Eigenvalue method for computing size effect of cohesive cracks with residual stress, with application to kink-bands in composites

Goangseup Zi, Zdeněk P. Bažant

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

The previously developed eigenvalue method for computing the size effect of cohesive crack model is extended to the cohesive crack model with a finite residual stress. In this model, the structure size for which a specified relative length of kink-band corresponds to the maximum load is obtained as an eigenvalue of a homogeneous Fredholm integral equation. This new method is direct and much more efficient than the classical finite element approach in which the entire load-deflection history must be computed to obtain the maximum load. A secondary purpose of the paper is to apply the new method to the effect of structure size on the compressive strength of unidirectional fiber-polymer composites failing by propagation of kink-band with fiber microbuckling. The kink-band is simulated by a cohesive crack model with a linear compressive softening law and a finite residual stress. The simulation shows that the specimens tested have a negative-positive geometry, i.e., the energy release rate of the kink-band for a unit load first decreases but at a certain length of propagation begins to increase. Finally the effect of shape of the softening law of cohesive crack on the size effect curve is studied by using the new eigenvalue method. It is shown that, for a negative-positive geometry, the size effect on the peak load depends on the entire softening curve if the specimens is not too small.

Original languageEnglish
Pages (from-to)1519-1534
Number of pages16
JournalInternational Journal of Engineering Science
Volume41
Issue number13-14
DOIs
Publication statusPublished - 2003 Aug 1

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Residual stresses
Cracks
Composite materials
Geometry
Fibers
Energy release rate
Compressive strength
Integral equations
Polymers

Keywords

  • Cohesive crack
  • Composite materials
  • Compressive failure
  • Eigenvalue analysis
  • Fracture
  • Scaling
  • Size effect

ASJC Scopus subject areas

  • Engineering(all)

Cite this

Eigenvalue method for computing size effect of cohesive cracks with residual stress, with application to kink-bands in composites. / Zi, Goangseup; Bažant, Zdeněk P.

In: International Journal of Engineering Science, Vol. 41, No. 13-14, 01.08.2003, p. 1519-1534.

Research output: Contribution to journalArticle

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