Page 336 - Fiber Fracture

3 18 C. Viney

(sample gauge length 50 mm; strain rate s-’) (Pkrez-Rigueiro et al., 1998), while
Argiope trifasciuta spider dragline has a Weibull modulus of 3.4 (sample gauge length
20 mm; strain rate 2.10-4 s-I) (Perez-Rigueiro et al., 2001). Thus, the impressively
high average strength of silk is compromised by a variability similar to that of common,
non-engineering ceramics and glasses.
The fact that the silkworm fibre has a higher Weibull modulus, i.e. a more re-
producible failure strength, than the spider dragline suggests that silkworm silk has
an intrinsically tougher microstructure. This makes sense biologically, in that cocoons
require optimised long-term toughness and durability while dragline requires optimised
short-term strength and stiffness. Even so, isolated silkworm cocoon fibre is unreliable
when compared against the standard of a high-toughness metallic alloy, so it is not
surprising that the cocoon is really a high-volume-fraction fibre composite in which the
load from fibres that break prematurely can be redistributed onto the higher-strength
fibres.
In the above-mentioned experiments, the silkworm fibre samples not only have a
longer gauge length, but they are also approximately five times thicker than the spider
silk. The silkworm fibre therefore is able to harbour a more polydisperse flaw size
distribution, which should increase its variability in fracture strength and decrease its
Weibull modulus relative to the results obtained from a set of smaller-volume samples.
In this context, the higher reliability of silkworm fibre, compared to spider dragline, is
further evidence that the silkworm product has an intrinsically tougher microstructure.
The microstructural distinction between the two silks is worth emphasising (Thiel et al.,
1997) because, erroneously and often, the microstructural description of silkworm silk
has been carried over into the literature of spider dragline. As a further demonstration
of microstructural variety in silks, the fracture surfaces of fibres from different species
of larva (Fig. 6) and from different arthropod classes (Poza et al., 2002) show
distinguishable degrees of ductile failure at a constant deformation rate.
Given that silks can show significant ductility, and, as noted in the section ‘The
Fracture Characteristics of Natural Fibres Can Be Sensitive to Prior Deformation’,
can be regarded as elastomeric, is a Weibull analysis appropriate for characterising the
failure strength variability of these materials? One justification can be formulated simply
on phenomenological grounds: after significant deformation, silk develops the statistical
failure characteristics of a brittle material, even though it initially deserves classification
as an elastomer. While the existence of strength-limiting defects can be inferred from
this description, their nature has yet to be determined; it is not clear whether they are
present in as-spun material, or whether they begin to develop during the earlier stages
of deformation. A possiblc candidate in silkworm cocoon fibre is the fine-scale voiding
that has been detected (Robson, 1999) in silver-sulphide- ‘stained’ samples viewed by
transmission electron microscopy.
The appropriateness of the Weibull analysis for a partially ductile material can also be
justified fundamentally. Although the Weibull method of reliability analysis is formally
developed for classically brittle materials (Kelly and Macmillan, 1986), i.e. materials
that fail before they can exhibit a yield point, its use can be generalised for materials
that exhibit flaw sensitivity. This generalisation can be arrived at simply by examining
the equation (Simon and Bunsell, 1984; Chou, 1992) which is plotted to obtain a value