Causes and symptoms of the absence of the bundle size effect in the Fibre-Element-Imposed Impregnated Fibre Bundle Model

  • Lomov, Stepan (KU Leuven)
  • Breite, Cristian (KU Leuven)
  • Swolfs, Yentl (KU Leuven)
  • Abaimov, Sergey (Skolkovo Institute of Science and Technology)

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The Finite Element-Imposed Stress Model (FEISM) was shown to predict a weak size effect (four times smaller than seen in [1]) for the case when the presence of free surface at boundary was accounted for, and no demonstration of size effect if boundary fibres were not taken into account. In the present study, we investigate behaviour of the FEISM for bundle sizes varying from 100 to 16,000 fibres not only for ultimate strain and strength, but also for the details of the statistical physics descriptive parameters of the fibre break system: (1) susceptibility (as damage response to increase in loading); (2) the size distribution of fibre break clusters and avalanches; (3) correlation length of breaks’ interactions; and (4) parameters of the last catastrophic avalanche. The investigation was done for T700 carbon fibres/epoxy composite, at VF = 50% and VF = 60%. The only parameter, where the size effect was present, was the strain corresponding to the first fibre break, which is clearly the consequence of the higher probability of sampling from the tale of the fibre strength distribution. Other parameters did not reveal any scaling with bundle size. Even being based on physically sound stress redistribution after a fibre break, FEISM physics may lack the necessary scale-dependent conditions which would create the size effect. The collective effect of fibre breaks is accounted for only in the stress equilibrating calculation, while clusters can also extend the length over which stress concentrations are significant. In FEISM, as it is implemented now, this manifested itself as a lack of fractal behaviour of the fibre break clusters and avalanches. Conclusion: Future development of FEISM and similar models should take into account these collective effects, which also may eliminate the discrepancy between the predicted and experimentally observed ultimate bundle strain .