Page 262 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 6. Interface mechanics und fracture roughness theories 243

6.1.3. Post-debond friction

After interface debonding has taken place the fiber and matrix move relative to
each other as the loading continues. Kelly (1970) has proposed a toughness
contribution due to post-debonding friction whose dissipated energy is equivalent to
the frictional shear force times the differential displacement between fiber and
matrix. The displacement is approximately equal to the product of the average td
and the differential strain, Ac = q - e,, between the fiber and matrix. Therefore, the
post-debonding friction toughness, Rdf, is given by

A6 can be approximated to q if E, is neglected in brittle matrix composites (Harris,
1980). It is shown that Rdf contributes substantially to the total fracture toughness of
glass fiber-polymer matrix composites (Harris et al., 1975; Kirk et al., 1978;
Beaumont and Anstice, 1980; Munro and Lai, 1988).

6.1.4. Stress redistribution
Once there is considerable debonding along the interface, the continuous fiber is
effectively loaded in tension over the debonded length. The fiber may break at a
weak point within this region near the main fracture plane. Upon fracture the fiber
instantly relaxes back and its ends are gripped by the matrix as it regains its original
diameter (Fig. 6.1(d)). There is another source of toughness of fiber composites, due
to the redistribution of strain energy from the fiber to the matrix after fiber fracture
(Piggott, 1970; Fitz-Randolph et al., 1972). Assuming the stress builds up linearly
from the broken end over a distance equivalent to half the critical transfer length,
&/2, for an elastic fiber, the strain energy lost from the fiber due to stress
redistribution, R,, is given by

It is noted that R, is 2lc/3& times the Outwater-Murphy debonding toughness given
in Eq. (6.1). The critical transfer length, C,, represents the shortest fiber length
required to bring the maximum fiber axial stress up to its tensile strength, a;, as
discussed in Chapter 4. It is shown that R, contributes substantially to the total
fracture toughness of boron fiber reinforced epoxy matrix composites (Fitz-
Randolph et al., 1972; Marston et al., 1974).

6.1.5. Fiber pull-out
As the external loading continues and the crack propagates, the broken fibers are
pulled out from the matrix (Fig. 6.1(e)), resulting in a continuation of the post-