FAILURE MECHANISMS
by bridging the delamination crack, it greatly increases resistance to shear loads (Sect. 4.5).
The minimum load for buckling or delamination crack growth does not fall indefinitely with
increasing delamination size, but approaches a constant value which depends on the
parameters of the through-thickness reinforcement [4.8-4.11]. Given adequate provision of
through-thickness reinforcement, ultimate failure must revert to the kink band mechanism,
which is largely unaffected by delaminations, and the compressive strength is then usually
close to that of pristine material.
Thus a transition exists in failure mechanism from delamination to kinking
depending on the efficacy of the through-thickness reinforcement. Rough estimates of the
minimum volume fraction,
t
, of through-thickness reinforcement required to suppress
buckling and assure failure by kinking can be deduced from the theory of buckling plates
on an elastic foundation [4.8-4.10]
(mid-plane delamination) (4.2a)
(surface delamination) (4.2b)
where
σ
k
is the applied stress at which kinking occurs, E
x
and E
t
are the stiffnesses of the
in-plane and through-thickness fibers; V
x
is the volume fraction of aligned, in-plane fibers;
and the dimensions h and t and the angle
θ
are defined in Fig. 4-4. Values found for V
t
from Eq. (4.2) are ~ 10
-3
, considerably less than the volume fractions of stitching or
interlock fibers in current composites. Equation (4.2) is based on the simplistic assumption
that the through-thickness reinforcement behaves as a linear spring with strain uniformly
distributed through the thickness of the composite. If loads were transferred by shear into
the surrounding laminate, the through-thickness reinforcement would provide a stiffer
foundation and even lower volume fractions would be required. Thus, for this particular
transition in failure mode and provided the through-thickness reinforcement remains intact,
Equation (4.2) should be a conservative estimate. However, if through-thickness
reinforcement is damaged, perhaps by impact, or crimped during manufacture, then
buckling will occur much more readily. Design rules for such situations have not yet been
established.
