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29 November, 00:53

A fiberglass composite is composed of a matrix of vinyl ester and reinforcing fibers of E-glass. The volume fraction of E-glass is 31%. The remainder is vinyl ester. The density of the vinyl ester is 0.79 g/cm3, and its modulus of elasticity is 4.04 GPa. The density of E-glass is 3.011 g/cm3, and its modulus of elasticity is 80 GPa. A section of composite 1.00 cm by 25.00 cm by 200.00 cm is fabricated with the E-glass fibers running longitudinal along the 200 cm direction. Assume there are no voids in the composite. Determine the modulus of elasticity of the composite in GPa.

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  1. 29 November, 01:05
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    Calculate the modulus of elasticity of the composite

    I. In the longitudinal direction of the glass fibre

    2. In the perpendicular direction of glass fibre

    Answer:

    1. 27.5876 GPa

    2. 5.725 GPa

    Explanation:

    Given

    Dimensions of the fibreglass is given by: 1.00 cm x 25.00 cm x 200.00 cm

    Volume = 1 * 25 * 200 = 5000cm³

    P1 = The volume fraction of the E-glass is 31%

    P2 = The remainder 69% is Vinyl Ester

    Volume of Vinyl Ester = 69% * 5000cm³ = 3450cm³

    I. In the longitudinal direction of the glass fibre

    Where

    Modulus of elasticity of glass, E1 = 80 Gpa

    Modulus of elasticity of vinyl ester, E2 = 4.04 Gpa

    Modulus of elasticity = E1P1 + E2P2

    Modulus of elasticity of vinyl esters = 31% * 80 + 69% * 4.04

    Modulus = 24.8 + 2.7876

    Modulus = 27.5876 GPa

    ii. In the perpendicular direction of glass fibre

    This is solved by

    E1. E2 / (P1. E2 + P2. E1)

    = (80 * 4.04) / (31% * 4.04 + 69% * 80)

    = 323.2 / (1.2524 + 55.2)

    = 5.725177317527687

    = 5.725 GPa
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