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 εc = εf = εm applies)
Ecl = (ff ⋅ Ef) + (fm ⋅ Em)
Ecl = Young's modulus of composite in parallel direction
ff = Fraction of the fibre
Ef = Young's modulus of the fibre
fm = Fraction of the matrix
Em = 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...
Ecl = (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%