Page 64 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 3. Measurements of interfacelinterlaminar properties 47

HI‘/ by = 92.6MPa

End of fragmentation

Acoustic
emission events
I 1 , I
(b) 75 fiber ruptures

Fig. 3.3. (a) Typical load4isplacement curve and (b) acoustic emission events for a fiber fragmentation
test on an AS4 carbon fiber-PEEK matrix composite. After Vautey and Favre (1990).

The average value of fiber fragment lengths obtained at the end of the test when
the application of stress does not cause any further fiber fragmentation is referred to
as the ‘critical transfer length’, (2L),. The critical transfer length represents the
complex tensile fracture characteristics of brittle fibers and the statistical distribu-
tion of fiber fragment lengths. Typical plots of the mean fragment length versus fiber
stress are shown in Fig 3.4 for carbon fiber-epoxy and Kevlar 49-epoxy systems. It
is interesting to note that the idea of the critical transfer length was originally
derived from the concept of maximum embedded fiber length, Lmax, above which the
fiber breaks without being completely pulled out in the fiber pull-out test, rather
than in the fiber fragmentation test. In an earlier paper by Kelly and Tyson (1965),
(2L), for the composite with a frictionally bonded interface is defined as twice the
longest embedded fiber length that can be pulled out without fracture, i.e.
(2L), = 2Lm,,. The solution of L,,, as a function of the characteristic fiber stresses
and the properties of composite constituents and its practical implications are
discussed in Chapter 4.
For analytical purposes, the critical transfer length is also defined as the fiber
length necessary to build up a maximum stress (or strain) equivalent to 97% of that
for an infinitely long fiber (Whitney and Drzal 1987). In this case, the knowledge of
the critical transfer length is related principally to the efficient reinforcement effect
by the fiber. (Compare this value with 90% of that for an infinitely long fiber for the
definition of “ineffective length” (Rosen, 1964; Zweben, 1968; Leng and Courtney,
1990; Beltzer et al., 1992).)
The average shear strength at the interface, z,, whether bonded, debonded or if
the surrounding matrix material is yielded, whichever occurs first, can be
approximately estimated from a simple force balance equation for a constant
interface shear stress (Kelly and Tyson, 1965):