Fiber Volume Fraction

Fiber volume fraction

A fiber composite material (glass or carbon fiber in a polymer matrix) is defined, first of all, by how much fiber it contains. There is a subtlety, though: what governs the mechanical properties is the fraction by volume (V_f), not by mass — and mass is what a shop can easily measure. Since fiber and matrix have different densities (the fiber is usually the denser one), a conversion is needed. The formula does exactly that, turning masses into volumes (volume = mass ÷ density) and taking the ratio: V_f = (W_f/ρ_f) ÷ [(W_f/ρ_f) + (W_m/ρ_m)] × 100%, where W and ρ are the mass and the density of the fiber (subscript f) and of the matrix (subscript m). The fiber volume fraction is the single most important parameter of a composite laminate, since most of the structural properties come from the fibers and the rule of mixtures weights them by volume. The higher the V_f, the greater the stiffness and strength along the fiber direction — which is why high-performance composites (aerospace, sporting goods) chase a high V_f. But there is a physical ceiling: the fibers cannot touch one another completely; the theoretical maximum packing of parallel cylindrical fibers is ~78–91%, yet in practice, to make sure the matrix wets out every fiber and transfers load between them, V_f rarely exceeds 60–70%. Above that, voids and dry spots appear and wreck the properties. An optimum V_f therefore exists. Measuring the actual fiber fraction of a finished part (by burning off the matrix or by acid digestion, then weighing the fiber left behind) is an essential quality control step. Enter the masses and densities of the fiber and of the matrix.