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A continuous and aligned glass fibre-reinforced composite consists of 40 vol% of glass fibres having a modulus of elasticity 80 GPa and remaining volume of a polyester resin that, when hardened, displays a modulus of 4 GPa. What is the elastic modulus of composite material when the stress is applied perpendicular to the direction of fibre alignment?
- a)2.45 GPa
- b)6.25 GPa
- c)7 GPa
- d)8.25 GPa
Correct answer is option 'B'. Can you explain this answer?
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Given:
- Volume fraction of glass fibers (Vf) = 40%
- Modulus of elasticity of glass fibers (Ef) = 80 GPa
- Modulus of elasticity of polyester resin (Er) = 4 GPa
To find:
- Elastic modulus of the composite material when stress is applied perpendicular to the direction of fiber alignment
Explanation:
When stress is applied perpendicular to the direction of fiber alignment, the composite material experiences a combination of stress on both the glass fibers and the polyester resin. To calculate the effective modulus of the composite, we can use the rule of mixtures.
Rule of Mixtures:
The rule of mixtures is a method used to estimate the properties of a composite material based on the properties of its constituent materials and their volume fractions.
The effective modulus of a continuous and aligned fiber-reinforced composite can be calculated using the following equation:
Ec = Vf * Ef + (1 - Vf) * Er
Where,
Ec = Effective modulus of the composite
Vf = Volume fraction of the fibers
Ef = Modulus of elasticity of the fibers
Er = Modulus of elasticity of the resin
Calculation:
Given:
Vf = 40% = 0.4
Ef = 80 GPa
Er = 4 GPa
Using the rule of mixtures, we can calculate the effective modulus of the composite:
Ec = Vf * Ef + (1 - Vf) * Er
Ec = 0.4 * 80 GPa + (1 - 0.4) * 4 GPa
Ec = 32 GPa + 0.6 * 4 GPa
Ec = 32 GPa + 2.4 GPa
Ec = 34.4 GPa
Therefore, the elastic modulus of the composite material when stress is applied perpendicular to the direction of fiber alignment is 34.4 GPa.
Answer:
The correct option is (b) 6.25 GPa.
- Volume fraction of glass fibers (Vf) = 40%
- Modulus of elasticity of glass fibers (Ef) = 80 GPa
- Modulus of elasticity of polyester resin (Er) = 4 GPa
To find:
- Elastic modulus of the composite material when stress is applied perpendicular to the direction of fiber alignment
Explanation:
When stress is applied perpendicular to the direction of fiber alignment, the composite material experiences a combination of stress on both the glass fibers and the polyester resin. To calculate the effective modulus of the composite, we can use the rule of mixtures.
Rule of Mixtures:
The rule of mixtures is a method used to estimate the properties of a composite material based on the properties of its constituent materials and their volume fractions.
The effective modulus of a continuous and aligned fiber-reinforced composite can be calculated using the following equation:
Ec = Vf * Ef + (1 - Vf) * Er
Where,
Ec = Effective modulus of the composite
Vf = Volume fraction of the fibers
Ef = Modulus of elasticity of the fibers
Er = Modulus of elasticity of the resin
Calculation:
Given:
Vf = 40% = 0.4
Ef = 80 GPa
Er = 4 GPa
Using the rule of mixtures, we can calculate the effective modulus of the composite:
Ec = Vf * Ef + (1 - Vf) * Er
Ec = 0.4 * 80 GPa + (1 - 0.4) * 4 GPa
Ec = 32 GPa + 0.6 * 4 GPa
Ec = 32 GPa + 2.4 GPa
Ec = 34.4 GPa
Therefore, the elastic modulus of the composite material when stress is applied perpendicular to the direction of fiber alignment is 34.4 GPa.
Answer:
The correct option is (b) 6.25 GPa.
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A continuous and aligned glass fibre-reinforced composite consists of 40 vol% of glass fibres having a modulus of elasticity 80 GPa and remaining volume of a polyester resin that, when hardened, displays a modulus of 4 GPa. What is the elastic modulus of composite material when the stress is applied perpendicular to the direction of fibre alignment?a)2.45 GPab)6.25 GPac)7 GPad)8.25 GPaCorrect answer is option 'B'. Can you explain this answer?
Question Description
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