Page 68 - Fiber Fracture

MODELS OF FIBRE FRACTURE 53

Fig. 14. Schematic structure of cotton fibres

by rupture of the microfibrils, since the matrix could continue to flow to higher strains.
Rupture mechanisms in the Feughelman model are less clear, but seem more likely to
be related to the microfibrils. In the Chapman-Hearle model, rupture is postulated as
starting in the matrix before the microfibrils have completed the a + transition. This
model fits the observed rupture at around 50% extension. While this approach may
reveal some fundamental features of the deformation mechanisms in keratin fibres, it
is evident that quantitative predictions of the failure strength need to include the fibre
structure at various length scales. A more detailed comparison of the three models is
given in Hearle (2000).
Collagen fibres are the building blocks of the biological soft tissues in the skeletal
system. Wang et al. (1997) used a different approach, based on viscoelastic models,
to simulate and predict the strain rate dependence, the viscoelastic behaviour and the
fracture of collagen fibres. They used the Zener model, with two nonlinear springs
and one dashpot. The critical values of stress and strain at failure at different strain
rates were explored using three different failure criteria: a stress criterion, a strain
criterion and the strain energy density criterion. The last one seems to be better than
the other two, although further quantitative study is needed to validate this conclusion.
According to the authors this approach provides the basis for interpretation of some
aspects of the viscoelastic and failure behaviour of hierarchically structured fibres with
more economical CPU than full finite element modelling of the whole structure would
have required.
Additional information on fracture of fibres hierarchically structured appears in the
paper by Viney and in the paper by Hearle (‘Fracture of Common Textile Fibres’).