Question

A continuous and aligned glass fibre reinforced composite consists of 40 vol% of glass fibres having a modulus of elasticity 69 GPa and 60 vol% of a polyester resin that when hardened displays a modulus of elasticity 3.4 GPa. What is the modulus of elasticity in longitudinal direction?

• A. 35 GPa
• B. 45 GPa
• C. 30 GPa
• D. 20 GPa

Hint:

The Rule of Mixtures is used to determine composite material properties, where the total property is the weighted sum of its components.

Answer 1

The Correct Option is C

For a continuous and aligned fiber-reinforced composite, the modulus of elasticity in the longitudinal direction (\( E_L \)) is given by the Rule of Mixtures: \[ E_L = V_f E_f + V_m E_m \] where: - \( E_L \) = Modulus of elasticity in the longitudinal direction, - \( V_f \) = Volume fraction of the fiber = 40% = 0.40, - \( E_f \) = Modulus of elasticity of the fiber = 69 GPa, - \( V_m \) = Volume fraction of the matrix = 60% = 0.60, - \( E_m \) = Modulus of elasticity of the matrix = 3.4 GPa.
Step 1: Substituting the Given Values \[ E_L = (0.40 \times 69) + (0.60 \times 3.4) \] \[ E_L = 27.6 + 2.04 \] \[ E_L = 29.64 \approx 30 \text{ GPa} \] 


Step 2: Evaluating the Options - Option (A) - Incorrect: 35 GPa is too high.
- Option (B) - Incorrect: 45 GPa is too high.
- Option (C) - Correct: 30 GPa matches our calculation.
- Option (D) - Incorrect: 20 GPa is too low.


Step 3: Conclusion Since the calculated modulus of elasticity in the longitudinal direction is 30 GPa, the correct answer is option (C).