Page 263 - Engineered Interfaces in Fiber Reinforced Composites

244 Engineered interfaces in fiber reinforced composites

debonding frictional work. The pull-out energy (Cottrell, 1964; Kelly, 1970) is the
work done against sliding friction in extracting the broken fiber. Based on the work
done by the frictional shear stress, zf which is assumed to be constant over a pull-out
distance, e,,, the fiber pull-out toughness, R,,, is given by

Since fiber pull-out length, e,,, is difficult to measure with any accuracy from the
fracture surface of composite specimens containing high &, R,, is often expressed in
terms of the inherent properties of the composite constituents. There are three cases
considered here depending on the fiber length relative to the critical transfer length.
(i) If the fiber length is less than the critical transfer length, e < e,, all the
debonded fibers are pulled out. Assuming the pull-out length, epo, varies between 0
and el2 with a mean value of &/4 (Kelly and Tyson, 1965; Cooper and Kelly, 1969),
R,, becomes

(ii) R,, is maximum when e = e,,

In Eq. (6.8) an upper bound estimate of zf is made by the apparent bond strength z,
for the critical transfer length, i.e., e, x ord/2zf, based on the early work of Kelly
and Tyson (1965). Therefore, R,, is shown directly proportional to the critical
transfer length.
(iii) If the composite contains fibers of lengths greater than the critical transfer
length, e > e,, then the fraction of fibers that can be pulled out is &/C on the basis of
normal probability, and e,, ranges from 0 to &/2. Thus, R,, becomes

Graphical presentation of Eqs. (6.7H6.9) are given in Fig. 6.2 where the fiber pull-
out toughness, R,, is plotted as a function of fiber length, e. It is worth noting that
for most polymer matrix composites reinforced with carbon, glass and aramid fibers,
the estimated fiber pull-out toughness values are approximately the same as the
measured composite fracture toughness (Harris et al., 1971, 1975; Atkins, 1975;
Gershon and Marom, 1975; Kim and Mai, 1991a, b).