Page 326 - Fiber Fracture

308 C. Viney

ulus) of the material, and y, the energy per unit area of new surface created by the
crack. The latter factor embraces both the intrinsic surface energy (Le. the energy
associated with breaking bonds in the interior of the material and replacing these with
materiaknvironment contacts) and the energy expended in effecting any associated
microstructural rearrangements. A brittle material is characterised by a low value of y.
(4) A statistical definition of brittleness can be formulated in terms of the Weibull
distribution of fracture probability for a material (Derby et al., 1992). The Weibull
modulus m (see Eq. 2) can range from zero (totally random fracture behaviour, where
the failure probability is the same at all stresses, equivalent to an ideally brittle material)
to infinity (representing a precisely unique, reproducible fracture stress, equivalent to an
ideally non-brittle material).

FRACTURE OF NATURAL SELF-ASSEMBLED FIBRES

Genetic engineering and supramolecular self-assembly offer a wide scope for con-
trolling fibre composition and microstructure. The number and variety of materials that
could be engineered with these techniques is extremely large. Much effort will be re-
quired to comprehensively characterise and efficiently refine the load-bearing properties
of the new fibres. It is therefore opportunc to reflect on the factors that determine the
characteristics of hierarchical microstructure in natural fibres, and the ability of such
microstructures to resist fracture.

Self-Assembly Favours the Formation of Fibrous, Hierarchical Structures

Fibrillar structures are a common consequence of supramolecular self-assembly in
nature. The association of polymer molecules that have an anisotropic shape will tend
to propagate that anisotropy at higher length scales, and globular polymers that have an
uneven distribution of charge at their surface will similarly reflect their molecular-scale
anisotropy when they aggregate. If there is a tendency towards anisotropic aggregation,
this will promote the formation of liquid crystalline phases, which synergistically
reinforces the tendency for anisotropic growth of the aggregates (Renuart and Viney,
2000).
Self-assembly additionally imparts a hierarchical structure to fibres. To maximise
fibre growth rates from solution, it is essential that material transport paths should be as
short as possible. A given cross-section can be assembled more effectively in a given
time if it consists of several fibrils developing in parallel, rather than a monolith. This
principle is evident in many collagens (Stryer, 1988; Rawn, 1989; Gorham, 1991), and
is advantageous for the construction of hollow tubes as exemplified by microtubules
(Hyams and Lloyd, 1994; Lodish et al., 1995). There is mounting evidence that silk
fibres, which must solidify quickly under significantly non-equilibrium conditions and
therefore can certainly benefit from short transport paths, also contain a hierarchy of
fibrils and sub-fibrils (Augsten et al., 2000 Putthanarat et al., 2000; Poza et al., 2002).
However, describing the mechanism whereby silk fibre microstructures self-assemble
remains a challenging question.