Occurrence Handle102211

    MathSciNet  Google Scholar 

  • C. F. Shih R. J. Asaro (1988) ArticleTitleElastic-plastic analysis of cracks on bimaterial interfaces; Part I: small scale yielding J. Appl. Mech. 55 299–316 Occurrence Handle10.1115/1.3173676

    Article  Google Scholar 

  • C. F. Shih R. J. Asaro (1989) ArticleTitleElastic-plastic analysis of cracks on bimaterial interfaces; Part II – structures of small-scale yielding fields J. Appl. Mech. 56 763–779

    Google Scholar 

  • E. Zywicz D. M. Parks (1992) ArticleTitleSmall-scale yielding interfacial crack tip fields J. Mech. Phys. Solids 40 511–536 Occurrence Handle10.1016/0022-5096(92)80002-8

    Article  Google Scholar 

  • L. Xia T. Wang (1993) ArticleTitleSingular behavior near the tip of a sharp V-notch in a power law hardening material Int. J. Fract. 59 83–93

    Google Scholar 

  • N. W. Klingbeil J. L. Beuth (2000) ArticleTitleOn the design of debond-resistant bimaterials Part II: a comparison of the free-edge and interface crack approaches Engng. Fract. Mech. 66 111–128 Occurrence Handle10.1016/S0013-7944(00)00003-5

    Article  Google Scholar 

  • A. Romeo R. Ballarini (1994) ArticleTitleThe influence of the elastic mismatch on the size of the plastic zone of a crack terminating at a brittle-ductile interface Int. J. Fract. 65 183–196

    Google Scholar 

  • Y. Y Yang D. Munz M. A. Sckuhr (1997) ArticleTitleEvaluation of the plastic zone in an elastic-plastic dissimilar materials joint Engng. Fract. Mech. 56 691–710 Occurrence Handle10.1016/S0013-7944(96)00121-X

    Article  Google Scholar 

  • C. W. Law F. Delale (1988) ArticleTitleInterfacial stress singularities at free edge of hybrid metal matrix composites J. Engng. Mater. Tech. 110 41–47 Occurrence Handle10.1115/1.3226008

    Article  Google Scholar 

  • J.-Q. Xu L.-D. Fu Y. Mutoh (2002) ArticleTitleA method for determining elastic-plastic stress singularity at the interface edge of bonded power law hardening materials JSME Int. J. Series A 45 177–183 Occurrence Handle10.1299/jsmea.45.177

    Article  Google Scholar 

  • M. R. H. Rudge D. M. Tiernan (1999) ArticleTitleStress singularities in composite wedge-shaped materials Fat. Fract. Engng. Matls. Structs. 22 11–15 Occurrence Handle10.1046/j.1460-2695.1999.00138.x

    Article  Google Scholar 

  • S. M. Sharma N. Aravas (1993) ArticleTitleOn the development of variable-separable asymptotic elastoplastic solutions for interface cracks Int. J. Solids Struct. 30 695–723 Occurrence Handle0825.73564 Occurrence Handle10.1016/0020-7683(93)90030-B

    Article  MATH  Google Scholar 

  • S. M. Sharma N. Aravas (1991) ArticleTitleDetermination of higher order terms in asymptotic elastoplastic crack tip solutions J. Mech. Phys. Solids 39 1043–1072 Occurrence Handle0761.73090 Occurrence Handle10.1016/0022-5096(91)90051-O

    Article  MATH  Google Scholar 

  • D. B. Bogy (1971) ArticleTitleTwo edge-bonded elastic wedges of different materials and wedge angles under surface tractions J. Appl. Mech. 38 377–386

    Google Scholar 

  • J. Dundurs (1969) ArticleTitleEdge-bonded dissimilar orthogonal elastic wedges under normal and shear loading J. Appl. Mech. 44 650–652

    Google Scholar 

  • A. R. Akisanya (1997) ArticleTitleOn the singular stress field near the edge of bonded joints J. Strain Anal. 32 301–311 Occurrence Handle10.1243/0309324971513427

    Article  Google Scholar 

  • A. R. Akisanya N. A. Fleck (1997) ArticleTitleInterfacial cracking from the free-edge of a long bi-material strip Int. J. Solids Struct. 34 1645–1665 Occurrence Handle0944.74626 Occurrence Handle10.1016/S0020-7683(96)00053-4

    Article  MATH  Google Scholar 

  • Z. Suo J. W. Hutchinson (1989) ArticleTitleSandwich test specimens for measuring interface toughness Maters. Sci. Engng. 107 135–143 Occurrence Handle10.1016/0921-5093(89)90382-1

    Article  Google Scholar 

  • J. R. Rice G. R. Rosengren (1968) ArticleTitlePlane strain deformation near crack tip in a power law hardening material J. Mech. Phys. Solids 16 1–12 Occurrence Handle0166.20703 Occurrence Handle10.1016/0022-5096(68)90013-6

    Article  MATH  Google Scholar 

  • J. W. Hutchinson (1968) ArticleTitleSingular behavior at the end of tensile crack in a hardening material J. Mech. Phys. Solids 16 13–31 Occurrence Handle0166.20704 Occurrence Handle10.1016/0022-5096(68)90014-8

    Article  MATH  Google Scholar 

  • K. Bose P. A. Mataga P. P. Castaneda (1999) ArticleTitleStable crack growth along a brittle/ductile interface-II: small scale yielding solutions and interfacial toughness predictions Int. J. Solids Struct. 36 1–34 Occurrence Handle0941.74045 Occurrence Handle10.1016/S0020-7683(97)00270-9

    Article  MATH  Google Scholar 

  • C. F. Shih (1974) ArticleTitleSmall-scale yielding analysis of mixed mode plane strain crack problems ASTM STP 560 187–210

    Google Scholar 

  • M. J. Ekman L. Marsavina A. D. Nurse (2000) ArticleTitleComplex fracture parameters for an interface crack between two hardening materials: a photoelastic study Fat. Fract. Engng. Matls. Structs. 23 619–630 Occurrence Handle10.1046/j.1460-2695.2000.00312.x

    Article  Google Scholar 

  • Rice, J. R., Tracey, D. M.: In: Numerical and computer methods in structural mechanics. (Fenves, S. J. et al., eds.), pp. 585–624. New York: Academic Press.

Download references

Author information

Authors and Affiliations

  1. Department Strength of Materials, University Politehnica Timisoara, Blvd. M. Viteazu, No. 1, Timisoara, 300 222, Romania

    L. Marsavina

  2. Department of Mechanical Engineering, Loughborough University, Loughborough, LE11 3TU, U.K

    A. D. Nurse

Authors
  1. L. Marsavina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. D. Nurse
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Marsavina.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marsavina, L., Nurse, A.D. The asymptotic structure of small-scale yielding interfacial free-edge joint and crack-tip fields. Acta Mechanica 190, 115–131 (2007). https://doi.org/10.1007/s00707-006-0387-7

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-006-0387-7

Keywords

Search

Navigation