NewDesignofComposites

The Design of Composite Materials and Structures
What is a composite material?
A composite material is a material in which two or more distinct materials
are combined together but remain uniquely identifiable in the mixture. The
most common example is, perhaps, fibreglass, in which glass fibres are
mixed with a polymeric resin. If one were to cut the fibreglass and, after
suitable preparation of the surface, look at the material, the glass fibres
and polymer resin would be easy to distinguish. This is not the same as
making an alloy by mixing two distinct materials together where the
individual components become indistinguishable. An example of an alloy that
most people are familiar with is brass, which is made from a mixture of
copper and zinc. After making the brass by melting the copper and zinc
together and solidifying the resultant mixture, it is impossible to
distinguish either between or where the atoms of copper and zinc are. There
are many composite materials and while we may be aware of some, such a
fibreglass and carbon epoxy, there are many others ranging from the
mundane, reinforced concrete ( a mixture of steel rod and concrete (itself
a composite of rock particles and cement), pneumatic tyres ( steel wires in
vulcanised rubber), many cheap plastic moldings (polyurethane resin filled
with ceramic particles such as chalk and talc) to the exotic metal matrix
composites used in the space program (metallic titanium alloys reinforced
with SiC ceramic fibres), and your automobile, such as engine pistons
(aluminium alloys filled with fibrous alumina) and brake discs (aluminum
alloys loaded with wear resistant SiC particles). Regardless of the actual
composite, the two [or more] constituent materials that make up the
composite are always readily distinguished when the material is sectioned
or broken.
Is it possible to design a composite material?
Obviously the answer to that question is "Yes"! First, we must identify the
numerous materials related variables that contribute to the mechanical and
physical properties of the composite material. Secondly, the appropriate
physical and mathematical models that describe how the properties of the
individual components of the composite are combined to produce the
properties of the composite material itself must be derived. So, "Yes", it
is possible to design a composite material such that it has the attributes
desired for a specific application. Those attributes might be as simple has
having a specified stiffness and strength, a desired thermal conductivity,
or have a minimum specified stiffness at the cheapest possible cost per
unit volume. Whatever the specifications it should be possible to design a
suitable composite material. As in all design processes, it may not be
possible to meet all the specifications exactly and compromise and trade
offs will be required, but by understanding the physical origin of the
required properties and developing an appropriate mathematical description,
a suitable composite can be designed. We should also keep in mind that
there may be an exisitng conventional material that is more suitable for
the application than a composite. So the composite must offer a specific
advantage in terms of cost or performance than conventional alternatives.
It is one of the goals of this resource to show you the logical steps
needed to implement the design process.
How do we get started?
Perhaps the easiest way to demonstrate how the design process required to
develop a composite material is implemented is to start with a familiar
composite material and examine just what factors control its properties. So
I will start by asking a simple question, "How strong is a piece of
fibreglass?" As you should be aware, there is no single answer to that
question and one might be tempted to reply, "How strong do you want it to
be?"
The amount of load that it takes to break a piece of fibre glass depends on
the size of the piece of fibreglass, its thickness, width and length,
whether we are simply pulling it in tension, compressing it, or bending it.
It also depends on what the fibreglass is made of. There are many types of
glass and many different polymeric resins that are used to make fibreglass.
There are also many different ways in which the glass can be combined into
the resin, for example, are the fibres all aligned in the same direction,
are the fibres woven into a cloth, what type of cloth, are the fibres
aligned at random, and are the fibres long or short? Then, if the fibres
are oriented, at what angle relative to the fibres, is the fibreglass being
loaded? Finally, just what is the ratio of fibres to resin and is that by
volume or by weight?
By looking at the range of fibreglass products available and by seeking
clarification on the structure and composition of the fibreglass we have
begun to identify the micro structural variables that will control the
properties of the composite. These may be summarised as
. The properties of the fibre reinforcement
. The properties of the matrix in which the reinforcement is placed
. The amount of reinforcement in the matrix.
