Density, Weight and Volume Fractions

The density of the composite is easily calculated by adding up the mass of each component, i.e. the mass of the fibres, Mf, and the mass of matrix, Mm

To convert from volume fraction of fibres, f, to weight fraction of fibres, fw, we just need to establish the ratio of the mass of the fibres to the total mass, this is simply

To convert from weight fraction, fw, to volume fraction, f, we need to establish the ratio of the volume of reinforcement to the total volume of the composite. Again this is simply

Now we need to implement the design rules in MATHCAD so that we can quickly find the required volume or weight fractions of fibres to produce the desired elastic properties. The following exercise is relatively trivial but, it demonstrates a number of important techniques, such as

• • How to set up a design model so that it is easy to change the properties of the materials used.

  • How to write equations in terms of the design variable.

  • How to solve for the design variable.

  • How to plot property variations as a function of the design variable.

  • How to simplify and re-use equations to solve more complex problems.

See the MathCad exercise