Page 57 - Fiber Fracture

42 M. Elices and J. Llorca

Fracture of thin metallic wires during cold drawing is also worth mentioning here.
Wire breakage in the industrial practice of wire drawing is often due to the presence
of non-metallic inclusions and a severe plastic deformation; the wire is pulled through
the dies and highly stressed, withstanding large plastic deformations. Voids, nucleated
at the interfaces between inclusions and matrix, generate cracks that eventually lead to
fracture. A physical insight into void initiation during wire drawing of pearlitic steels,
an important part of commercial metallic fibres, appears, for example, in Nam and Bae
(1995). At high strains, globular cementite particles whose size is much larger than the
thickness of cementite lamella, provide sites for void formation due to the enhanced
stress concentration. These observations may be helpful when modelling fibre fracture
at the mesolevel. Numerical predictions of the rupture stress and initiation sites can
be obtained using finite element methods (EM), where elasto-plastic behaviour of
elements is complemented by a fracture criterion. In general, these fracture criteria have
the following functional form:
SEf
F(deformation history) dE = C

where E is the effective strain, Ef the effective fracture strain and C is a parameter,
usually known as a damage parameter, obtained experimentally. Different forms of the
integrand are summarised in Doege et al. (2000). Yoshida, in his paper in this volume,
summarises the E modelling of a superfine wire with a cylindrical inclusion placed on
the wire axis.

Highly Oriented Polymer Fibres

Fracture of highly oriented polymer fibres during tensile loading may exhibit different
forms: brittle fracture, usually due to transverse crack propagation, ductile fracture, as
a consequence of plastic flow after necking, or fibrous axial splitting, where cracking
or splitting occurs along planes close to the fibre axis. Modelling the first two types of
fracture can be done according to the ideas previously commented, although the strong
transverse anisotropy poses additional difficulties. Axial splitting is typical of polymer
fibres although it may also happen in severely cold drawn metallic fibres.
Phenomenological aspects of fibre fracture have been discussed elsewhere (see
Kausch, 1987 for example). It suffices to remind that the details of the failure process are
highly complex and depend upon many factors such as polymer structure, environment,
type of loading and time. Molecular fracture does not occur to the same extent in all
polymer fibres and the micromechanisms differ in different types of fibres.
The structure of highly oriented polymer fibres is characterised by a fibrillar
microstructure; fibrils are clusters of partially aligned molecules. Fibril diameters range
from 1 to 100 nm. Forces betwccn fibrils are weak, so fibrils can be observed in
fibre fractures. Micrujbn'ls, the most elementary fibrils, consist of alternating layers
or ordered (crystalline) and disordered (amorphous) regions along the fibril length. In
poorly oriented fibres the amorphous regions within the microfibrils still contain more
than 90% of non-extended chain segments which support most of the load (Kausch,
1987). This is different in ultra-highly oriented fibres where the number of non-extended