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A continuous and aligned glass fibre-reinforced composite consists of 40 vol% of glass fibres modulus of elasticity 69 GPa and 60 vol% of a polyester resin that, when-hardened, displays a modulus of 3.4 GPa. What is the modulus of elasticity of this composite in the longitudinal direction?
- a)15 GPa
- b)30 GPa
- c)45 GPa
- d)60 GPa
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A continuous and aligned glass fibre-reinforced composite consists of ...
ECL = Em Vm + Ef Vf = 3.4 x 0.6 + 69 x 0.4
= 2.04 + 27.6 = 30 GPa
= 2.04 + 27.6 = 30 GPa
Most Upvoted Answer
A continuous and aligned glass fibre-reinforced composite consists of ...
Given information:
- Volume fraction of glass fibres = 40%
- Modulus of elasticity of glass fibres = 69 GPa
- Volume fraction of polyester resin = 60%
- Modulus of elasticity of polyester resin = 3.4 GPa
To find:
- Modulus of elasticity of composite in the longitudinal direction
Solution:
1. We can use the rule of mixtures to calculate the modulus of elasticity of the composite:
E_longitudinal = V_glass x E_glass + V_polyester x E_polyester
where,
V_glass = volume fraction of glass fibres
E_glass = modulus of elasticity of glass fibres
V_polyester = volume fraction of polyester resin
E_polyester = modulus of elasticity of polyester resin
2. Substituting the given values in the above equation, we get:
E_longitudinal = 0.4 x 69 GPa + 0.6 x 3.4 GPa
E_longitudinal = 27.6 GPa + 2.04 GPa
E_longitudinal = 29.64 GPa
3. Therefore, the modulus of elasticity of the composite in the longitudinal direction is 30 GPa (approx).
Answer: Option B (30 GPa)
- Volume fraction of glass fibres = 40%
- Modulus of elasticity of glass fibres = 69 GPa
- Volume fraction of polyester resin = 60%
- Modulus of elasticity of polyester resin = 3.4 GPa
To find:
- Modulus of elasticity of composite in the longitudinal direction
Solution:
1. We can use the rule of mixtures to calculate the modulus of elasticity of the composite:
E_longitudinal = V_glass x E_glass + V_polyester x E_polyester
where,
V_glass = volume fraction of glass fibres
E_glass = modulus of elasticity of glass fibres
V_polyester = volume fraction of polyester resin
E_polyester = modulus of elasticity of polyester resin
2. Substituting the given values in the above equation, we get:
E_longitudinal = 0.4 x 69 GPa + 0.6 x 3.4 GPa
E_longitudinal = 27.6 GPa + 2.04 GPa
E_longitudinal = 29.64 GPa
3. Therefore, the modulus of elasticity of the composite in the longitudinal direction is 30 GPa (approx).
Answer: Option B (30 GPa)
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A continuous and aligned glass fibre-reinforced composite consists of 40 vol% of glass fibres modulus of elasticity 69 GPa and 60 vol% of a polyester resin that, when-hardened, displays a modulus of 3.4 GPa. What is the modulus of elasticity of this composite in the longitudinal direction?a)15 GPab)30 GPac)45 GPad)60 GPaCorrect answer is option 'B'. Can you explain this answer?
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