Page 137 - Engineered Interfaces in Fiber Reinforced Composites

120 Engineered interfaces in jiber reinforced composites
depending on the relative values of the interfacc bond strength and the external
stress.
Finally, the solution for the mean fiber fragmentation length, 2L, which is the sum
of the debonded and bonded lengths in the partial debond model, is derived from
the fiber fragmentation criterion given by Eq. (4.70)

(4.78)

Eq. (4.78) is plotted in Fig. 4.16 where the bond length (2L - 2.l) and the debond
length 2t! balance each other to determine the instantaneous mean fiber fragmen-
tation length, 2L, at a given applied strain. At low strains the bond length
component dominates, but at high strains the debond length component becomes
increasingly more important, and eventually the debond length outpaces the bond
length under certain favorable circumstances. When the mean fiber fragment length
is sufficiently short at a high applied strain, an infinitesimal increase in debond
length or additional fiber fragmentation requires the applied strain to increase
dramatically toward an infinite value. A severalfold increase in the applied strain at
this stage would not cause any further fiber fragmentation. In practical fiber
fragmentation tests, the mean fiber fragment length obtained after substantial
increase in load application without further fiber fragmentation is called the 'critical
transfer length'. In the present analysis, the shortest mean fiber fragment length
determined at the end of the curve shown in Fig. 4.16 can be regarded as the critical
transfer length, (2L),, theoretically predicted for the carbon fiber-epoxy matrix
composite.

0.01 0.02 0.03 04
Applied strain E

Fig. 4.16. Variation of mean fiber fragmentation length, 2L, versus applied strain, E, in the partially
debonded interface model for zb = 50MPa. After Kim et al. (1993b).