Page 67 - Engineered Interfaces in Fiber Reinforced Composites

50 Engineered interfaces in fiber reinforced composites

(Favre et al., 1991; Curtin, 1991; Yabin et al., 1991; Merle and Xie, 1991; Gulino
and Phoenix, 1991; Ling and Wagner, 1993; Jung et al., 1993; Baxevanakis et al.,
1993; Andersons and Tamuzs, 1993; Liu et al. 1994).
However, the basic form of the relationship between the critical transfer length
and the IFSS remains virtually unchanged from the solution given by Kelly and
Tyson (1965) three decades ago. A clearly emerging view in recent years, contrary to
the conventional view of either perfect bonding or complete debonding, is that there
are both bonded and debonded regions simultaneously present at the fiber-matrix
interface during the fiber fragmentation process (Favre et al., 1991; Gulino et al.,
1991; Lacroix et al., 1992). For composites containing ductile matrices, the fiber-
matrix interface region tends to be yielded in preference to clear-cut debonding. A
proper micromechanics model should accommodate these phenomena. Therefore,
the limitation of this test associated with Eq. (3.3) has been addressed and improved
analytical models have been presented (Kim et al., 1993; Kim, 1997), deriving the
solutions required to satisfy the interface conditions, namely full bonding, partial
debonding/yielding and full debonding/yielding. Recently, Zhou et al. (1995) have
presented a fracture mechanics analysis of the fragmentation test including the
Weibull distribution of fiber strength. Transverse matrix cracking at the sites of fibcr
breaks has also been considered by Liu et al. (1995). Further details of these various
analyses will be discussed in Chapter 4.
Moreover, the validity of z, being determined based on the measurement of
fragment length depends not only on the interface properties but strongly on the
properties of the constituents, e.g. matrix shear yield strength, z,, and the difference
in Poisson ratios between the fiber and matrix. The relative magnitude of these
properties influences the actual failure mechanisms occurring at the interface region
(Le., interface debonding versus matrix yielding), which in turn determines the fiber
fragmentation behavior. Bascom and Jensen (I 986) argued that the shear stress
transfer across the interface is often limited by the matrix z, rather than the
interface T,.
Adding to the above problem, the critical transfer length, (2L),, has also been
shown to be strongly dependent on Young’s modulus ratio of fiber to matrix, Ef/Em.
Interestingly enough, some researchers (Galiotis et al., 1984; Asloun et al., 1989;
Ogata et al., 1992) identified through experimental evidence that (2L), varies with
as the early shear-lag model by Cox (1952) suggests. (See Chapter 4 for
solutions of fiber axial stress and interface shear stress). Finite element analyses on
single fiber composites with bonded fiber ends, however, show that there is an
almost linear dependence of (2L), with Ef/E,, if the modulus ratio is relatively small
(Le. Ef/Em < 20). Experimental evidence of the dependence of the critical transfer
length on Young’s modulus ratio is shown in Fig 3.5, and is compared with
theoretical predictions (Termonia, 1987, 1993). Additionally, Nardin and Schultz
(1993) also proposed a strong correlation of the critical transfer length with the
interface bond strength, which is represented by the thermodynamic work of
adhesion, W,, at the fiber-matrix interface.
Apart from the mechanical properties of the composite constituents that
dominate the fiber fragment length, peculiar structural properties of the fiber may