Page 157 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 4. Micromechanics of stress transfer 139

(iii) Thirdly, combining Eqs. (4.1 10) and (4.11 1) allows 2 and 8 (and thus p and qo
from Eqs. (4.23) and (4.24)) to be determined. Alternatively, the asymptotic
debond stress, 5, can be directly estimated at a long embedded length through
linear regression analysis of the maximum debond stress, 0;. Once ;2. and are
known, Eq. (4.102) may be used to evaluate the optimum value of Gi, (and also
for zmax) that would give the best fit to the 0; versus L experimental results. In this
procedure theoretical values for the maximum debond stress, o:, have to be
obtained at instability. Alternatively, data for the initial debond stress, GO, versus
L, if available from experiments, can be directly evaluated to determine Gi, based
on the debond criterion of Eq. (4.99) for infinitesimal debond length. Application
of this procedure to obtain Gic, 11 and 40 have been demonstrated in fiber pull-out
for several fiber composites materials (Kim et al., 1992, Zhou et al., 1993).

Having determined the relevant interface properties (Table 4.3), the maximal
debond stress, a:, and the initial frictional pull-out stress, ofr, are compared with
experimental data in Figs. 4.26-4.28 for three different composite systems of carbon
fiber-epoxy matrix, steel fiber-epoxy matrix and Sic fiber-glass matrix. In general,
there is very good agreement between theories and experiments over the whole range
of the embedded fiber length, L, for all the composite systems considered. A new
methodology has also been proposed recently by Zhou et al. (1994) to determine
systematically the longest embedded fiber length for instability, zmax, without
iteration and curve fitting of Eq. (4.102).

4.3.6. Multiple~fiber composite model

From the review of the theoretical studies of the fiber pull-out test as discussed in
Section 4.3.1, it is identified that most micromechanics theories are developed based
on a shear-lag model of single fiber composites where the cylindrical surface of the
matrix is invariably assumed to be stress free. Although this assumption is required
to obtain the final solutions in closed form for the stress distributions it often leads
to an unacceptably high applied stress required to initiate/propagate interface
debonding when the radial dimension of the matrix is similar to that of the fiber (Le.
for a high fiber volume fraction, F), This in turn implies that the application of the
conventional models to practical composites is limited to those with a very small Vi
where any effects of interactions between neighboring fibers are completely
neglected. Therefore, a three-cylinder composite model is developed (Kim et al.,
1994b) to simulate the response of practical composites of large vf and thus to
accommodate the limitation of the shear-lag model of single fiber microcomposite
test properly. Both the micromechanics analysis and the FE method are employed
in parallel for fully bonded interface to validate the results obtained from each
model.
To analyze the stress transfer in the fiber pull-out test of a multiple fiber
composite, the specimen is treated as a three-cylinder composite (Zhou and Mai,
1992) where a fiber is located at the center of a coaxial shell of the matrix, which, in
turn, is surrounded by a trans-isotropic composite medium with an outer radius B,