Page 61 - Fiber Fracture

46 M. Elices and J. Llorca

Fig. 8. Termonia model of highly oriented fibre.

between entanglements. No defects are considered other than chain ends resulting from
a finite molecular weight. It is based on the kinetic theory of fracture, in which the bond
ruptures are simulated by a Monte-Carlo process on a three-dimensional array of nodes,
as shown in Fig. 8. The nodes in the figure represent the elementary repetition units of
the polymer chains. In the longitudinal direction, the elastic constant K1 accounts for the
primary bonds (Le. C-C bonds in polyethylene). In the transverse directions, the elastic
constant K2 accounts for the secondary bonds (i.e. hydrogen bonds in nylon or van
der Waals forces in polyethylene). Results agree quite well with experimental measures
of strength of highly oriented fibres. In polyethylene fibres of low molecular weight,
intermolecular slippage involving rupture of secondary bonds occurs in preference to
chain fracture, yielding tensile curves that at the end are bell-shaped. At high molecular
weights primary as well as secondary bond rupture occurs, yielding tensile curves with
brittle fracture. In PPTA fibres, the model predicts that fracture is initiated by the
breaking of a small number of primary bonds and not by secondary hydrogen-bond
failure; this leads to a brittle fracture of the fibre. This simple model does not predict a
fibrillated fracture, as observed in PPTA, PBO and PBT fibres, but this behaviour can
be implemented by considering a bundle of fibrils, each one modelled with the simple
model, joined by weaker secondary bonds. More details about this model are given in
the paper by Termonia (this volume).

Heterogeneous Fibres

Composite Fibres

The simplest composite fibres are the B and Sic monofilaments manufactured by chem-
ical vapour deposition of boron halide or silane gases onto a heated substrate, normally
W or C. Their diameter is in the range of 50-150 km, and they exhibit a concentric
microstructure in which four different regions can be distinguished, the composition and
thickness of each one depending on the actual fibre characteristics (Fig. 9). A thin (1-2
km) layer of pyrolytic graphite is deposited onto the C core before the deposition of