Page 152 - Engineered Interfaces in Fiber Reinforced Composites

134 Engineered interfaces in fiber reinforced composites

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Fig. 4.24. Plot of partial debond stress, uz, as a function of debond length, e, for untreated Sic fiber-glass
matrix composite. After Kim et al. (1991).

In light of the foregoing discussion concerning the functional partitioning of the
partial debond stress, the characteristic debond stresses can be evaluated. The initial
debond stress, ao, is obtained for an infinitesimal debond length where the frictional
stress component is zero, i.e.,

60 = aele,o . (4.101)
The maximal debond stress, 6:. is determined immediately before the load
instability (Karbhari and Wilkins, 1990; Kim et al., 1991) of the partial debond
stress, a:, when the debond length becomes t = L - zmax:

% oe + (8 - at){ 1 - exp[-A(L - ~max)]} . (4.102)

Details of the instability conditions of the debond process and Zmax are discussed in
Section 4.3.4. Further, the solution for the initial frictional pull-out stress, ofr. upon
complete debonding is determined when the debond length, f?, reaches the embedded
length, L, and the crack tip debond stress, at, is zero:

(4.103)

In Eq. (4.103), it is assumed that the influence of the instantaneous fiber
displacement relative to the matrix due to the sudden load drop after instability is
negligible.