Page 335 - Fiber Fracture

FRACTURE OF NATURAL POLYMERIC FIBRES 317

PCrez-Rigueiro et al., 1998). To complicate matters, silks usually have small average
cross-sectional dimensions. B. mori cocoon silk (bave, consisting of a pair of filaments)
has a diameter of around 20 p,m, while spider dragline diameters are approximately
1-5 pm and spider cribellate silk (Foelix, 1982) can have a diameter as small as 0.01
pm. Characterisation of failure strength in a tensile test requires knowledge of the
cross-sectional area at the position where failure occurred. This position is likely to (but
not required to) coincide with the smallest initial cross-sectional area of the sample, and
is difficult to identify ahead of the tensile test. Therefore, tensile tests will often (but not
necessarily) underestimate the stiffness, yield strength and failure strength of silk.
A micro-tensile stage used in conjunction with (environmental) scanning electron
microscopy offers a promising route to the necessary area characterisation. The stage
will record the load while deforming the sample at a set rate, while the microscope is
used to locate the likely region of fracture and to monitor whether the sample draws
down uniformly or necks locally. After fracture, the sample cross-section at the point
of fracture can be measured, and the results used to obtain the nominal or true fracture
stress.

Force Characterisation

To obtain an idea of the intrinsic strength of natural fibres we must be able to
acquire tensile data from the smallest constituent fibrils. At these small length scales,
characterisation of load-bearing cross-section may be easier than at the overall fibre
length scale, since the dimensions of interest can be determined accurately from
crystallographic data and/or packing considerations. It is the measurement of load (and
of extension, if strains and thence elastic modulus are to be measured as well) that
becomes challenging at these length scales. Another challenge arises in disrupting the
structural hierarchy to the level necessary for specimen preparation. Combinations of
optical tweezers and video-assisted fluorescence microscopy (Tsuda et al., 1996), or
optical tweezers, a nanometre-resolution piezo-stage and laser interferometry (Luo and
An, 1998) have been successful in characterising the stress-strain response of single
actin filaments and collagen molecules, respectively. The G-actin/G-actin bond strength
under conditions that mimic a physiological environment was determined as 600 pN
(Tsuda et al., 1996); this equates to an intrinsic material strength of approximately
50 MPa, similar to the strength of polyurethane (Warner, 1995). Some of the above
methodologies might usefully be applied to the cribellate silks referred to in the section
‘Cross-Sectional Area Characterisation’.

The Statistical Basis of Fibre Failure Analysis
We turn again to silk as an instructive example. Even if steps are taken to minimise
uncertainties in the measurement of sample cross-sectional area, the values of breaking
strength obtained for a given type of silk are poorly reproducible (Work, 1976, 1977;
Cunniff et al., 1994; Dunaway et a]., 1995b; Pkrez-Rigueiro et al., 1998, 2000). It is
useful to perform a Weibull analysis (Chou, 1992) of the fracture data to quantify this
variability in engineering terms. The Weibull modulus of B. mori cocoon fibre is 5.8