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?

Answer: A. About 5.8 GPa

Perpendicular to the fibers, fiber and resin are treated as lying in series and carrying the same stress, so 1/E₂ = Vf/Ef + Vm/Em is used. 1/E₂ = 0.50/72 + 0.50/3.0 = 0.00694 + 0.1667 = 0.1736 GPa⁻¹, so E₂ = 1/0.1736 ≈ 5.76 GPa, about 5.8 GPa. About 37.5 GPa is the modulus in the fiber direction from the isostrain form 0.50 × 72 + 0.50 × 3.0. About 0.17 GPa forgets to take the reciprocal. The transverse modulus stays close to that of the compliant resin, only about 15% (about 1/6.5) of the modulus in the fiber direction. This is why unidirectional material is not used in parts loaded perpendicular to the fibers.