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International Journal of Fracture

, Volume 17, Issue 4, pp 389–407 | Cite as

Influence of voids on shear band instabilities under plane strain conditions

  • Viggo Tvergaard
Article

Abstract

The effect of microscopic voids on the failure mechanism of a ductile material is investigated by considering an elastic-plastic medium containing a boubly periodic array of circular cylindrical voids. For this voided material under uniaxial or biaxial plane strain tension the state of stresses and deformations is determined numerically. Bifurcation away from the fundamental state of deformation is analysed with special interest in a repetitive pattern that represents the state of deformation inside a shear band. Both in the fundamental state and in the bifurcation analysis the interaction between voids and the details of the stress distribution around voids are fully accounted for. Comparison is made with the shear band instabilities predicted by a continuum model of a ductile porous medium. Based on the numerical results an adjustment is suggested for the approximate yield condition in this model of dilatant, pressure sensitive plastic behaviour.

Keywords

Shear Band Plane Strain Plane Strain Condition Bifurcation Analysis Periodic Array 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Résumé

Les effets de lacunes microscopiques sur le mécanisme de la rupture d'un matériau ductile ont été étudiés en considérant un milieu élastoplastique comportant une double rangée périodique de lacunes circulaires cylindriques. Pour ce matériau soumis à une tension en état plan de déformations uniaxiales ou biaxiales, on détermine par voie numérique l'état des tensions et des déformations. On analyse une déviation par rapport à l'état fondamental des déformations en s'intéressant plus particulièrement à l'aspect répétifif représentant l'état de déformation à l'intérieur d'une bande de cisaillement. L'interaction entre les lacunes et les détails de la distribution des contraintes autour de ces lacunes sont pris en compte dans une approche fondamentale et dans l'analyse de la déviation. Une comparaison est établie avec les instabilités des bandes de cisaillement prédites par un modèle continu dans un milieu poreux ductile. En se basant sur les résultats numériques, on suggère un ajustement à la condition approchée de cédage dans ce modèle de comportement plastique en dilatation et sensible à la pression.

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Viggo Tvergaard
    • 1
  1. 1.Department of Solid MechanicsThe Technical University of DenmarkLyngbyDenmark

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