Page 124 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 4. Micromechanics of stress transfer 107

for the partially debonded interface, and

4(0) = cq(a+o)[l -exp(-AL)] (4.43)

for the fully debonded interfaces. For the fully bonded interface, the corresponding
maximum FAS can be obtained by substituting the debond length C = 0 and of = 0
into Eq. (4.42)

$(O) = -o[l - sech(fiL)] . (4.44)
A2
A1
Therefore, combining Eqs. (4.41)-(4.44), the fiber fragmentation criterion is derived
in terms of the applied stress, oa = oofr at the remote ends of the matrix

(4.45)

for the fully bonded interface, and

2
(f) o~s(2L) cosh[fi(L - .e)] - wlZ[l - exp(-&?)] (4.46)
00f=:!2{cosh[fi(L-E)] - l}+ol[l -exp(-M)]

for the partially debonded interface. The corresponding equation for the fully
bonded interface is given by

(4.47)

4.2.3.4. Debond length and mean ,fiber fragment length

The effect of interface properties on the debond process is shown in Fig. 4.8 where
the debond length, e, is plotted as a function of the applied stress, 0,. Three different
coefficients of friction, p, are used at a given fiber length (2L) = 2.0mm for this plot.
In general, C decreases exponentially with increasing oa towards a plateau value. A
lower coefficient of friction, p, results in a longer i? at a given oa. It should be
emphasized that there is a critical value of applied stress below which no debonding
takes place at the interface. This value corresponds to the initial debond stress where
a sharp transition occurs from the fully bonded interface to the partially debonded
interface, and is found to increase slightly with increasing p as a result of the
enhanced frictional resistance discouraging debond propagation.
From Eqs. (4.45) and (4.46), the solutions for the mean fiber fragment length are
derived