Page 155 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 4. Micromechanics of Stress trunsfer 137

debond length reaches e = L - z,,,, followed by unstable debonding leading to
complete debonding. Therefore, this debond process is partially stable.
(iii) In the extreme case of z,,, value approaching zero, as in some ceramic matrix
composites, the debond process is always stable until complete debonding
independent of embedded fiber length, L. The rising portion of the debond stress
versus displacement curve (Fig. 4.25(c)) is typically linear without apparent ‘stick-
slips’ and there is no appreciable load drop after complete debonding (Bright et al.,
1991). This is because the interface is in principle frictionally bonded and there is
little chemical bonding. That is Gi,, or Tb is very small. Therefore, the linear increase
in stress represents primarily the frictional shear stress transfer across the interface
without virtual debonding until the frictional resistance over the entire embedded
fiber length is overcome. The maximum debond stress, cri, is then approximately
equal to the initial frictional pull-out stress, qr, because the frictionless debond
stress, op, is negligible (due to small Gi, or Q,).
The concept of z,,, with regard to the issue of the stability of the debond process
has practical implications for real composites reinforced with short fibers. There is a
minimum fiber length required to maintain stable debonding and thus to achieve
maximum benefits of crack-tip bridging between fracture surfaces without the
danger of catastrophic failure. It should also be mentioned that in practical fiber
pull-out experiments the stability for interface debonding deviates significantly from
what has been discussed above, and is most often impaired by adverse testing
conditions (e.g. soft testing machine, long free fiber length, etc.). Therefore.
debonding could become unstable even for L > z,,, and in composites with
zmay = 0. Moreover, when L is very short, as is the normal case in the microdebond
test, the precipitous load drop after complete debonding may be aggravated by the
release of the strain energy stored in the stretched fiber. The load drops to zero if the
fiber is completely pulled out from the matrix. Alternatively, if the fiber is regripped
by the clamping pressure exerted by the surrounding matrix material frictional pull-
out of the fiber is possible to resume.
Another important parameter related to the fiber length in the fiber pull-out test is
the maximum embedded fiber length, L,,,, above which the fiber breaks instead of
being completely debonded or pulled out. L,,, value for a given composite system
can be evaluated by equating 02 of Eq. (4.102) to the fiber tensile strength, CJTS,
(which is measured on a gauge length identical to the embedded fiber length used in
fiber pull-out test), Le.,

(4.109)

where (J[ is the crack tip debond stress determined for bond length z,,, = (L t).
~
L,,, values calculated for a constant fiber tensile strength CJTS = 4.8, 1.97 and
2.3 GPa for carbon fiber, steel fiber and Sic fiber, respectively, are included in Table
4.3. These predictions are approximately the same as the experimental L,,, values,
e.g., the predictions for L,,, = 49.3 and 23.4 mm compare with experimental values
L,,, = 5 1 .0 and 21.7 mm, respectively, for the untreated and acid treated Sic fibers