Questions: Composite Materials

Question 1

Carbon fiber reinforced polymer (CFRP) achieves a specific strength (strength per unit weight) exceeding that of steel. What chemical properties of carbon fibers contribute to this?

Model answer: Carbon fibers consist of graphite-like layers aligned along the fiber axis by high-temperature processing (carbonization and graphitization of polymer precursors, typically polyacrylonitrile). The strong C-C covalent bonds within the graphene layers provide tensile strength up to 7 GPa and modulus up to 900 GPa along the fiber direction. The low atomic weight of carbon (12 g/mol vs. 56 for iron) gives a density of only 1.7-2.0 g/cm3, about one-quarter that of steel. The combination of high strength from covalent bonding and low density from light atoms produces the exceptional specific strength.

The anisotropy of carbon fiber properties reflects the anisotropy of graphite bonding: strong covalent bonds in-plane, weak van der Waals forces between planes. Fibers are strong along their axis (aligned graphene layers) but weak in the transverse direction. The polymer matrix (typically epoxy) fills the space between fibers, transfers shear loads, and protects fibers from environmental damage. The resulting composite has directional properties that must be managed through layup design.

Question 2

The most critical factor determining composite performance is usually not the properties of the fiber or matrix individually, but the chemistry of the interface between them.

• T. True
• F. False

Answer: True

The interface must accomplish two contradictory goals: it must be strong enough to transfer stress from the matrix to the reinforcement (requiring good adhesion — chemical bonding, wetting, or mechanical interlocking) but weak enough to deflect cracks along the interface rather than through the fiber (preventing brittle failure). In carbon fiber/epoxy composites, fiber surface treatments (oxidation, sizing agents) create controlled chemical bonding to the epoxy matrix. Too little surface treatment gives poor adhesion and delamination; too much gives a brittle composite that fails catastrophically.

Question 3

The rule of mixtures predicts that a composite containing 60 vol% continuous aligned carbon fibers (modulus 230 GPa) in an epoxy matrix (modulus 3.5 GPa) will have a longitudinal modulus of approximately:

• A. 117 GPa — the arithmetic mean of fiber and matrix moduli
• B. 139 GPa — calculated as V_f x E_f + V_m x E_m = 0.60(230) + 0.40(3.5)
• C. 7.8 GPa — dominated by the weaker epoxy phase
• D. 230 GPa — dominated by the stiffer carbon fiber phase

Answer: (B)

The Voigt (iso-strain) rule of mixtures gives the upper bound for longitudinal modulus of a continuous-fiber composite: E_c = V_f x E_f + V_m x E_m = 0.60(230) + 0.40(3.5) = 139.4 GPa. This assumes equal strain in fiber and matrix (valid for continuous aligned fibers loaded parallel to the fiber direction). The transverse modulus is much lower, predicted by the Reuss (iso-stress) model: 1/E_c = V_f/E_f + V_m/E_m, giving about 8.5 GPa. This extreme anisotropy is characteristic of unidirectional composites.