Page 60 - Fiber Fracture

MODELS OF FIBRE FRACTURE 45

macromolecules with a skin-core distribution of ends similar to the model; the skin will
exhibit a more continuous structural integrity in the fibre direction than the core, and the
core will fail more readily by transverse crack propagation. Panar et al. (1983) proposed
a similar model. Both emphasise the structural features as observed on etched specimens
of PPTA fibres, but do not provide a quantitative interpretation of the tensile properties
of these fibres.
Yoon (1990) developed a model for fibre strength similar in reasoning to that of a
model for the tensile strength of short fibre-reinforced composites due to Fukuda and
Chou (1982). Both the chain length distribution and chain orientation effects of the fibre
are included jointly with the molecular weight dependence. The model is based on the
consideration that the macroscopic load is transferred along the fibre sample mainly
by interchain interaction, and the fibre breakage occurs when the interchain interaction
force exceeds a critical value. Then the chains are separated and fibre failure is caused
by the rapid accumulation of the interchain voids, resulting in the observed fibrillar
fracture. The chain ends act as sites for stress concentration and the molecular weight
dependence of the tensile stress is due to the relation between the number of chain ends
and the molecular weight. Good agreement with experimental results was obtained for
wholly aromatic polyesters.
Another model, along the same line of reasoning, was proposed by NorthoIt and van
der Hout (1985) and Baltussen and Northolt (1996) based on observations by X-ray and
electron diffraction. The fibre is considered as being a build-up of a parallel array of
identical fibrils. Each fibril consist of a series of crystallites arranged end to end, and
the polymer chains run through these crystallites parallel to their symmetry axes, which
follow an orientation distribution in relation to the fibre axis (Fig. 7d). The parameters of
the model are the chain orientation distribution, the average modulus for shear between
the chains, the chain modulus and a simple yield condition based on the critical resolved
shear stress. This model provides expressions for the compliance, the elastic tensile
curve and the yield stress of the para-aromatic polyamide and other high-modulus fibres.
Recently, Picken and Northolt have extended the model to predict fibre fracture stress
(Picken and Northolt, 1999), as a function of the degree of orientational order, making
use of an expression similar to the Tsai-Hill criterion for the strength of uniaxial
composites:

where a(@) is the rupture stress, 8 the angle between the chain segment and the fibre
axis, and ZS, a~ an UT are respectively the shear stress, the longitudinal stress and the
transverse stress of the molecular composite. With this model, the authors find that it is
possible to explain the effect of molecular orientation in the strength of as-spun fibre
and suggest that for highly oriented aramid fibres, the transverse term can be ignored
and that OL is about 6 GPa and ts about 0.3 GPa.
An alternative theoretical approach to exploring the limits of the tensile stress
of fibres with perfectly oriented and packed polymer molecules was developed by
Termonia et al. (1986; Termonia, 2000). The model bypasses details of the deformation
on an atomistic scale and focuses instead on a length scale of the order of the distance