JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition - 58

BVID
condition on delaminations in composite
structures and hence it is on the initiation of
damage growth that the focus is placed.

The Strip model approach

Fig. 1: BVID: (left) Plan-view ultrasonic C-scan
of a damaged laminate showing considerable
internal separation of layers (delamination),
(right) X-ray CT cross section showing throughthickness damage

Among these, the latter is currently one of
the most limiting cases for minimum mass
design. The morphology of near-surface
delaminations (both size and through-thickness position) and the residual strength
of composite structures are inextricably
interlinked. Under compressive load (and
for special cases tensile load), delaminated
outer layers can buckle open causing damage
growth (Figure 2) and eventually catastrophic failure.
Depending on the through-thickness position of damage and the plies in the buckled
sublaminate, damage growth can be either
stable or unstable and can occur under both
static and fatigue loading conditions [1, 2].
Damaged areas may also be susceptible to
locally increased loading (causing premature
failure) due, for instance, to interaction of
damage with structural buckling. Aerospace
regulations currently place a no-growth

For the past 30 years, the problem of modelling delamination-induced failure has been a
significant topic of research for the aerospace
composites community. As with many other
aerospace structural problems, the analysis
approaches taken so far can be broadly split
into finite element, analytical and experimental categories. Each of these approaches
has its place on the way to aircraft certification, and is more or less time consuming
depending on the required accuracy. The
University of Bath Strip model for sublaminate-buckling-driven delamination propagation differs from previous analytical approaches in that it retains the computational
efficiency of an analytical approach but in
comparative studies equals (or even betters,
see Figure 3) the accuracy of a finite element
approach requiring 3-4 orders of magnitude
more degrees of freedom and computational
run-time [3]. The Strip model is adaptable
to a range of structural problems and can
account for mixed material laminates with
varied thickness and impact damage (see
Applications). Furthermore, the initial set of
material parameters required by the model is
limited to the commonly obtained properties of longitudinal and transverse Young's
moduli, shear modulus, Poisson's ratio
and the Mode I fracture toughness of the
resin (GIC). This furthers adds to the Strip
model's flexibility and ease of application.
The resulting analytical model, which is
based on a comparative energy method, has
two forms [1]. The first one:
(1)

Fig. 2: Compression after impact: Digital image
correlation images of an impacted damaged
laminate under compression. Compression is
applied vertically: (upper) local buckling of delaminated plies nearest the surface is followed by
(lower) sublaminate buckling induced delamination growth at a deeper critical interface

provides physical insight into the behaviour
of delaminated surface plies as a function
of the thickness and stacking sequence
(see Figure 4). Here, GI is the strain energy
release rate (SERR) or the energy available
per unit area to cause resin fracture, Ann is the
greater of the axial or transverse stiffnesses
of the delaminated sublaminate, ε is the
applied axial strain and εC is the buckling
strain of the sublaminate. εC is calculated
using the computationally efficient finite

58 jec composites magazine / No88 April 2014

strip program VICONOPT (typically
using 6 Strips), which solves the underlying
buckling equations exactly [4]. Figure 4
shows the build-up in the SERR for nearsurface sublaminates from two quasi-isotropic laminates each with different surface
plies. Propagation occurs when
GI = GIC, the critical Mode I fracture toughness of the resin matrix.
The second form of the Strip model, derived
from the first by inverting it and replacing GI
with GIC, is:
(2)
It calculates the applied laminate strain, εth,
below which propagation of delaminations
will not occur. The Strip model is applied
to each sublaminate/delamination in the
laminate in isolation. The propagation
strain for each interface is compared and the
lowest taken as the allowable strain for the
full laminate.
A number of assumptions are built into the
Strip model: for unbuckled plates, loading
is assumed to be uniaxial and compressive;
delaminations are assumed to be circular or
can be approximated by a circle; and energy
for delamination growth is only available
from the delaminated sublaminate. Energy
for resin fracture is assumed to be released
in proportion to either the longitudinal or
transverse sublaminate in-plane stiffness
(A11 or A22) depending on which is the greater for the sublaminate in question [1]. In the
case of large flexible panels, a modification
is made to the Strip model [5] to account for
the occurrence of additional compressive
strains following bending/buckling of the
panel. Such strains are a consequence of a
loading eccentricity driven by a partial panel
stiffness loss following sublaminate buckling.
None of the computational efficiency of the
Strip model is lost through this modification.

Strip model variables
Sublaminate axial stiffness
For sublaminates with fibres principally
aligned in the 0° direction, A11 dominates
the propagation calculation. Conversely,
for fibres aligned in the 90° direction, A22
dominates. A joint minimum in A11 and
A22 occurs at 45° and coincides with a local

JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition

Table of Contents for the Digital Edition of JEC COMPOSITES MAGAZINE - Issue #88 - April 2014 - Special JEC Americas Spring Edition