Page 363 - Fiber Fracture

FRACTURE OF COMMON TEXTILE FIBRES 345

In the theoretical model described above, the drawing and locking conditions are not
directly taken into account, but are implicit in that the fibre is regarded as fully drawn.
The tie-molecules are locked into rigid crystallites. At low stress, there is no cause for
crystal yielding to occur. At high stress, the tensions in the tie-molecules reach a level
at which they break. There is a sequence of chain breakage, which starts with those that
are most strained and continues to the least strained.
So far no account has been taken of stress distributions. The experimental evidence,
described in the 3rd paper in this volume (fig. 3), is that there is ductile fracture with a
crack which progressively opens into a V-notch until catastrophic failure occurs when
the notch covers about half the fibre cross-section. If there is a defect, usually on the
surface but sometimes internally (when the V-notch becomes a double cone), the stress
concentration will lead to the start of the rupture, although it has a negligible effect on
the mean fibre stress at which this occurs. If there is no defect, the evidence is that an
initial crack will form by a coalescence of voids that form under high stress. Variation
in the degree of orientation across a fibre may well play a part. If the skin of the fibre is
more highly oriented, it will reach its limiting extension before the core.
In contrast to brittle fracture, the crack does not grow catastrophically, but increases
steadily in size as extension continues. Material on the other side from the crack extends
by further yielding, which appears to be spread over lengths of several fibre diameters
in opposite directions along the fibre. The link between the low stress material in line
with the crack and the extended material on the other side is by a band of plastic shear
deformation.
A quantitative explanation of the effect requires an advance in fracture mechanics.
Griffiths' theory explains fracture in a perfectly elastic material as dependent on crack
depth. This has been extended to cover the situation where there is a small zone of
plastic deformation ahead of the crack. The problem is more difficult when the plastic
deformation is large compared to the crack size, and, as far as I know, there has been
no treatment of the situation when plastic deformation covers the whole thickness of the
specimen over an appreciable length. Any analysis would also require an understanding
of the transition in material from crystallinc yiclding to locking and chain breakage and
the form of the local stress-strain curve beyond that which is measured.
The above discussion relates to tests at or near room temperature. There is an
interesting paper by Moseley (1963) on the effect of internal structure and local defects
on fibre strength, which reports experiments at different temperatures on nylon and
polyester. When a 1 mil (25 Fm) nick was made in an 8 mil (200 Fm) nylon monofil,
the strength of 4 g/den at 2 1 "C was unchanged, but the strength at - 196°C dropped
from 6 g/den to 3 g/den. With a 5 mil (125 IJ-m) nick, which is more than half the fibre
thickness, the strength at both 21 "C and - 196°C fell to 1.5 g/den. In another experiment
a single polyester filament was repeatedly hit by an electric typewriter key. The strength
at -196°C decreased with the number of hits, but that at 21°C was unchanged. Moseley
concluded that at relatively high temperatures, strength depended on the whole internal
fibre structure and local defects were of negligible importance, whereas below - 100°C
local defects were the dominant factor. This conclusion was supported by the different
effects of test length on the break statistics at low and higher temperatures.