# Modulus of a composite sheet

1. Aug 11, 2012

### iceman5

1. The problem statement, all variables and given/known data

A crossply composite is comprised of 3 plys of fiberglass reinforced epoxy with the fiber direction parallel to the test direction and 2 plys of carbon fiber reinforced epoxy with the fiber direction transverse to the fiberglass direction. Each ply is of equal thickness and each ply has 0.50 volume fraction epoxy.

a.) What is the modulus of the composite in the testing direction?

b.) What is the modulus of the composite tested at 90º to the initial testing direction?

2. Relevant equations

Modulus of Epoxy = 4 GPa
Modulus of Fiberglass = 85 GPa
Modulus of Carbon Fiber - 450 GPa

3. The attempt at a solution

I think that this is the direction that I need to go but I'm not sure.

Calculate the modulus of the epoxy and fiberglass composite with the following equation.

$$E_{fe} = σ_{fg} * E_{fg }+ σ_{epoxy} * E_{epoxy}$$

where

$$σ_{fg} = \text{volume fraction of fiberglass}\$$
$$E_{fg} = \text{modulus of fiberglass}\$$
$$σ_{epoxy} = \text{volume fraction of epoxy}\$$
$$E_{epoxy} = \text{modulus of epoxy}\$$

Repeat this process with the carbon fiber and epoxy structure, but use the shear modulus of the carbon fiber since it is perpendicular to the test direction. I assume that the shear modulus of the carbon fiber will be 1/3 of the tensile modulus given.

Then use this for the composite.

$$E_c = \frac{2}{3} E_{fe} + \frac{1}{3} E_{carbon fiber}$$

This should yield a modulus of 55.3 GPa.

If this logic is correct, then I just need to exchange the shear modulus values for the perpendicular test direction.

Thanks for any help.

Last edited: Aug 12, 2012