Mass Fractions:

Let  and  be the mass of fibres, matrix and composite, respectively. We know that

The mass fractions, similar to volume fractions, are defined as the ratio of mass of respective phase to the mass of composite. Thus, we can write,

where,  is fibre mass fraction and  is matrix mass fraction. Now, let us write the mass of each phase in terms of density and volume of respective phase as

where,  and  are the densities of fibre, matrix and composite, respectively. Now, mass fractions can be written in terms of density and volume fractions as

This relation between mass and volume fractions is given in terms of individual constituent properties (using Equations (7.6) and (7.8)) as

Thus, it is clear from the above equation that the volume and mass fractions are not the same. One should always state the basis for calculating the fibre content in a composite.

Density:
           
The density of composite is derived in terms of densities and volume fractions of the individual phases as follows. The mass of composite is given by Equation (7.6). We can write this in terms of respective volume fractions and densities (with rearrangement) as

This is written using the definition of volume fraction for fibre and matrix as

We will write the density of composite in terms of mass fraction from Equation (7.9) as