Page 290 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 6. Interface mechanics and,fracture toughness theories 27 I

configuration. In the case of interlaminar/intralaminar fracture where the crack
propagates parallel to the fiber direction, the fibers are peeled off or fractured rather
than being pulled out. The fiber bridging in interlaminar fracture arises mainly from
the misalignment of fibers across the main crack plane, localized concentration of
fibers and matrix material (i.e. fiber rich and resin rich regions) and the growth of
the crack on more than one plane.
Based on the 'inherent flaw model' (IFM) proposed earlier by Waddoups et al.
(1 97 I), Caprino et al. (1 979, 1980) predicted eo to be approximately 2 mm for double
edge notch (DEN) and CN tension specimens of continuous epoxy matrix
composites containing carbon, glass and boron fibers. The IFM was originally
developed to predict the notch strength of laminates with finite width and an
inherent flaw of length, 2co. eo is found to be sensitive to the variations in ply layup
sequence, fiber orientation and type of fibers used. Slightly higher values of eo have
been obtained for CN and SEN tension specimens of carbon-poxy system based on
the 'damage zone model (DZM)': eo = 2-4 mm (Hillerborg et al., 1976; Aronsson
and Bachlund, 1986). In the DZM, the closure stresses due to the bridging fibers act
on the entire crack surfaces in accordance with a particular closure stress-crack face
relationship which is consistent with the damage mechanisms taking place. The
predictions of eo and the notched strength, on, using the DZM are shown (Aronsson
and Backlund, 1986) to agree better with experimental measurements than the IFM
model. For example, the experimental value of co for three-point bend specimens of
short glass-polyester systems is about 6 mm which is almost the same as the DZM
prediction of 6-7 mm, while the IFM model predicts a lower value of 4.1 mm. A
summary of all these previous models including the well-known Mar-Lin model
(Mar and Lin 1979) and a recent effective crack growth model to predict the residual
strength of composite laminates with notches and other forms of discontinuities
have been given by Afaghi-Khatibi et al. (1996a,b).
Because cracks in multi-angle ply laminates seek the easiest paths to propagate
preferentially along the fiber-matrix and laminar interfaces, the shape and size of
the damage zone in these composites depend strongly on the loading configuration
relative to the fiber orientation within the individual plies. The damage zone sizes are
compared between the laminates of different layup configurations for varying notch
lengths in Fig. 6.26. It is noted that the [90°] sub-cracks in [0°/900], carbon-epoxy
laminates are approximately 10 times longer than [45"] sub-cracks in [O0/ f 45"/0"],
laminates, while [O"] sub-cracks for the former laminates are about twice those for
the latter laminates. The complex appearance of the damage zone together with the
interactions between laminae make the quantitative characterization of the damage
zone size in multi-angle laminates extremely difficult.
In short fiber composites, energy absorption mechanisms, such as interfacial
debonding and matrix cracking, most often occur at the fiber ends (Curtis et al.,
1978). The damage model proposed by Bader et al. (1979) assumes that short fiber
composites fail over a critical cross-section which has been weakened by the
accumulation of cracks, since the short fibers bridging this critical zone are unable to
carry the load. In fatigue loading, sudden fracture takes place as a direct result from
the far-field effect of the composite, rather than due to the near field of the crack tip