Page 147 - Engineered Interfaces in Fiber Reinforced Composites

130 Engineered interfaces in fiber reinforced composites

The solutions in the debonded region (O<z<C) are obtained previously (Gao et al.,
1988) for the boundary condition that the FAS at the loaded end (z = 0) is the same
as the applied stress, o

tq0) = u (4.94)
Thus,

G(z) = o - o(a - o)[exp(h) - 11 , (4.95)

O’,(z) = yo@ - o)[exp(h) - 11 , (4.96)

(4.97)

UlW
zi(a,z) =-((a-o)exp(h) , (4.98)
2
where the coefficients A1 and A2 are given in Eqs. (4.20) and (4.21). The stress
distributions in the constituents along the axial direction are schematically
illustrated in Fig. 4.22 for a partially debonded interface during the debond process
for the carbon fiber-epoxy matrix composite whose properties are given in Tables
4.2 and 4.3. Similar plots for the interface before debond initiation or after complete
debonding can be taken simply from the respective regions of the stress distribution.
The stress gradients for FAS and IFSS increase (or that for MAS decreases) rapidly
from the fiber end (z = L) toward the debond crack tip at the bonded region, while
the gradients of all these stresses become almost constant at the debonded region.
The high level of stresses concentration near the debond crack tip for the IFSS is a
direct reflection of the imminent debond crack propagation.
Unlike the axial stress in the fiber or matrix, the IFSS is discontinuous at the
boundary between the bonded and debonded regions. The non-linear variations of
the stresses in the debonded region, and particularly the decrease of IFSS towards
the loaded fiber end, reflect the prominent Poisson effect of radial contraction of the
fiber under axial tension. If the embedded fiber length is sufficiently long, the
maximum debond stresses, o;, to be shown in Figs. 4.26(a), 4.27(a) and 4.28(a)
would become a plateau value, 5, such that the induced residual stress, ql (u, z), in
the radial direction compensates completely for the residual clamping (compressive)
stress, 40. Under this circumstance, the IFSS at the debonded region given by Eq.
(4.29) will be equivalent to zero. Complete separation ensues between the fiber and
matrix at the loaded end (z = 0), which will further extend along the debonded
interface upon continuing loading. This can be proven in Eq. (4.29) by substituting
qo and qI(a,z) with Eqs. (4.24) and (4.18) for $(O) = o and .‘,(O) = 0.