Page 287 - Fiber Fracture

270 J.W.S. Hearle

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Fig. 4. Staudinger’s (1933) view of the continuous structure of an oriented polymer.

For finite molecular-weight polymer, a model drawn by Staudinger (1933), remains
valid as an ideal structure (Fig. 4). This brings in the first factor to reduce stiffness and
strength, slippage at the ends of molecules. This is a feature extensively studied at the
larger scale of whole fibres for short-fibre composites and textiles. Strength is reduced
by a slip factor, which takes account of the loss of tension from the free ends of the
fibres or molecules up to the limiting state in the middle of components, where they are
fully gripped. The slip factor has a greater effect when the bonding between components
is weak and when the aspect ratio of the components is small. A simple presentation of
the theory by Hearle (I 982, p. 103) indicated that the stress at a given strain would be
reduced by a slip factor S given by:
s = (1 - &K/#m) (1)
where K is the ratio of shear-bonding stress between molecules to tensile stress in
molecules, p is the aspect ratio of a polymer repeat unit and N is the degree of
polymerisation. With the high molecular weights used in HM-HT fibres this effect will
be small.
Two other factors, which influence stiffness and strength, are the degree of orientation
of molecules and disorder in molecular packing. Although mean orientation angles can
be determined, the detail of the departures from the ideal structure of Fig. 4 is an area
of uncertainty. Diagrams drawn by different researchers (Fig. 5) give different views
of structure. The pictures, which are attempts at a two-dimensional representation of
what the stmcture might be despite the lack of adequate experimental evidence, show up
contrasting ideas. Fig. 5a-c suggest regions where the crystal lattice is perfect, separated
axially and transversely, by zones of disorder. Fig. 5d-f are para-crystalline models with
a low level of uniform disorder. Fig. 5g suggests a distribution of local defects in the
crystal lattice. My own view is that disorder might be due to defects associated in larger
groups than indicated in Fig. 5a. What is needed to solve these problems is a large-scale
exercise using all available methods of experimental structural analysis linked to 3-D
computer modelling of putative structures. Fig. 5h represents a larger-scale, regular
disorientation in Kevlar, which shows up as banding in optical microscopy between
crossed polarisers.
As a first approximation, orientation reduces stress by a factor equal to the mean
value of cos40, where 8 is the angle between the polymer axis and the fibre axis. There