Page 337 - Fiber Fracture

FRACTURE OF NATURAL POLYMERIC FIBRES 319

Fig. 6. Fracture surfaces produced in lepidopteran silk by hand-drawing under liquid nitrogen. Different
degrees of ductility are evident in the two materials, suggesting that there are significant microstructural
differences between them. Left: Bombyx mori (domesticated silkworm) cocoon silk. The white line
emphasises the fact that the fibre (bave) consists of two filaments (brins). Right: Rothschildiu erycinu
cocoon silk. The sample has deformed to an extent that precludes identification of the individual brins.

of the Weibull modulus m:
F=l-exp(-$) m

where F is the cumulative probability that a sample has a fracture strength of n, and no
is a constant. If F is to be independent of (T, which is the hallmark of an ideally brittle
material (section “Some Thoughts on the Meaning of ‘Brittle”’), Eq. 2 requires m to
be equal to zero. Since practical Weibull analysis admits to non-zero values of m, it is
implicit that ductile contributions to failure can be accommodated too.
The use of Weibull statistics to characterise failure probabilities in batches of natural
fibre is therefore appropriate, and can highlight the existence of significant microstruc-
tural differences between different materials. Comparison of different materials is most
straightforward if similar sample volumes can be used, but this is difficult if the materi-
als have different and irregular fibre cross-sections. A further complication is introduced
by viscoelasticity, which will make strength depend on the detailed stress-strain profile
of the material and the rate at which samples are loaded. Comparisons should therefore
be conducted at defined and reproducible strain rates. It must be recognised, however,
that comparison of different polymers under exactly equivalent conditions can never
be achieved in practice, because it is most unlikely that different polymers will have
identical viscoelastic characteristics. Silks are especially ‘unusual’: while increased
deformation rates are associated with higher strength, higher stiffness and lower elon-
gation to failure in most viscoelastic materials, silk exhibits an increased elongation to
failure (Kaplan et al., 1997). This observation supports the idea that the propagation
characteristics of defects, rather than bulk viscoelastic behaviour, governs the fracture of
natural silk fibres.