Define fiber volume fraction (Vf) and provide typical Vf values for carbon/epoxy laminates and their effect on stiffness.

• A. Vf is the ratio of resin to fiber by volume; typical Vf 0.2–0.3; higher Vf reduces stiffness.
• B. Vf is the length of fiber in the lamina relative to laminate thickness; typical Vf is 1.0; higher Vf increases ductility.
• C. Vf is the ratio of fiber surface area to total surface; typical Vf 0.8; higher Vf increases processing ease.
• D. Vf is the volume fraction of fibers in the composite; typical Vf for carbon/epoxy is 0.55–0.70; higher Vf generally increases stiffness and strength but reduces toughness and processability.

Answer: (D)

Fiber volume fraction is the proportion of the composite’s volume that is taken up by reinforcing fibers, a dimensionless quantity between 0 and 1 (often expressed as a percent). For carbon/epoxy laminates, Vf is typically about 0.55 to 0.70, depending on manufacturing method and layup. Higher fiber content increases stiffness because carbon fibers have a much higher modulus than the epoxy matrix, so the overall laminate modulus rises with Vf (a simple way to see this is the rule of mixtures). However, increasing Vf also reduces toughness and can make processing more difficult, since there’s less resin to flow and wet and bind the fibers, which can lead to poorer impact resistance and potential processing defects. So while higher Vf generally boosts stiffness and strength, it comes at the cost of ductility and manufacturability. The other descriptions either misdefine what Vf measures or give inaccurate typical values and effects on stiffness.