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?

Answer: B. About 94%

In tension parallel to the fibers, fiber and resin have equal strains, so the force each carries is proportional to the product of volume fraction and Young's modulus. The fiber share is VfEf/(VfEf + VmEm) = 0.40 × 72 / (0.40 × 72 + 0.60 × 3.0) = 28.8/30.6 ≈ 0.94, about 94%. About 40% assumes the load is proportional to the volume fraction and ignores the difference in modulus. About 6% is the share carried by the resin, mistaken for the fiber share. Even with less than half the volume as fiber, the fibers support almost all the load, so the strength and stiffness in the fiber direction are set almost entirely by the fiber properties.