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Investigations into Multi-Stable Laminates
Abstract
The cured shapes of multi-stable composite laminates
are investigated. In certain cases, composite laminates
featuring an unsymmetrical lay-up sequence have been
observed to differ in shape from the predictions of
Classical Laminate Theory (CLT). Continuing from
existing theory, a mathematical model has been
developed to predict the cured shape of unsymmetrical
laminates. Current research aims to characterize
viscoelastic and environmental effects, using numerical
analyses and experimental techniques, such as Dynamic
Mechanical Analysis (DMA), Differential Scanning
Calorimetry (DSC), Finite Element (FE) modelling, and
MATLAB. Digital Image Correlation (DIC) will be used
to record the cured shape of laminates to compare
experimental results with theory.
1. Introduction
Carbon Fibre Reinforced Plastic (CFRP) is a composite
material that has a polymer (typically epoxy) and a fibre
(carbon) as its two base constituents. The material can
offer an excellent strength-to-weight ratio, an increase in
fatigue life, a reduction in corrosion issues, and an
increase in stiffness when compared to many metals.
Use of this material in high performance applications
has increased steadily, with the latest generation of
airliners (such as the Boeing 787) now using CFRP for
50% of its primary structure. One of the most popular
methods of manufacturing composite parts involves
using pre-preg plies (sheets of carbon fibres already
impregnated in a polymer). Stacking these sheets (i.e.
‘laying up’) in a particular order allows engineers to
tailor the properties of the structure to suit the loading it
will experience. Once stacked, the laminate is cured in
an autoclave at an elevated temperature and pressure.
Multi-stable laminates are a family of unsymmetrical
laminates, which, once cured, can display two or more
stable shapes. The shapes can be ‘snapped’ from one
shape to the other by a manual force application. No
force is required to hold a laminate in a particular shape.
This property is considered to offer several novel
engineering applications; from simple access panels and
shut-off valves, to morphing (i.e. adaptable) aircraft
wings. As force is only required to snap the laminate
from one shape to another, multi-stable composites can
reduce the requirements of actuating mechanisms and
thus reduce the weight and complexity of the system.
2. Manufacture of multi-stable laminates
Multi-stable composite laminates are manufactured
by exploiting a property that, in normal applications, is
Robert Telford, supervised by Dr. Trevor Young
University of Limerick
Robert.Telford@ul.ie
182
negated by the symmetry of the lay-up – this is, the
difference in Coefficient of Thermal Expansion (CTE)
between the longitudinal and transverse direction of a
CFRP ply. The laminate is initially flat, at the elevated
temperature in the autoclave. During cool-down from
the curing temperature, the miss-match in CTE produces
residual stresses within the laminate. Due to the
unsymmetrical lay-up sequence of the laminate, the
residual stresses are unbalanced about the mid-plane
and thus cause the laminate to warp. Classical Laminate
Theory (CLT) can be used to predict the room
temperature shapes of such laminates. For a cross-ply
laminate (e.g. a [02/902] lay-up), CLT predicts a ‘saddle’
shape, with curvatures about the x and y axes. However,
when manufactured with certain characteristics (i.e.
length-to-thickness ratio, temperature change), the
laminates exhibit multi-stable behaviour. The two
shapes are cylindrical, with their generators lying on
two mutually perpendicular axes and with opposite
curvature. CLT does not predict this behaviour.
3. Current research
Several techniques are being used to study this
behaviour – these include (1) mathematical modelling to
predict the shapes; (2) Finite Element Analysis (FEA) to
validate the experiments; (3) Digital Image Correlation
(DIC) to record the shapes of the manufactured panels;
and (4) Dynamic Mechanical Analysis (DMA) and
Differential Scanning Calorimetry (DSC) to investigate
polymer properties. A mathematical MATLAB model
that uses the Rayleigh-Ritz method and the
minimization of potential energy has been developed,
based on existing theory. The theory differs from CLT
as a geometric non-linearity is introduced, and can
predict the shapes of a cured laminate, as well as the
bifurcation point. Future work (which is poorly
addressed in the literature) will explore other factors
that affect the residual stresses within the laminate (e.g.
moisture and viscoelasticity). DMA and DSC will be
used in conjunction with FEA (ABAQUS) to
characterise the changes in residual stress state caused
by these factors. The results of this work will be
introduced into the MATLAB model to predict the
shapes of multi-stable laminates over time. To compare
experimental work against theory, DIC will be used as a
non-contact method of measuring and recording the
shape of laminates. Additionally, the effect of externally
applied stresses on the residual stress state, and the
resulting changes in stable shapes will be investigated.
This is required to determine the behaviour of such
laminates when used as part of a structural component.