= Fibre volume fraction
{title2=$V_f$}
The <fibre volume fraction> is the fraction of a <composite material>'s total <volume> occupied by reinforcing fibres:
$$
V_f=\frac{\text{fibre volume}}{\text{total composite volume}}.
$$
For a specimen with only fibres and a <composite matrix>, their fractions sum to one. Voids require a third fraction; they must not be silently counted as <composite matrix>. The <fibre volume fraction> is different from the fibre mass fraction because the constituents can have different <mass densities>.
For a void-free material, a measured fibre mass fraction $w_f$ gives
$$
V_f=\frac{w_f/\rho_f}{w_f/\rho_f+(1-w_f)/\rho_m},
$$
where $\rho_f$ and $\rho_m$ are the constituent <mass densities>. For example, masses in the ratio $3:2$ and <mass densities> in the ratio $3:1$ give $V_f=1/3$, not $3/5$. Inserting $V_f$ into the <longitudinal rule of mixtures> estimates axial <Young's modulus>; orientation and <fibre-matrix load transfer> remain separate requirements.
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