Page 272 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 6. Interface mechanics and fracture toughness theories 253

of the contributions from fiber-matrix interfacial debonding, Rd of Eq. (6.1), post-
debonding friction, Rdf of Eq. (6.4), fiber pull-out, R,, of Eq. (64, and matrix
fracture, R,, (Lauke et al., 1985), in much the same manner as for continuous
unidirectional fiber composites and is given by Eq. (6.10)

CO
Rt = (Rd +Rdf)e+RPo + (1 - &)R, , (6.16)

where co is the size of the damage zone which corresponds to a critical distance from
the tip of the main crack where the local stress is just sufficient to initiate an interface
crack. A factor co/C is applied to the Rd and Rdf terms to account for the localized
process of intensive energy dissipation by interface failure at the fiber ends. The
contribution of fiber fracture has not been specifically considered here because of the
assumption of subcritical fiber length, i.e., C < e,.
The matrix material becomes brittle under dynamic loading or at low temper-
atures, in which case the fracture process is dominated by interface failures, such as
debonding, post-debonding friction and fiber pull-out. The implication is that the
fracture toughness value is at its maximum for a relatively small fi when increasing
number of effective fiber ends for interface failure prevails. On the contrary, with
larger V,, this trend is dominated by the decreasing length of interface debond and
pull-out, resulting in a smaller toughness contribution. The fracture work of brittle
matrix gives only an insignificant contribution to Rt. In contrast, with ductile matrix
composites and under static loading conditions intensive plastic flow occurs locally
and the matrix toughness term in Eq. (6.16) can be replaced by the matrix shear
work, R,,, in Eq. (6.13). In this case, Rt is dominated mainly by the work of matrix
fracture decreasing monotonously with fiber volume fraction, fi, and the contri-
bution of fiber pull-out work is negligible because of the plastic flow and necking of
the matrix material. Yielding occurs preferentially near the fiber ends with high
stress concentrations. Fig. 6.10 shows schematically the dependence of fracture
toughness contributions on V, at different loading rates (Lauke et al., 1985).
Mai (1985) has also given a review of the fracture mechanisms in cementitious
fiber composites. The total fracture toughness, Rt, is given by the sum of the work
dissipation due to fiber pull-out, fiber and matrix fractures, fiber-matrix interfacial
debonding and stress redistribution, i.e.,

(6.17)

where X(M Cc/C) is the fraction of fibers that are broken when e > C, as in glass and
polymeric fiber-cement composites. The third and fourth terms in Eq. (6.17), Le.
stress redistribution and fiber fracture, respectively, can be neglected for high
strength fibers such as carbon. However, for ductile fibers such as glass, Kevlar and
PP, fiber fracture work can be quite substantial. Since the fiber reinforcement in
cementitious matrices is always randomly oriented, the orientation efficiency factor,
i.e. either 0.41 or 0.637 for planar or three-dimensional randomness, respectively,