Page 328 - Fiber Fracture
P. 328

310                                                              C. Viney

                  the domains is crossed twice by the protein backbone, forming a hinge that enables
                  actin fibre to exhibit torsional flexibility. Thus, one mechanical property of the fibre
                  is controlled at the molecular length scale, by primary (covalent) bonds.
                  The ability of actin fibre to maintain rigidity and strength under tension (necessary in
                  its load-transmitting roles) depends on the forces that bind G-actin into aggregates.
                  Thus, some mechanical properties of  the fibre are controlled at a supramolecular
                  length scale, by secondary (non-covalent) bonds.
                  Because the  intermolecular secondary  bonds  are  weaker  than  the  intramolecular
                  primary bonds, the fibre can fail without destroying the integrity of the constituent
                  molecules. The molecules are therefore immediately available for repairing the fibre.
                  A hierarchical structure can therefore enable different mechanical properties to be
               selectively and independently tailored by  different aspects of  that structure. While it
               is  possible  in  the  case  of  actin  to  identify  specific structural features  and  bonding
                types with specific mechanical properties, there are many hierarchical biological fibres
                for  which  the  corresponding  associations  are  more  complex  and  have  yet  to  be
               determined fully. As  an  example, let  us  consider  spider dragline  silk  (strictly:  silk
                from the major ampullate glands of  spiders). The unique combination of  mechanical
                properties exhibited by  this  fibre can be  described qualitatively in  terms of  a multi-
                phase microstructure (Viney, 2000). Progress has also been made towards developing
                quantitative links between microstructure and some individual mechanical properties of
                this material (Termonia, 2000). However, several microstructure-property  relationships
                for silk - including the nature of  the flaws that appear to be ultimately responsible for
                fracture (PCrez-Rigueiro et al., 1998) - remain to be resolved.
                  If  we know how the hierarchical microstructure of  a material is assembled, we are
                in a good position to understand how that microstructure will be deconstructed as the
                material fails. Which bonds are most susceptible to being disrupted will depend on how
                the sample is loaded (in tension, compression, bending or torsion); we have noted in
                the case of  actin how different microstructural features confer resistance to failure in
                different loading geometries.

               A Hierarchical Structure Optimises Toughness

                  In  courses on materials engineering, we learn almost from day one that toughness
                requires afine microstructure, with no mention of hierarchy. Here we consider whether
                a  hierarchical  microstructure  confers  any  toughening  benefits  additional  to  those
                associated with a fine microstructure.
                  The need for a fine microstructure is usually encountered and justified in the context
                of the Griffith formula, which quantifies the stress CT  needed to propagate a pre-existing
                    2 (y’
                crack through a metal or ceramic material (Cottrell, 1975):



                where c is the length of a surface crack (or half the length of an internal crack), E is
                Young’s modulus, and y  is the energy per unit area of new surface created by the crack.
                According to Eq.  1, the breaking strength remains high  if  crack lengths can be kept
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