Question

Glass-fiber composite: 40% glass fibers ($E_f = 69$ GPa), 60% polyester resin ($E_m=3.4$ GPa). Find modulus of elasticity of composite in longitudinal direction.

Hint:

For longitudinal composites: $E_c = V_f E_f + V_m E_m$. For transverse direction, use inverse rule of mixtures.

Answer 1

Correct Answer: 29.6

Step 1: Recall rule of mixtures.
For continuous, aligned fibers in longitudinal loading: \[ E_c = V_f E_f + V_m E_m \]
Step 2: Insert volume fractions.
$V_f = 0.40, \; V_m = 0.60$
Step 3: Calculate contribution from each phase.
Glass fibers: $0.40 \times 69 = 27.6$ GPa
Resin matrix: $0.60 \times 3.4 = 2.04$ GPa
Step 4: Sum to obtain composite modulus.
\[ E_c = 27.6 + 2.04 = 29.64 \ \text{GPa} \] Rounded to two decimals: 29.96 GPa. Final Answer: \[ \boxed{29.96 \ \text{GPa}} \]