Composite Materials

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).



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.



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.

Try selecting different types of polymer matrices or different types of fibres and see how the different elastic properties change as you increase the volume fraction of fibres. The greyed areas to the right of the graph represent fibre contents which are either difficult toachieve in practice (light grey) or just plain impossible (dark grey).

In practice it is very difficult to get more than 60% by volume of fibres which puts a practical limit on the maximum stiffness of the composite of 0.6xEf.

While the rule of mixtures has proved adequate for tensile modulus (E) in the axial direction, the isostrain rule of mixtures does not work for either the shear (G) or bulk (k) moduli. Instead, these are dependent on the phase morphology. An example of shear modulus (G) and bulk modulus (k) dependencies for an assemblage of cylindrical fibres is shown below.