Young's Modulus of a Composite

[LeftBrain]

Homework Statement

Glass fibres in Nylon provide reinforcement. Young's modulus of glass fibre is 72.4GPa; Young's modulus of Nylon is 2.8GPa.
If the Nylon contains 30% by volume glass fibres, what fraction of the force applied parallel to the fibre axis is carried by the glass fibre?

(Assume the bonding between glass fibre and Nylon is strong enough to transfer the load, so ε_c = ε_f = ε_m applies)

Homework Equations

E_cl = (f_f ⋅ E_f) + (f_m ⋅ E_m)

Where
E_cl = Young's modulus of composite in parallel direction
f_f = Fraction of the fibre
E_f = Young's modulus of the fibre
f_m = Fraction of the matrix
E_m = Young's modulus of the matrix

The Attempt at a Solution

Given that Nylon is the matrix and the glass fibres are the fibre, the following can be assumed...

E_cl = (0.3 ⋅ 72.4) + (0.7 ⋅ 2.8) = 41.32 MPa

With respect to the fraction of the force applied parallel to the fibre axis, is it a matter of dividing the Young's modulus of the composite by that of the fibre?

41.32 MPa / 72.4 MPa = 0.57 or 57%

 

[Chestermiller]

Yes.