How Do You Calculate the Modulus of a Composite Sheet?

[iceman5]

Homework Statement

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?

Homework Equations

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

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.

[tex] E_{fe} = σ_{fg} * E_{fg }+ σ_{epoxy} * E_{epoxy} [/tex]

where

[tex] σ_{fg} = \text{volume fraction of fiberglass}\ [/tex]
[tex] E_{fg} = \text{modulus of fiberglass}\ [/tex]
[tex] σ_{epoxy} = \text{volume fraction of epoxy}\ [/tex]
[tex] E_{epoxy} = \text{modulus of epoxy}\ [/tex]

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.

[tex] E_c = \frac{2}{3} E_{fe} + \frac{1}{3} E_{carbon fiber} [/tex]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.

 

[KataKoniK]

Your approach is correct, but there are a few things to note:

1. The shear modulus of carbon fiber is not necessarily 1/3 of the tensile modulus. It can vary depending on the specific type of carbon fiber used. It would be best to use the actual value for the shear modulus if it is given.

2. When calculating the modulus of the composite in the testing direction, you should use the volume fraction of fiberglass and epoxy in the testing direction, not the overall volume fractions. This will give a more accurate result.

3. When calculating the modulus of the composite tested at 90º to the initial testing direction, you should use the volume fraction of carbon fiber and epoxy in the perpendicular direction.

Taking these into account, the correct equations to use would be:

E_{fe} = σ_{fg} * E_{fg in testing direction}+ σ_{epoxy} * E_{epoxy in testing direction}

E_{c} = σ_{carbon fiber} * E_{carbon fiber in perpendicular direction}+ σ_{epoxy} * E_{epoxy in perpendicular direction}

Using the values given in the problem, the calculations would be:

E_{fe} = 0.5 * 85 GPa + 0.5 * 4 GPa = 44.5 GPa

E_{c} = 0.4 * 450 GPa + 0.6 * 4 GPa = 181.6 GPa

So the modulus of the composite in the testing direction would be 44.5 GPa and the modulus of the composite tested at 90º to the initial testing direction would be 181.6 GPa.