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.

Full Question

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