Page 121 - Engineered Interfaces in Fiber Reinforced Composites

104 Engineered interfaces in fiber reinforced composites

ri(a,z) -dqo + q~(a,z)l (4.29)
The radial (compressive) stress, 90, is caused by the matrix shrinkage and differential
thermal contraction of the constituents upon cooling from the processing temper-
ature. It should be noted that q1 (a, z) is compressive (i.e. negative) when the fiber has
a lower Poisson ratio than the matrix (vf < v,) as is the normal case for most fiber
composites. It follows that ql (a,z) acts in synergy with the compressive radial stress,
40, as opposed to the case of the fiber pull-out test where the two radial stresses
counterbalance, to be demonstrated in Section 4.3. Combining Eqs. (4.1 l), (4.12),
(4,18) and (4.29), and for the boundary conditions at the debonded region

$(L) = O,O',(L) = 0- . (4.30)

Solutions for the stress components are obtained as:
.;.(z) = ol(a + o){ 1 - exp[-I(L - 41) , (4.31)
drn(z) = 0 - yol (a + a){ 1 - exp[-I(L - 41) , (4.32)

(4.33)
la
ri(a,z) =-i~l(~+c~a)exp[-i(L-z)] . (4.34)
2
Fig. 4.7 shows the approximate stress distributions in the constituents along the axial
direction of the left half of the fiber for the carbon fiber-epoxy matrix composite
with the relevant interface properties for the XAlOO fibers given in Table 4.2. The
FAS increases from the end towards the center while the MAS decreases in the same
direction, both of which are opposite to the axial stress distributions in fiber pull-out
and fiber push-out, to be shown in Sections 4.3 and 4.4. The IFSS increases from the
debond crack tip towards the fiber ends in the debonded region. This response makes
the debond propagation very difficult and is attributed to the radial compressive
stress, 91, arising from the differential Poisson contraction between the fiber and
matrix, which should be added to the residual compressive stress, qo. If the Poisson
effects are completely neglected in the fiber fragmentation analysis, the frictional
shear stress would become constant over the whole debonded region.

4.2.3.2. Interface debond criterion
The interface debond criterion used in this analysis is based on the concept of
fracture mechanics where the strain energy release rate against the incremental
debond length is equated to the interface fracture toughness, Gi,, which is considered
to be a material constant

(4.35)

where Ut is the sum of the strain energy stored in the bonded region (ub, for
t<z<L) and debonded region (ud, for O<z<e), which can be obtained by