Determine the volume fraction of fibers required to obtain a longitudinal tensile strength of 812 MPa in a unidirectional carbon fiber reinforced composite. You are given that the tensile strength of the carbon fibers are 1240 MPa and that the stress in the matrix at fiber failure will be 300 MPa. Answer Format X. XX Unit: Unitless (fraction, example: 50 vol% fiber would be entered as 0.50)

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Chemistry

23 June, 07:27

Determine the volume fraction of fibers required to obtain a longitudinal tensile strength of 812 MPa in a unidirectional carbon fiber reinforced composite. You are given that the tensile strength of the carbon fibers are 1240 MPa and that the stress in the matrix at fiber failure will be 300 MPa. Answer Format X. XX Unit: Unitless (fraction, example: 50 vol% fiber would be entered as 0.50)

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Bethany Stark · Answer 1

V = 0.544

Explanation:

Given that

σ=812 MPa

σ₁=1240 MPa

σ₂=300 MPa

Lets take volume fraction V

The strength of composite fiber given as

σ = σ₁ V + σ₂ (1-V)

By putting the values

812 = 1240 V + 300 (1-V)

812 = 1240 V + 300 - 300 V

812 - 300 = 1240 V - 300 V

512 = 940 V

V = 0.544

The percentage volume = 54.4 %