Page 146 - Fiber Fracture

STRENGTH OF GLASS FIBERS 131

BASIC CONCEPTS

Flaws and Cracks

A flaw is an extrinsic defect in a glass. Common examples of (3-dimensional)
flaws are scratches, indents, inclusions, devitrified regions, and bubbles. Sometimes,
one speaks of ‘intrinsic flaws’ when refemng to the intrinsic inhomogeneities present
in a glass. Examples of intrinsic inhomogeneities are point defects, structural inho-
mogeneities caused by frozen-in density and composition fluctuations, and nanoscale
roughness on glass surface (Gupta et al., 2000). In this paper, the term flaw is used to
indicate extrinsic flaws.
A crack is a 2-dimensional flaw; an area across which the bonds are broken. The
boundary of this area is called the crack tip. The curvature (normal to the plane of the
crack) at the tip is assumed to be infinitely sharp in the continuum models but is of
atomistic dimensions in real materials. The detailed atomistic structure of a crack tip
is unresolved at present (Lawn, 1993). In silicate glasses, a crack tip has a radius of
curvature on the order of 0.3 nm which is approximately the size of a single siloxane
bridge [E Si-0-Si GI.
Under the application of a tensile stress, 3-dimensional flaws (e.g., pores and
inclusions) cannot grow. Only cracks can grow under tensile stress. Sometimes one
speaks of the ‘growth of a flaw’ (not a crack), implying the growth of a microcrack
nucleated at or near that flaw. It is clear that, when a material does not have a
pre-existing crack, a crack must nucleate at some moment of time prior to fracture.

Pristine and Non-Pristine Fibers

Fibers without flaws are called pristine or ‘flawless’. Fibers with flaws are called non-
pristine. Routinely manufactured fibers are generally non-pristine. Measuring strength
of pristine fibers is tedious. It requires a careful preparation of the starting materials
(melt in the case of E-glass and preform in the case of silica fibers) to ensure that they
are free of flaws, careful forming of fibers in ultra-clean environments, capturing bare
fiber samples before they come in contact with any other surface (such as the coating
applicator or the collection drum), and testing of a large number of small fiber lengths
immediately after capture with minimum additional handling. Even after all these
precautions, it is often not easy to establish whether pristine fiber strengths are being
measured in an experiment. This is usually accomplished by accumulating data over
many expcrirnents as a function of several experimental parameters and making sure that
the measured strengths are amongst the highest ones measured and are reproducible.

Statistics of Measured Strengths

Measured strengths of identically prepared glass fibers always show a distribution.
Although without any fundamental basis, it is customary to plot the measured strength
distribution on a Weibull plot where the ordinate is ln(ln [ 1/(1 - P)]) and the abscissa is
In S. Here P(S) is the cumulative probability of failure for strengths less than or equal to