. The orientation of the reinforcement
. The size and shape of the reinforcement.
In order to get started, it is tempting to rephrase the initial question
"How strong is fibreglass?" to "What is the tensile strength of fibreglass
?" thus eliminating the size and loading mode variables, or better still,
"What is the tensile strength of fibreglass when all the fibres are aligned
in the same direction?" Now we only need consider the mechanical properties
of the glass fibres, the polymeric resin used to bind them and the relative
proportions of the two. It would be relatively simple, having selected a
resin and a fibre, to manufacture a number of flat plates of the composite
with various ratios of fibre to resin, test them and produce a graph of
tensile strength vs. volume fraction from which we could select a volume
fraction of fibre that gives a composite with the required strength.
However, if strength outside the range of measured strengths was required
or other factors dictated a change in resin or fibre then the whole process
would have to be repeated. While this approach does work, it rapidly
becomes very time consuming and costly.
If we were to look at the various test materials that were made in the
first trial and error experiments and observe the stress-strain behaviour
up to the point of fracture we could infer that failure resulted from
either a critical strain in the matrix or fibre being exceeded or a
critical stress in either component being exceeded. We would also observe
that for the most part, the composite behaved elastically almost to the
point of failure, primarily because the glass fibres and the polymeric
resin were both linear elastic solids with a brittle fracture mode, i.e.,
no plastic deformation. We would also note from the mechanical tests that
the elastic modulus of the composite also varied with the amount of fibre
added to the resin. Since we are already familiar with HookeÕs Law that
defines the elastic modulus as the ratio of stress to strain, then to start
answering the question "How strong is fibreglass?" we will first examine
how the elastic modulus of the composite, measured parallel to the aligned
fibres, varies as a function of the volume fraction of fibres.
Aligned Continuous Fibres
If the composite material is to stay in equilibrium then the force we apply
to the composite as a whole, F, must be balanced by an equal and opposite
force in the fibre, Ff and the matrix Fm. When considering 'Strength of Materials' problems we usually work in terms
of stress (?) (force per unit area) rather than force itself. So the force
on the fibres is simply the stress on the fibres, ?f, multiplied by the
cross-sectional area of the fibres lying perpendicular to the stress. The
cross sectional area of the composite occupied by the fibres is just f, the
volume fraction of the fibres multiplied by the cross-sectional area of the
composite itself - we'll call that "A" - i.e. f.A. Similarly the force on
the matrix is just the stress in the matrix multiplied the cross-sectional
area of the matrix in the composite, i.e. (1-f).A . Since the cross-
sectional area of the composite itself, A, is in each term on both sides of
the equation we can cancel it out. So the stress in the composite is just
the sum of the stresses in the fibre and the matrix multiplied by their
relative cross-sectional areas.
The stress in the fibre and the stress in the matrix are not the same. Now
the tricky bit! We can now use Hooke's Law, which states that the stress (or Force)
experienced by a material is proportional to the strain (or deflection).
This applies as long as the stresses are low (below the elastic limit -
we'll come to that soon) and the material in question is linear elastic -
which is true for metals, ceramics, graphite and many polymers but not so
for elastomers (rubbers). [pic]
Where E is the elastic modulus; the bigger these number the stiffer the
material. For compatibility, the strain, ?, must be the same in both the
fibres and the matrix otherwise holes would appear in the ends of the
composite as we stretched it. This is known as the ISOSTRAIN RULE. [pic]
Since the fibre and matrix often have quite different elastic moduli then
the stress in each must be different - in fact the stress is higher in the
material with the higher elastic modulus (usually the fibre). In
fibreglass, the elastic modulus of the glass (~75GPa) is much greater than
that of the polyester matrix (~5GPa) so as the volume fraction of fibres is
increased, the elastic modulus of the composite (measured parallel to the
fibres) increases linearly. [pic]
[pic] Try selecting different types of polymer matrices or different types of
fibres and see how the different elastic properties change as