Page 204 - 3D Fibre Reinforced Polymer Composites

Stitched Composites 193

Micromechanical models have been proposed by Jain and Mai (1994e, 1995) and Cox et
al. (Cox, 1999; Cox et al., 1997; MassabB et al., 1998, 1999; Massabb and Cox, 1999)
for determining the mode I1 delamination resistance of stitched composites. The
models by Jain and Mai use first order shear deformation laminated plate theory and
Griffith's theory for strain energy release rate in fracture to calculate the effect of
stitching on the mode I1 interlaminar fracture toughness (GIIR). Models have been
proposed for stitched composites subject to shear loading using the end notched flexure
(ENF) and end notched cantilever (ENC) test methods, which are methods for
measuring the mode I1 interlaminar fracture toughness of laminated materials. In both
models it is assumed that as a delamination crack propagates under shear the stitch
failure process consists of elastic stretching of the threads due to relative slip of the top
and bottom sections of the delaminated region, followed by rupture of the stitch in the
crack plane. These assumptions do not accurately reflect the actual stitch failure
process that has been observed in many stitched composites, which as described above
consists of axial plastic shear rotation, splittinglspalling, and ploughing of the stitches.
Jain and Mai (1994e, 1995) state that the mode I1 strain energy release rate for crack
propagation is given by:

where z is the applied shear stress and is related to the applied load, a is a correction
factor accounting for shear deformation, a] and @ are stitching parameters, and R is
related to materials properties through A" and a/. Using the steady-state crack
propagation condition, G,, = G//c, where GI/, is the mode I1 critical strain energy release
rate for the unstitched composite, the shear stress zneeded for crack propagation can be
determined. The critical strain energy release rate for a stitched composite can then be
calculated from:

G, = A*~~(a-t-&,:)~

The accuracy of the Jain and Mai models for determining the mode I1 interlaminar
fracture toughness of stitched composites is shown in Figure 8.28. This figure presents
a comparison of the measured and theoretical GIN values for stitched composites, and
there is good agreement. However, some studies (eg. Cox, 1999) show significant
disagreement between the model and experimental data.
Cox and colleagues have formulated one-dimensional analytical models for
predicting the traction shear stress generated in through-thickness fibres (including
stitches) when subject to mode I1 loading (Cox et al., 1997; Cox, 1999; Massab6 et al.,
1998; Massab6 and Cox, 1999). The models are based on the relationship between the
bridging tractions applied to the fracture surfaces by the unbroken stitches and the
opening (mode I) and sliding (mode 11) displacements of the bridged crack. The models
consider the micromechanical responses of stitches bridging a delamination crack,
including the elastic stretching, fibre rotation and some other affects that occur under
mode 11. Criteria for failure of the bridging tow by rupture or pull-out is also