Page 355 - Fiber Fracture

FRACTURE OF COMMON TEXTILE FIBRES 337

WOOL AND HAIR

Structure and Stress-Strain Curve

Wool and hair have the most complex structures of any textile fibres. In the paper
by Viney, fig. 1 shows how keratin proteins, of which there are more than one
type, all having a complicated sequence of amino acids, assemble into intermediate
filaments (IFs or microfibrils). But, as shown in Fig. 5a, this is only one part of
the story. The microfibrils are embedded in a matrix, as shown in Fig. 5b. The
keratin-associated proteins of the matrix contain substantial amounts or cystine, which
cross-links molecules by -CHz-S-S-CH*- groups. Furthermore, terminal domains
(tails) of the IFs, which also contain cystine, project into the matrix and join the
cross-linked network. At a coarser scale, as indicated in Fig. 5c, wool is composed of
cells, which are bonded together by the cell membrane complex (CMC), which is rich
in lipids. As a whole, wool has a multi-component form, which consists of para-cortex,
ortho-cortex, meso-cortex (not shown in Fig. 5a), and a multi-layer cuticle. In the para-
and meso-cortex the fibril-matrix is a parallel assembly and the macrofibrils, if they
are present, run into one another, but in the ortho-cortex the fibrils are assembled as
helically twisted macrofibrils, which are clearly apparent in cross-sections.
A review by Hcarle (2000) of three current theories concludes that the stress-strain
curve can be essentially explained in terms of a fibril-matrix composite, which is
referred to as the Chapman/Hearle (C/H) model. In a total model, account should be
taken of secondary influences of other structural features. The stress-strain curve of
wet wool, Fig. 6a, shows initial stiffness up to 2% extension, a yield region (2% to
30%), subsequent stiffening in the post-yield region (30 to 50%) and breakage at 50%
extension. This is not unusual for polymers, but typically the yield extension would not
be recovered on reducing the stress. In wool and hair, there is complete recovery up to
the end of the yield region, and almost complete recovery from the post-yield region,
but along lines that are different to the extension curve.
The model of the mechanics by Chapman (1969) is based on the two-phase model
of microfibrils in a matrix, originally proposed by Feughelman (1959) and illustrated by
the internal structure of the macrofibril in Fig. 5. In the unstrained state the IFs have a
crystal lattice with the molecules following a modified form of Pauling’s a-helix, with
intra-molecular hydrogen bonding, but under tension this transforms to the extended chain
b-lattice with inter-molecular bonding. The elongation in the ideal structures is 120%, but
in the more complicated IFs of wool is probably 80%. The stress-strain curve assumed
for the microfibrils is shown by the a-fi line in Fig. 6b, where Chapman assumes that the
transition is governed by acritical stress, c, and an equilibrium stress, eq. The matrix of the
composite structure is treated as a fairly highly cross-linked rubber. Experiments reported
by Chapman (1970) on chemically treated wool, which disrupts the structure and leads to
supercontraction, indicate that the matrix has the stress-strain curve shown as M in Fig. 6b.
This curve follows the theoretical rubber elasticity curve, using the inverse Langevin
function form with two free links between network junctions, up to 30% extension. The
rubber elasticity curve would be asymptotic to infinite stress at 40% extension, but beyond
30% there is rupture of cystine cross-links, which leads to a turnover in the curve.