Page 133 - Engineered Interfaces in Fiber Reinforced Composites

116 Engineered interfaces in fiber reinforced composites

Having satisfied the requirements for full bonding, the mean fiber fragmentation
length, 2L, is determined from Eq. (4.72)

(4.74)

The mean fiber fragment length, 2L, is plotted as a function of applied strain,
E(= oa/Em), in Fig. 4.12. Also superimposed are the results obtained when the fiber
tensile strengths are assumed to be constant. The fully bonded model predicts that
2L decreases drastically within a narrow range of E. The decrease is even more
instantaneous if a constant CJTS is used, which is followed immediately by an almost
constant value as E is further increased. The threshold value of the applied strain for
the precipitous drop in fiber fragment length increases with increasing CTS. In
contrast, there is no such threshold observed when CTS is given by the Weibull
equation. It is also worth noting that the mean fiber fragment length becomes almost
identical, regardless of whether the fiber tensile strength is Weibull-controlled or
constant, when the applied strain is sufficiently large. This result suggests that for the
fully bonded interface, the critical transfer length obtained at a large value of E at the
end of the fragmentation test would be almost independent of the fiber tensile
strength model employed.
However, it should be emphasized here that only the initial decending part of the
curves at low applied strains would satisfy the requirements of full bonding
according to Eq. (4.73) and Fig. 4.11. The characteristic length, (2L),, which is the
maximum fiber length obtainable before debond initiation, is controlled by the
interface bond strength, Zb, of the composite. In other words, unless Tb is sufficiently
large to prevent the interface from debonding (or, alternatively the matrix can

Weibull strength 0, (2L)

0 0.02 0.04 0.06 0 18
Applied Strain, E

Fig. 4.12. Variation of mean fiber fragment length, 2L, versus applied strain, E, in the full bonded interface
model: (------) varying u~s(2.L); (- ) constant fiber tensile strength am. After Kim et al. (1993b).