As the fiber volume fraction approaches 1 in a unidirectional composite, the axial modulus E1 tends toward which modulus?

• A. Matrix modulus Em.
• B. A value between Ef and Em.
• C. Fiber modulus Ef.
• D. Infinite modulus.

Answer: (C)

When loading a unidirectional composite along the fiber direction, the axial stiffness follows the rule of mixtures under iso-strain: E1 ≈ E_f V_f + E_m V_m. If the fiber volume fraction approaches 1, the matrix fraction goes to zero, so E1 → E_f. The fibers dominate the load-bearing capability in this direction, making the axial modulus approach the fiber modulus. This isn’t infinite—the modulus remains finite, equal to the fiber modulus as the matrix essentially disappears from contributing to stiffness along the fiber direction. (Note: transverse properties behave differently and wouldn’t trend to the fiber modulus.)