Page 199 - 3D Fibre Reinforced Polymer Composites

188 30 Fibre Reinforced Polymer Composites

The first model proposed by Jain and Mai is known as the ‘continuous stitching model’.
With this model it is assumed the stitches are interconnected and fail along the
delamination crack plane (Figure 8.22a). This type of failure is also shown in Figure
8.18a. The analytical expression for crack closure traction in the model contains terms
for frictional slip and elastic stretching of the stitches in the bridging zone as well as an
analytical term to predict when the stitches will rupture at the crack plane. The second
model by Jain and Mai is known as the ‘discontinuous stitching model’. For this model
it is assumed the stitches behave independently under mode I loading, and interlaminar
toughening occurs by the frictional resistance of the stitches as they are pulled from the
composite under increasing crack opening displacement (Figure 8.22b). To model this
failure process the expression for calculating the crack closure traction contains terms
for frictional slip and pull-out of the stitches. In some composites, stitch failure occurs
during elastic stretching at the outer surface of the DCB specimen at the stitch loop, and
the stitch thread subsequently pulls-out. In this case, the continuous and discontinuous
stitching models are combined into the so-called ‘modified model’ to account for the
two stitch failure events.
The mode I delamination resistance in terms of stress intensity factor, KIR(Aa), of a
composite with bridging stitches can be calculated from the expression (Jain and Mai,
1994a, 199b, 1994~):

where KI, is the critical interlaminar fracture toughness of the unstitched composite, da
is the crack growth length, h, is the half-thickness of the composite, t is the distance
from the crack tip to the specimen end, P(f) is the closure traction due to stitches, and Y
and f(t/h,) are orthotropic and geometric correction factors, respectively. Y is defined
by:

(8.3)

where Eo is the orthotropic modulus and E, is the flexural modulus of the stitched
composite. The termf(t/hc) in equation 8.2 is determined using:

The closure traction, P(f), which is required to determine KIR(h), is obtained by
iteratively solving the Euler-Bernoulli beam equation. Once KIR(da) has been
determined, the Mode I interlaminar fracture toughness, G~dda). may be obtained by: