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Polymers and composites

A composite contains carbon fibers (Young's modulus 230 GPa) aligned in one direction in an epoxy resin (Young's modulus 3.5 GPa) at a volume fraction of 60%. Using the rule of mixtures, which value is closest to the Young's modulus in the fiber direction?

  1. AAbout 8.6 GPa
  2. BAbout 94 GPa
  3. CAbout 139 GPa
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Answer: C. About 139 GPa

When load is applied along the fibers, fiber and resin strain by the same amount (isostrain), so the modulus is the volume-fraction-weighted average E = VfEf + VmEm = 0.6 × 230 + 0.4 × 3.5 = 138 + 1.4 ≈ 139 GPa. About 94 GPa swaps the volume fractions of fiber and resin. About 8.6 GPa comes from the isostress expression 1/E = Vf/Ef + Vm/Em, which estimates the modulus perpendicular to the fibers. Because unidirectional material differs in stiffness by more than a factor of ten depending on direction, real components stack plies with different fiber orientations.

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