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FRACTURE OF NATURAL POLYMERIC FIBRES                                31 1

             small. Provided that cracks are initially smaller than the grain size, high toughness is
             ensured: grain boundaries are effective as obstacles to crack growth, and they contribute
             to the factor y  in Eq.  1. In the case of a fibrous polymer we have to interpret ‘grain
             size’ as the  linear dimension of  a  structural subunit in  the direction of  initial crack
             growth, and  ‘grain  boundaries’ become the interfaces between such subunits. A  fine
             microstructure, which is able to deflect cracks along complex paths, is synonymous with
             high toughness. A coarse microstructure can accommodate large crack lengths within
             a grain (or crystal, or other subunit), and so is associated with a low stress to trigger
             catastrophic failure.
               However, sometimes a crack will not  initiate within a  microstructure but  will be
             imposed  on  the  material  from  outside,  for  example  by  impact  or  cutting.  In  such
             circumstances, it is useful if the material contains interfaces that can impede the growth
             of  an  initially  large  crack. Such interfaces must  (a) be  separated by  large distances
             (to accommodate a large crack between them, while not significantly diminishing the
             load-carrying capacity of the material as a whole), and (b) have geometrical and failure
             characteristics that interact optimally with the stress field of a large crack.
               These  requirements  can  be  met  by  a  microstructure that  is  hierarchical,  where
             different scales of structure can stop different sizes of crack. Although microstructural
             hierarchy  of  natural  fibres  is  a  fortuitous  consequence of  fibre  self-assembly,  it  is
             also a fortunate consequence. It allows independent optimisation of several mechanical
             properties, and it confers damage tolerance as well as toughness. Fibrous materials that
             have a hierarchical microstructure are able to fail gracefully.

             Water Plays Multiple Roles in the Assembly and Stabilisation of Natural Fibres

               Most  of  the  steps  involved  in  the  synthesis  and  assembly  of  biological  fibrous
             materials take place in the presence of water. The water acts as a solvent and transport
             medium for reactants. It also can play a significant role in promoting adhesion between
             biological macromolecules, for example the G-actin monomers in F-actin. The driving
             force  is  entropic.  G-actin  molecules  that  have  become  aggregated will  immobilise
             significantly fewer water molecules compared to the same number of  independent G-
             actins, so the entropy of the water increases. Although aggregation necessarily decreases
             the G-actin entropy, the accompanying increase in the disorder of  water is more than
             enough to compensate (Steinmetz et al., 1997; Tuszynski et al., 1997). For every G-actin
             molecule that is added to an aggregate, several water molecules can be liberated. Thus,
             the water does not act as a ‘glue’ linking G-actin molecules, but rather serves to promote
             association of G-actins by  virtue of being excluded from the space between them. An
             analogy is provided by  ‘non-stick’ hydrophobic Teflona surfaces, which can develop a
             strong affinity for other hydrophobic materials when immersed in water.
               Many natural fibrous materials are stabilised by  this type of  hydrophobic  bonding
             between  structural  subunits  at  one  or  more  length  scales.  Examples  (Renuart  and
             Viney,  2000) include keratins, collagen, silk, viral spikes, actin and tubulin. Materials
             such as the latter three are optimised for continuous use in an aqueous environment,
             in  which  case  hydrophobic bonds  may  provide  a  particularly  significant source  of
             stability. Property measurements, including tensile testing to failure, performed in air
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