Page 151 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 4. Micromechanics of srress transfer 133

embedded fiber length, L. The friction stress component is directly proportional to
(F - ct), and is also controlled by I (or, in turn by the coefficient of friction, p).
The partial debond stress, c:, calculated based on Eq. (4.100) using the properties
given in Table 4.1 and the interface properties in Table 4.3 are plotted as a function
of debond length, l, in Figs. 4.23 and 4.24, respectively, for carbon fiber-epoxy
matrix and untreated Sic fiber-glass matrix composites. These two composite
systems are considered to be typical of those with adhesion mechanisms at the fiber-
matrix interface which are chemical and frictional in nature, respectively. It is clearly
shown that the crack tip debond stress, oe, decreases toward zero depending on the
fiber embedded length L. For short L, it decreases from the beginning whereas for
long L it is initially constant and decreases toward zero as increases. In contrast,
the friction stress component always increases with increasing .t for a given L, the
increase being non-linear due to Poisson contraction of the fiber in the debonded
region. These two stress components balance each other to determine the
instantaneous values of n:. It can thus be summarized that the variation of the
partial debond stress with respect to the debond length during the fiber debond
process is largely controlled by the embedded fiber length given the properties of the
composite constituents. Figs. 4.23 and 4.24 also indicate that when the embedded
fiber is sufficiently long, the frictional properties at the debonded interface relative to
the interface fracture toughness, Gic, (or interface shear bond strength, Zb) in the
bonded region are a key factor that determines the stability of the debond process.
The interfacial property-dependent debonding process is reflected by the amount of
stress drop (i.e. from the maximum debond stress, r~:, to a lower value ofr,
corresponding to the initial frictional pull-out at C = L, which is commensurate with
the load drop frequently observed in pull-out stress versus displacement curves in
experiments (Fig. 3.7).

Fig. 4.23. Plot of partial debond stress, oi, as a function of debond length, e, for a carbon fiber-epoxy
matrix composite. After Kim et al. (1992).