Page 172 - Engineered Interfaces in Fiber Reinforced Composites

154 Engineered interfaces in Jiber reinforced composites

w[l - exp(-fi)]
Ofr = a
1 - w[l - exp(-fi)]
E a[exp(fi) - I] . (4.138)

One can easily note that Eq. (4.138) is similar to the solution given by Eq.
(4.126), which is derived from the assumption of a constant friction and complete
neglect of the Poisson expansion. The solution for zmax, which is the shortest
bond length required to maintain a stable debonding process, is obtained from
Eq. (4.137)

(4.139)

4.4.3. Comparisons between fiber pull-out and fiber push-out

When comparing with the solution given in Eq. (4.100) for partial debond stress
in fiber pull-out, it is noted that Eq. (4.133) is similar in that it is composed of two
stress components: a crack tip debond stress, at, which is a function of the
interfacial fracture toughness, Gi,, and the debond length, I, relative to L; a friction
stress component which is proportional to (a + .e) and is controlled by 1. There are
also differences between fiber pull-out and fiber push-out particularly in the
magnitude of debond stresses. To illustrate these functional similarities and
differences in the failure processes between the two loading geometry, specific
results are calculated (Zhou et al., 1992b) for the composite systems studied in the
previous sections. From the plots of partial debond stress, a:, as a function of
debond length, I, as shown in Fig. 4.38, the rate of stress increase (or decrease) is
found to be slightly larger in fiber push-out than in fiber pull-out, although the
functional relationship between 01; and I is basically similar for a given embedded
fiber length, L. Therefore, for a given L, larger stresses 00 and 0; are required for
debond crack initiation and propagation in fiber push-out than in fiber pull-out as
shown in Fig. 4.39.
All these results are apparently associated with the difference in the friction stress
component in the debonded region. In fiber push-out, the Poisson expansion of the
fiber under axial compression generates radial compressive stresses across the
interface, while the fiber is contracted radially in fiber pull-out. These stresses
balance the existing residual clamping stress, 40, controlling further debond
propagation. This conclusion is further manifested in Fig. 4.40 where the difference
in IFSS distribution is clearly illustrated, in the debonded region in particular,
between the two loading geometry.
To evaluate the stability of the debond process, the instability parameter, zmax, is
compared. zmax values calculated based on Eqs. (4.104) and (4.139) respectively for
fiber pull-out and fiber push-out give z,,, = 6.5, 6.2 mm for coated steel wire-epoxy
matrix and z,,, = 0.5, 0.49 mm for the untreated Sic-fiber-glass matrix composite