Page 135 - Engineered Interfaces in Fiber Reinforced Composites

118 Engineered interfaces in fiber reinforced composites
the stress drop). Near the fiber ends of the debonded interface, the IFSS increases
non-linearly towards the fiber ends as a result of the smaller Poisson contraction of
the fiber than the matrix.
The basic requirement necessary to satisfy the partially debonded interface is that
the crack tip debond stress, oe, (and the debond length, l) must be greater than zero.
From the debond criterion given by Eq. (4.68)

(4.75)

In the partially debonded model, whether debonding continues or not depends
strictly on the relative magnitude of the stresses required for debond propagation,
bod, and for fiber fragmentation, cof, at a given debond length e. If cod of Eq. (4.69)
is smaller than cof of Eq. (4.70) interfacial debonding continues in preference to fiber
fragmentation, and vice versa if cod is greater than cor. These requirements can be
expressed as

for debond crack propagation and,

(4.77)

for fiber fragmentation.
The relationship between the applied stresses Ood and o0f is plotted as a function
of normalized debond length, !/a, in Fig. 4.14. It is interesting to note that cod is
almost independent of the mean fiber fragment length, 2L, with respect to [/a, and
hence only one curve for bd is shown. The implication of this figure is that when the
fiber is sufficiently long (e.g. 2L = 4mm), it fractures without debonding (because
bod > oaf) until its length reaches a characteristic value (X),. (2L)d = 2.71 mm is
obtained for Zb = 72.7 MPa by equating bod = o0f (i.e. = 0, in Fig. 4.14(a)), which
is exactly identical to the value obtained for the full bonded interface (Fig. 4.11).
The relationship between the applied stresses cod and go[ is further evaluated in
Fig. 4.15 in which Zb is plotted as a function of the debond length, !/a, for different
fiber lengths based on Eqs. (4.76) and (4.77). The solid lines represent the upper
bounds for interface debond (or, the lower bounds for fiber fragmentation), and the
dotted lines represent the upper bounds for fiber fragmentation. There are three
diflerent regions identified: region A for debonding only; region B for fiber
fragmentation without further debonding; region C for neither debonding nor fiber
fragmentation. It is found that if Zb is greater than a certain value (i.e.
fb = 94.7 MPa for 2L = 2mm and fb = 78.8 MPa for 2L = 1 mm), further fiber