Page 58 - Fiber Fracture

MODELS OF FIBRE FRACTURE 43

chain folds decreases and the structure is more oriented, approaching that of a perfect
crystal. For example, in ultra-high molecular weight polyethylene (UHMWE), with a
drawn ratio of 247, the fibre elastic modulus approached a value of 220 GPa (Kanamoto
et al., 1983), which is close to the theoretical modulus of a perfect crystal (240-290
GPa) .
According to all observations it has to be expected that the ultimate properties of
ultra-highly oriented fibres should depend on the properties of the crystalline blocks and
on the way these blocks are linked together. Starting from this idea, theJibriZ model has
been used to predict the mechanical behaviour; this is one of the oldest models and still
enjoys considerable popularity. Many modifications and improvements have been made
since then to consider imperfections, degree of crystallinity, molecular weight and so
on. All these models give reasonable predictions of Young’s modulus, the shape of the
stress-strain curve, and to some extent the yield stress. On the contrary, little progress
has been made in predicting the ultimate tensile stress, most probably because fracture
models rely on imperfections and not enough information is yet available to devise a
general enough model.
Peterlin (1981) made interesting comments on the rupture of highly oriented aliphatic
fibres and suggested a phenomenological model of rupture, due to crack nucleation and
coalescence. The microcracks seem to form primarily at defects of the microfibrilar
structure, particularly at the ends of microfibrils (see Fig. 7a). In these places the
connection between crystallites by taut tie molecules is poor and these regions favour
microcrack nucleation much earlier than the amorphous layers inside the microfibrils.
The stress concentration resulting from the opening of these microcracks may rupture
also some of the adjacent microfibrils. This nucleation and subsequent lateral growth
of the microcrack ruptures the taut tie molecules in its path. Interestingly, the ruptured
molecules yield free radicals which can be monitored by electron spin resonance. The
failure of the fibre seems to occur when the ratio between the average distance and the
diameter of the microcracks reaches a value of about 3. This criterion was checked in
nylon, polyethylene and polypropylene.
Morgan et al. (1983) also made very interesting phenomenological comments on the
rupture of aromttic fibres, particularly poly@-Phenylene Terephthalamide) (PPTA), the
basis of Kevlar . The deformation and failure processes, together with the structure of
the fibre, were commented in the light of fracture topography. The authors conclude
that the chain-end concentration and its distribution within the fibre are the primary
structural factors affecting the deformation and failure of PPTA fibres, and propose
the following model, illustrated in Fig. 7b. The rod-like PPTA macromolecules are
assumed to be aligned parallel to the fibre axis. The chain ends are arranged essentially
randomly relative to one another but become progressively more clustered in the fibre
interior, resulting in periodic transverse weak planes every 200-250 nm, approximately.
The chain ends cluster in the vicinity of these weak planes. The fibre core consists of
cylindrical crystallites, of about 60 nm in diameter, aligned in the fibre direction. The
fibre exterior is assumed to be less crystalline than the interior. The chain-end model,
although it does not provide quantitative results for the tensile stress, is consistent
with the observed deformation and failure processes of Kevlar fibres. Fig. 7c illustrates
the path of a crack that transverses the molecular chain ends of an array of aligned