Page 138 - Engineered Interfaces in Fiber Reinforced Composites

Chapter 4. Micromechanics of stress trunsler 121

(iii) Complete debonding: Complete interfacial debonding means that the fiber
length and the debond length are identical, and the IFSS is maximum at the debond
crack tip, which now coincides with the fiber center (z = 0). These requirements
cannot be satisfied in practice because the FAS always has to be at a maximum in
the center regardless of debond length. However, if the interfacial bonding consists
solely of friction where the IFSS is governed wholly by the Coulomb friction law,
then the above requirements can be satisfied. In this case, which is most likely in
some ceramic matric composites, the IFSS is minimal in the center where no radial
contraction takes place due to the difference in Poisson ratio between the fiber and
matrix. For the frictionally bonded interface, the solutions for the FAS and IFSS
given by Eqs. (4.64) and (4.63) are valid with ap being substituted by the FAS in the
center, $(O), and C = L for the non-dimensional coefficients Q, (where j = 1,2,3.4)
given in the Appendix C:

(4.79)

(4.80)

where
e;. = 4?,lkL . (4.81)

In Eqs. (4.79) and (4.80) G(0) can be determined for the boundary condition that
the IFSS is minimal in the center, i.e. Ti(a,O) = -pqo from Eq. (4.29)

(4.82)

The normalized FAS and IFSS are shown in Fig. 4.17. Both the FAS and IFSS
distributions are higher for larger values of residual clamping stress, qo, (in absolute
terms) for a given fiber length. Varying the coefficient of friction, p, would have
similar effects on the stress distributions. The predominant effect of differential
Poisson contraction between the fiber and matrix is obvious, particularly in Fig.
4.17(b), where the IFSS values at the fiber ends are several-fold the values obtained
in the center.
For the fully frictional interface model, the external stress corresponding to fiber
fragmentation is determined from Eq. (4.82) and OTS(2L)

(4.83)