Past exam of the materials science course of the University of Cambridge / 2017 / Paper 1 / 5 / c / Solution

Let $V_c$ be the carbon-fibre volume fraction of the whole composite. Then $V_m=0.4$ and $V_g=0.6-V_c$. Under the same longitudinal rule of mixtures,Setting $E=71.94\mathrm{GPa}$ givesThus carbon occupies 17.8% of the complete composite, or about $29.6\%$ of its total fibre volume. The resulting $60\%$ total fibre fraction is much more plausible than the glass-only estimate. This remains an ideal stiffness calculation requiring aligned, effectively loaded fibres; strength and fatigue checks are separate.