Page 52 - Fiber Fracture

MODELS OF FIRRE FRACTURE 37

Silica glass fibres are a further example of simple atomistic computations. An early
attempt, following the technique of counting broken bonds, is due to NBray-Szabb
and Ladik (1960); using a Morse potential, the breaking force for a Si-0 bond was
estimated as 2 x N and the average member of bonds per m2 12.5 x lo'*. Hence,
the theoretical tensile stress for a perfect fibre should be 25 GPa. The Orowan-
Polanyi approximation (Eq. 1) gives 16 GPa. Experimental values of the same order of
magnitude, 15 GPa, were measured in silica fibres at 4.2 K, and 10 GPa in argon at
room temperature (Proctor et al., 1967). Room temperature values for silica, S-glass and
E-glass fibres are not above 5 GPa (see paper by Gupta, this volume). These values are
in good agreement with predictions based on molecular dynamics, yielding a stress of
6.7 GPa at 625 K for soda-lime glass (Soules and Busbey, 1983).

CONTINUUM APPROACH

High-performance fibres usually have diameters ranging from 10 pm to 150 wm
and are amenable to be modeled using a continuum approach. Unfortunately, fracture
strength does not depend only on bulk properties and it is very sensitive to the type
and shape of defects. Pertinent information on such microscopic defects is crucial to an
understanding and modelling of fracture behaviour at a continuum level.
This section begins with the simplest type of fibres: homogeneous fibres. Among
them, those exhibiting a linear elastic and brittle behaviour are the easiest to model,
and fracture stresses can he predicted using the well established techniques of linear
elastic fracture mechanics (LEFM). Ductile fracture is a more involved problem and
some aspects of fibre failure using the techniques of elasto-plastic fracture mechanics
(EPFM) are briefly mentioned. Fracture of highly oriented polymer fibres deserves a
separate treatment because, although homogeneous, they have a fibrillar microstructure
and display characteristic fracture behaviour.
Fracture of heterogeneous fibres is a more complex problem and the few available
models are based on linear elastic fracture mechanics concepts and thus restricted to
this area. An outstanding aspect of heterogeneous fibre failures is the role of interfaces:
neither strong or very weak interfaces give optimum results.
The section ends with some comments on fracture of biological fibres. These fibres
are characterised by a hierarchical structural design with length scales ranging from
molecular to macroscopic. Clearly, detailed quantitative models for prediction of tensile
strength of biological fibres are far from being available. However, some trends in
connection with cellulose and keratin fibres are briefly discussed.

Homogeneous Fibres

Brittle Behaviour

Brittle failure of homogeneous fibres can be modelled, at a continuum level, using the
tools of linear elastic fracture mechanics (LEFM) because usually the main hypotheses
on which LEFM is based are satisfied when the rupture of a fibre is brittle, Le.: the