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A composite of carbon fiber and epoxy has a carbon fiber mass fraction of 70%. Taking the density of carbon fiber as 1.80 g/cm³ and that of epoxy as 1.20 g/cm³, and assuming no voids, which value is closest to the fiber volume fraction?

  1. AAbout 70%
  2. BAbout 78%
  3. CAbout 61%
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Answer: C. About 61%

Volume is mass divided by density. In 100 g of composite, the fiber volume is 70/1.80 ≈ 38.9 cm³ and the resin volume is 30/1.20 = 25.0 cm³, so the fiber volume fraction is Vf = 38.9/(38.9 + 25.0) ≈ 0.61, about 61%. Because the fiber is denser than the resin, the volume fraction is smaller than the mass fraction. About 70% takes the mass fraction directly as the volume fraction; rule-of-mixtures calculations need the volume fraction. About 78% is the value calculated with the fiber and resin densities swapped. Real moldings may contain voids, so Vf and void content are checked by density measurement or the burn-off method.

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More Composite materials questions

  1. For a composite of aligned continuous fibers, which correctly describes when to use the isostrain and isostress forms of the rule of mixtures?
  2. A composite of glass fibers (Young's modulus 72 GPa) aligned in one direction at a volume fraction of 40% in a resin (Young's modulus 3.0 GPa) is loaded in tension parallel to the fibers. In the elastic range, which value is closest to the fraction of the load carried by the fibers?
  3. A composite contains glass fibers (Young's modulus 72 GPa) aligned in one direction at a volume fraction of 50% in a resin (Young's modulus 3.0 GPa). Using the isostress rule of mixtures, which value is closest to the Young's modulus perpendicular to the fibers?
  4. Which correctly compares carbon-fiber-reinforced plastic (CFRP) and glass-fiber-reinforced plastic (GFRP)?
  5. Which value is closest to the ratio CFRP/steel of the specific modulus (Young's modulus/density) in the fiber direction, for unidirectional CFRP (Young's modulus 140 GPa in the fiber direction, density 1.6 g/cm³) and steel (Young's modulus 210 GPa, density 7.9 g/cm³)?