The properties of composites are governed by the properties of the constituent materials, the volume contents of the constituents and their interaction. The reinforcement contents are defined by their volume fraction. Surface effects are used to modify the properties and such surface effects should be proportional to the ratio of (total interface area) / (volume of the resin), y. Derive an equation relating y to the fiber volume fraction and the fiber surface/volume ratio.
Make a plot of y vs fiber volume fraction for single-walled carbon nanotubes (~1.3 nm), multi-walled carbon nanotubes (~15 nm), ceramic whiskers (~1 micro m), advanced fibers (glass/carbon) (~10 m) and boron fibers (~150 micro m). You may wish to use a logarithmic scale.